MASARYK UNIVERSITY
Faculty of Science
Ondˇrej Caha
Thin films of topological insulators
Habilitation thesis
Brno 2023
© Ondˇrej Caha, Masaryk University (Brno, Czech Republic), 2023.
Contents
1 Introduction 2
2 Topological insulators 3
2.1 Topological invariant in quantum Hall state . . . . . . . . . . . . . . . . . . . 4
2.2 Z2 topological invariant of two-dimensional topological insulators . . . . . . . 6
2.3 Three-dimensional topological insulators . . . . . . . . . . . . . . . . . . . . . 11
2.4 Properties of strong topological insulators . . . . . . . . . . . . . . . . . . . . 12
2.5 Bi2Te3, Bi2Se3 and Sb2Te3 family of topological insulators . . . . . . . . . . . 13
2.6 Topological crystalline insulators . . . . . . . . . . . . . . . . . . . . . . . . . 16
3 Experimental methods 19
3.1 Structural analysis of thin films by X-ray scattering . . . . . . . . . . . . . . 19
3.1.1 Basics of x-ray scattering from thin films . . . . . . . . . . . . . . . . 19
3.1.2 X-ray scattering from the thin film with randomly alternating motifs . 22
3.1.3 Substitutional and anti-site defects . . . . . . . . . . . . . . . . . . . . 25
3.1.4 Reciprocal space mapping: lattice parameters and domain size . . . . 27
3.1.5 Temperature dependent XRD experiments . . . . . . . . . . . . . . . . 29
3.2 Other methods of structural analysis . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.1 X-ray absorption spectroscopy . . . . . . . . . . . . . . . . . . . . . . 32
3.2.2 Transmission electron microscopy . . . . . . . . . . . . . . . . . . . . . 37
3.3 Angle-resolved photoemission spectroscopy . . . . . . . . . . . . . . . . . . . 40
3.4 Electrical transport measurements . . . . . . . . . . . . . . . . . . . . . . . . 42
4 Reprinted papers 44
4.1 Properties of thin films of topological insulators Bi2Te3 and BiTe . . . . . . . 48
4.2 Structure of BixTey thin films with general stoichiometry . . . . . . . . . . . 62
4.3 Optical and structural properties of Bi2(SexTe1−x)3 alloy . . . . . . . . . . . 75
4.4 Manganese doping of Bi2Se3 topological insulator . . . . . . . . . . . . . . . . 86
4.5 Manganese doping of Bi2Te3 topological insulator . . . . . . . . . . . . . . . . 107
4.6 Band gap in manganese doped topological insulators Bi2Te3 and Bi2Se3 . . . 119
4.7 Ferromagnetic transition in magnetic topological insulators MnSb2Te4 . . . . 139
4.8 Doping induced topological phase transition of (Pb,Sn)Se . . . . . . . . . . . 184
4.9 Giant Rashba effect in (Pb,Sn)Te . . . . . . . . . . . . . . . . . . . . . . . . . 210
5 Conclusion and outlook 226
6 List of publications 232
i
Preface
My research activities during the last 15 years concentrated at the x-ray laboratory at the
Department of condensed matter physics and later also CEITEC Nano core facility (since
2012, I have been responsible for a universal x-ray diffractometer with the rotating anode).
As a person responsible for running an x-ray laboratory at the Faculty of Science and partially
in CEITEC Nano, I have participated in an extensive range of various research topics emphasizing
the x-ray scattering methods as a primary research tool. I have studied the structural
properties of various epitaxial and polycrystalline thin films: III-V semiconductors, especially
GaN, transition metal oxides, and magnetic metallic films, among others. The x-ray
scattering experiments were primarily performed at standard laboratory conditions and high
and low temperatures to study structural phase transitions in ferroelectric materials. The
research also included structural characterization of bulk semiconductor crystals (Si, SiC),
semiconductor nanostructures, and real devices (transistors, diodes). The principal method
is laboratory-based x-ray scattering: x-ray diffraction, x-ray reflectivity, and small angle-xray
scattering. Also, my research included more advanced synchrotron methods such as x-ray
absorption spectroscopy, anomalous x-ray diffraction, or x-ray magnetic circular dichroism.
The bulk crystals were also studied using x-ray diffraction imaging techniques (x-ray diffraction
topography), and we have adapted rocking curve imaging (RCI) to the laboratory-based
diffractometer. In recent years we have also adapted the x-ray fluorescence detector to the
diffractometer and performed standing wave x-ray fluorescence experiments to study atomic
positions in thin films.
Apart from plenty of smaller projects, my research focuses on two main research topics:
topological insulator materials and structural analysis of semiconductor materials. The first
idea of the topic was applications of x-ray scattering methods, but that approach would lead
to quite diverse work composed of several non-related topics. Instead, I have decided to focus
this work solely on topological insulators. This way, it can be more compact and broader
since I have participated in x-ray scattering and other experimental techniques such as x-ray
spectroscopy, photoemission spectroscopy, electron microscopy, and transport measurements.
The research activities in this field started ten years ago in close collaboration with the group
of prof. Gunther Springholz at Johannes Kepler University in Linz and prof. Oliver Rader at
Helmholtz Zentrum Berlin.
I want to thank all my collaborators mentioned above and many other collaborators whose
name list would be too long. I will mention especially prof. V´aclav Hol´y and prof. G¨unther
Bauer for their continuous support. Lastly, I want to thank my wife and family.
1
Chapter 1
Introduction
The thesis deals with the work performed with topological insulators thin films. In collaboration
with coworkers, we started the growth and characterization of the topological insulators
relatively soon after their discovery in 2011. Our research at first focused on topological insulator
thin film growth optimization and physical properties of bismuth chalcogenide thin films.
Later we started to include magnetic doping with manganese since ferromagnetic topological
insulators have unusual physical properties such as quantum anomalous Hall effect. We have
published one of the early works showing high-quality epitaxial thin films of bismuth telluride
4.1 and structural properties of natural heterostructures combining Bi2Te3 and Bi2 layers
4.2. The most significant results deal with ferromagnetic topological insulators. Our paper
has demonstrated for the first time the direct observation of band gap opening in topological
surface states due to ferromagnetic order in Bi2Te3/MnBi2Te4 heterostructures 4.6. Later
we have shown a high ferromagnetic ordering temperature of 50 K in MnSb2Te4 topological
insulator 4.7. Last but not least, we have also worked with topological crystalline insulator
layers. We have demonstrated a phase transition from a topological crystalline insulator to
a strong topological insulator by doping-induced symmetry breaking 4.8. The author’s contribution
was mainly in the structural characterization of the prepared films using XRD and
later HRTEM, but also to band structure measurements at synchrotron sources.
The first part of the thesis briefly introduces the topological insulator theory and physical
properties of selected topological insulator materials. The second chapter presents experimental
methods used in the thesis by the author. Special attention is devoted to x-ray scattering
methods as a primary specialization. The last part of the thesis includes a series of research
papers divided into three groups:
• Topological insulators thin films Bi2Te3, BixTey, and Bi2(SexTe1−x)3 studied by x-ray
scattering, and other methods.
• Magnetically doped topological insulator thin films Bi2Te3, Bi2Se3 and Sb2Te3.
• Topological crystalline insulators, i.e., (Pb,Sn)Se and (Pb,Sn)Te alloys.
2
Chapter 2
Topological insulators
Topological insulators are materials with unique electronic structure of surface states. The
bulk electronic structure of the topological insulators is topologically non-trivial. The boundary
between topologically trivial and non-trivial material hosts surface (interface) states with
Dirac cone-like dispersion. The bulk states have an ordinary band gap; thus, the volume
electronic properties are identical to an ordinary insulator or semiconductor. In an ordinary
insulator or semiconductor, the surface states are susceptible to particular surface morphology,
impurities, and other defects. The typical surface states are usually localized at surface
defects and cannot serve as a transport channel in a device. On the contrary, the interface
between topologically non-trivial and trivial material has unique boundary states with linear
dispersion, which are robust against boundary shape or impurities. Thus they are called
topologically protected, and electric transport via boundary states has interesting quantum
properties.
For the two-dimensional materials the surface states are one-dimensional edge states, in
case of three-dimensional materials the surface states are two-dimensional. From the topological
point of view normal materials are called topologically trivial insulators. The basic
reason for the topological nontrivial systems is peculiar behavior of the half-integer spin under
symmetry operations. The momentum in quantum mechanics under rotation by an angle
ϑ along z-axis transforms as ˆR(ϑ) = e−iϑsz . Interestingly, full rotation by ϑ = 2π of an
electron with half-integer spin of sz = ±1/2 does not produce identical state but leads to
inversion of the wave function ˆR(2π) = e iπ = −1. Similar behavior has wave function of
spin one-half particles under mirror symmetry ˆM or time reversal symmetry ˆΘ. Two subsequent
applications of mirror or time-reversal operations invert sign of the wave function
ˆM2 = ˆΘ2 = −1 in any half-integer spin system. This property of half-integer spin is counterintuitive;
one would naively expect two subsequent mirror operations to project back to the
original state as is valid for integer spin particles ˆM2 = 1. This transformation is related
to the Pauli spin-statistics theorem and Pauli exclusion principle for fermions. The central
statement of spin-statistics theorem is that many particle wave function is antisymmetric
upon exchange of pair of half integer spin particles ψ(x, y) = −ψ(y, x). All of these antisymmetric
transformations can be seen as various projections of a single general symmetry. The
topological insulators have certain topology of the electronic states protected by one of the
above symmetries. Three-dimensional topological insulators are protected by a time-reversal
symmetry; topological crystalline insulators by real space symmetry such as mirror symmetry,
space-inversion or rotational axis.
3
CHAPTER 2. TOPOLOGICAL INSULATORS 4
The most prominent properties of the topological insulators are the quantum Hall effect
(QHE), quantum spin Hall effect (QSHE), and quantum anomalous Hall effect (QAHE).
Three-dimensional topological insulators possess other properties such as topological magnetoelectric
effect (TME), Majorana fermions at the topological insulator-superconductor interface,
and others. There are also higher-order topological phases [1]; there can be topologically
protected one-dimensional states (at sample edges) in 3D material. For practical purposes,
2D and 3D topological insulators have attracted the most interest.
Several review papers were published describing the theoretical and experimental progress
of the topological insulator field [2–5]. The theory of topological insulators divides into two
main groups: Topological field theory (TFT) based on more general topological concepts
and topological band theory (TBT). Topological field theory [6] is more general and deals
with interacting particles and disorders in the material. Topological band theory [7–11] is
limited to the system with non-interacting particles but gives simple criteria of the non-trivial
topology. In the limit of non-interacting particles, the TFT transforms into TBT; thus, both
theories are consistent and equivalent.
The extensive search for topologically non-trivial materials has been recently performed
by Vergniory et al. [12] and, in a limited case, by two other groups [13, 14]. These groups
performed first-principle band structure calculations of many non-magnetic crystalline structures
in the crystallographic database. They have found that 10–20% out of non-magnetic
crystalline structures are topologically non-trivial materials.
This chapter briefly describes the theory of topological insulators. The first section is
devoted to the quantum Hall effect, described using TFT. The following sections deal with
quantum spin Hall insulators using TBT in two and three dimensions. The fourth section
describes the fundamental properties of Bi2X3 family of topological insulators. The last
section presents a short introduction to topological crystalline insulators.
2.1 Topological invariant in quantum Hall state
The first experimentally observed topologically non-trivial state was the quantum Hall effect
state [15]. The quantum Hall effect is an unusual behavior of two-dimensional electron gas
in a strong magnetic field. Two-dimensional electron gas can form at the interface of two
semiconductors with a different band gap. In strong magnetic field and low temperatures the
longitudinal electrical resistance drops to zero
ρxx =
Vxx
I
= 0, (2.1)
while the transversal (i.e., Hall resistance) equals a value defined only by fundamental physical
constants
ρxy =
Vxy
I
=
1
ν
h
e2
=
1
ν
25812.807 Ω, (2.2)
and an integer number ν to very high precision. The resistivity and conductivity tensors are
then
ˆρ =
0 −ρxy
ρxy 0
, ˆσ =
0 σxy
−σxy 0
, σxy = ν
e2
h
. (2.3)
Qualitative analysis of the problem has shown that electrons inside the material occupy Landau
levels and do not contribute to the electrical conductivity of the sample. Edge states
CHAPTER 2. TOPOLOGICAL INSULATORS 5
Vxx
Vxy
I
Figure 2.1: Schematic arrangement of quantum Hall effect and magnetic field dependence of
transverse and longitudinal resistance. The right part of the figure is reprinted from [16]
b
E
F
E
k
a
B
Figure 2.2: (a) Schematic representation of electrons’ orbits in the quantum Hall effect. (b)
Energy levels of bulk states (Landau levels and edge states in quantum Hall insulator).
dominate the transport properties [17]. The edge states at a particular edge can propagate
only in one direction due to the strong magnetic field, as schematically shown in figure 2.2.
Since no states with opposite propagation directions exist, electron backscattering is prohibited,
and the longitudinal resistivity drops to zero. Moreover, the edge states are not affected
by defects, impurities, sample shape, or other irregularities. Such topologically protected
edge states are in considerable contrast to the ordinary edge and surface states which are
extremely sensitive to defects. The schematic dispersion of the edge states is presented in
figure 2.2(b).
A complete quantitative analysis has to consider the integer number ν. This number
equals the first known topological invariant in solid state physics, called TKNN invariant
after its definitions by Thouless, Kohmoto, Nightingale, and den Nijs [18] or Chern number.
The TKNN invariant is defined using Berry’s connection
Am(k) = i um(k)| k |um(k) , (2.4)
where um(k) is a periodic part of Bloch wavefunction ψm(k)
ˆH|ψ(k) = Em(k)|ψm(k) , |ψm(k) = eik·r
|um(k) . (2.5)
Wavefunction um(k) can be written as eigenfunction of Bloch Hamiltonian ˆH(k) defined as
ˆH(k) = e−ik·r ˆHeik·r
, ˆH(k)|um(k) = Em(k)|um(k) . (2.6)
CHAPTER 2. TOPOLOGICAL INSULATORS 6
The integral of Berry’s connection Am(k) over the closed line surrounding the twodimensional
Brillouin zone is called the first Chern number and could have only integer values
Cm =
1
2π ∂BZ
Am(k)dk =
1
2π BZ
Fm(k)d2
k. (2.7)
The Chern number can be evaluated using Stokes theorem as surface integral of Berry curvature
Fm(k) = × Am(k). The Hall conductivity can be evaluated as a sum of particular
Chern numbers over occupied bands [18]
σxy =
e2
h m
Cm =
e2
h
C, (2.8)
where total Chern number C = m Cm called, in this case, TKNN invariant (Thouless,
Kohmoto, Nightingale, den Nijs). One can rewrite the preceding formula into the real space
coordinates
C =
i
2π m BZ
d2
k d2
r
∂u∗
∂kx
∂u
∂ky
−
∂u
∂kx
∂u∗
∂ky
=
i
4π m ∂BZ
dki d2
r u∗ ∂u
∂kj
−
∂u∗
∂kj
u .
(2.9)
The quantum Hall state has a nonzero value of topological invariant inside the sample and
zeroes outside. These edge states are then so-called topologically protected. The dispersion
of the edge states is not sensitive to a particular sample shape, impurities, or other defects.
The Chern number equals the number of filled Landau levels, and through the bulk-boundary
correspondence, it corresponds to the number of chiral edge modes [19].
2.2 Z2 topological invariant of two-dimensional topological in-
sulators
The following research focused on the possible topologically non-trivial materials without a
high external magnetic field. Haldane predicted topologically non-trivial states in graphene1
in a periodic magnetic field [20]. The subsequent theoretical works have suggested materials
with large spin-orbit coupling leading to similar effects to the band structure as a magnetic
field. The prediction by Kane and Mele [8] defines topological invariant in the time-reversal
symmetry system. Let us define the time-reversal operator ˆΘ. Time reversal invariant Hamiltonian
commutes with time reversal operator [ ˆH, ˆΘ] = 0. The Bloch Hamiltonian has to
satisfy relation
ˆΘ ˆH(k)ˆΘ−1
= ˆH(−k). (2.10)
The time reversal operator in the spin 1/2 system also satisfies the relation
ˆΘ2
= −1. (2.11)
This formula leads directly to Kramers theorem, i.e. each eigenstate of the time-reversal
invariant Hamiltonian has to be at least two-fold degenerate. Using formula (2.11) one can
show any eigenstate |ψ and its time-reversal state are in fact orthogonal
Θψ|ψ = ΘΘψ|Θψ = − Θψ|ψ = 0. (2.12)
1
Haldane made his prediction years before the word “graphene” came into use. The original paper published
in 1988 uses the term “2D graphite”.
CHAPTER 2. TOPOLOGICAL INSULATORS 7
If no spin-orbit interaction is present, the Hamiltonian eigenstates are spin-degenerate for any
Bloch wavevector k and any band m
Em↑(k) = Em↓(k) = Em↑(−k) = Em↓(−k), (2.13)
where the degeneracy of states with inverted wavevector follows from the formula (2.10). The
degeneracy of each state is then at least two-fold; the material is topologically trivial.
The spin-orbit interaction lifts spin degeneracy but keeps time-reversal symmetry. The
time-reversal image of any state in the crystal is the state with an inverse value of Bloch wave
vector k → −k and inverted spin. The Kramers theorem is satisfied when these pairs have
the same energy eigenvalue
Em↑(k) = En↓(−k), (2.14)
where m, n are band indices. However, band indices m, n do not have to form pairs over the
whole Brillouin zone; we discuss this topic in more detail at the end of this section as one of
the topological criteria.
There exist number of possible methods to calculate Z2 topological invariant [8,10,21,22].
One method of evaluation Z2 invariant ν is using sewing matrix w [23]
wmn(k) = um(−k)|ˆΘ|un(k) . (2.15)
From the properties of the time-reversal operator follows
wT
(k) = −w(−k). (2.16)
There are several high symmetry points in Brillouin zone where k is equivalent to −k, which
we will note as Γa – time-reversal invariant momenta (TRIM) points
Γa = −Γa + G, Γa =
G
2
, (2.17)
where G is a reciprocal lattice vector
G = n1b1 + n2b2, (2.18)
where n1 and n2 are arbitrary integer numbers. Only the lowest-order reciprocal lattice
vectors count inside the first Brillouin zone. We can use the following notation
Γn1,n2 =
n1
2
b1 +
n2
2
b2, n1, n2 = 0, 1. (2.19)
Negative values of n1, n2 = −1 can be omitted since they are equivalent to points with n1,
n2 = 1. In general, there are four TRIM points in any 2D system; one is Γ = (0, 0) point.
In TRIM points Γa, the matrix w is antisymmetric. The determinant of an antisymmetric
matrix is the square of its Pfaffian. We can define the time-reversal parity of the antisymmetric
matrix
δa =
Pf[w(Γa)]
Det[w(Γa)]
= ±1. (2.20)
The total ν invariant is then the parity of the product of all individual values δa
(−1)ν
=
4
a=1
δa. (2.21)
CHAPTER 2. TOPOLOGICAL INSULATORS 8
It is possible to choose the sign of the square root in the formula (2.20), and the sign of δa
is arbitrary. However, the branch of the square root has to be chosen continuously over the
Brillouin zone, and the product of an even number of δa is independent of branch selection.
The invariant ν denotes two equivalence classes of the band structure, which can be continuously
deformed, changing time-reversal symmetric Hamiltonian without closing a gap. The
consequence leads to the existence of “topologically protected” surface states at the interface
between material with ν = 1 and ν = 0. The topological surface states have to cross the band
gap, and they have to be spin-polarized. The 2D topologically non-trivial system is known
as a quantum spin Hall insulator. As in the quantum Hall state, the electron orbits inside
the bulk are insulating with a band gap, and only the edge states contribute to the transport
properties. Since the system is without an external magnetic field, the edge states have to
differ from QHE edge states. The spin-up electrons propagate in a single direction, while
opposite spin electrons propagate in the opposite direction.
b
k
E
EF
CB
VB
k
E
CB
VB
d
k
E
CB
VB
c
ν=1
ν=0
a
Λ −Λ−Λ abb b b
ΛΛa
Λ
Figure 2.3: (a) Schematic representation of surface electronic orbits in the quantum spin Hall
insulator. Red and blue lines correspond to spin-up and spin-down states, respectively. (b)
Energy levels of bulk conduction and valence band states. The red and blue lines show the
dispersion of spin-up and spin-down edge electron states. (c) and (d) Schematic energy levels
of surface states in a topologically trivial and non-trivial case. The figure shows necessary
Kramers degeneration in two nonequivalent time-reversal invariant momenta (TRIM) points
Λa and Λb.
The dispersion of the surface states in this system was studied theoretically using an
effective model by Bernevig, Hughes, and Zhang (BHZ) [24]. The effective model is developed
for HgTe quantum well in a CdTe buffer. HgTe is a material with a large spin-orbit coupling
CHAPTER 2. TOPOLOGICAL INSULATORS 9
leading to an inverted band structure, while CdTe is an ordinary semiconductor. While CdTe
is an ordinary semiconductor with p-type valence band Γ8 (J=3/2) and s-type conduction
band Γ6 (J=1/2), HgTe has an inverted band structure due to strong spin-orbit splitting.
Figure 2.4 shows the schematic band structure. The edge states of the BHZ Hamiltonian
Figure 2.4: (a) Schematic band structure of HgTe and CdTe. (b) Schematic energy levels
in the HgTe quantum well for the non-inverted case (left) and inverted case (right). Image
reprinted from [24]. (c) Experimental Hall resistance and (d) longitudinal resistance concerning
Fermi energy level tuning via gate voltage. Reprinted from [25]
have a simple form of its effective Hamiltonian [3] in the space defined by states |ψ ↑ and
|ψ ↓
Hedge = Akyσz, (2.22)
where A is a material parameter connected to a Dirac velocity A = v, σz Pauli spin matrix
and edge is parallel with y axis. This is precisely the dispersion shown in figure 2.2(b) with
two linear lines each for opposite spin polarization and Dirac point in its intersection. The
defects or impurities can change the dispersion of the state. However, as long as time-reversal
symmetry is conserved, the linear dispersion in the Dirac point is not changed; it only can be
shifted upwards or downwards in the energy scale. Perturbation of the Hamiltonian without
time-reversal symmetry opens a gap in the surface states.
Experimental demonstration of quantized electrical conductivity in this system was performed
by K¨onig et al. [25]. They have observed quantized Hall conductivity σxy = e2
h and
longitudinal conductivity G = 2e2
h . The factor of 2 in longitudinal conductivity is caused by
two transport channels available – each edge has a contribution of e2
h . The QSH effect was
observed for HgTe quantum wells thicker than critical thickness dc ≈ 6.5 nm. The interpreta-
CHAPTER 2. TOPOLOGICAL INSULATORS 10
tion of the critical thickness is straightforward – confinement energy has to be small enough
to allow inversion of the quantum well states. Historically, the first theoretical prediction of
quantized conductivity in HgTe quantum well was by Pankratov as early as 1987 [26].
There exists certain correspondence of Z2 invariant ν to Chern number. In a system
with conserved Sz spin component, the solution splits for spin-up and spin-down with Chern
number for each spin direction n↑ and n↓, respectively. The time-reversal symmetry leads to
a result the total Chern number has to equal zero
ntotal = n↑ + n↓ = 0, n↑ = −n↓. (2.23)
Half of their difference evaluated modulo 2 is Kane-Mele Z2 topological invariant ν
ν =
n↑ − n↓
2
mod 2. (2.24)
Z2 topological invariant defines parity of the particular Chern number n↑ or n↓.
The above-presented definition of the topological invariant ν is not unique. Several alternative
but equivalent definitions exist; see, for instance, [27]. Each of the equivalent definitions
presents a different point of view on the concept of topological theory.
The first developed topological invariant concept was the Pfaffian invariant presented by
Kane and Mele [28]. This concept historically preceded the above formulation with sewing
matrix invariant. This invariant uses matrix m representing time-reversal operator in the
basis of Bloch states
mmn(k) = um(k)|ˆΘ|un(k) . (2.25)
The topological invariant is defined as an integral over a closed loop
ν =
1
2πi ∂EBZ
dPf[m]
Pf[m]
(mod 2), (2.26)
where the integration goes over the boundaries of the effective Brillouin zone. The effective
Brillouin zone is half of the whole Brillouin zone, where only one of each pair of time-reversal
symmetric points (k,−k) is present. The definition of the effective Brillouin zone is not
unambiguous; the integration over the effective Brillouin zone boundaries has to omit vortices
in the Pfaffian of m matrix. This invariant counts the number of the Pfaffian vortices pairs;
vortices in Pfaffian come in pairs in k and −k. Two pairs of Pfaffian vortices can cancel with
each other. The Pfaffian invariant is a parity of the number of vortices pairs. Thus invariant
value ν = 1 corresponds to an odd number of vortices pairs, and at least one pair of them
must be present in the system as long as the time-reversal symmetry is preserved.
In this text, we will present one more definition of the topological invariant ν presented
by Fu and Kane [29], so-called obstruction interpretation. The topological invariant ν is
evaluated using the integral formula
ν =
1
2π ∂EBZ
A −
EBZ
F (mod 2), (2.27)
where A = m Am is the total Berry connection (sum of Berry connections over all occupied
bands) constructed from Kramers pairs and F = × A is the Berry curvature. In a normal
situation, the path integral of the Berry connection and the integral of the Berry curvature
have the same value according to Stokes’ theorem. The system is topologically trivial with the
CHAPTER 2. TOPOLOGICAL INSULATORS 11
invariant ν equals zero. In the topologically trivial system we can also choose a continuous
basis of the filled states (ei)2n
i=1 such that ˆΘe2j−1(k) = e2j(−k). Such a case corresponds
to the example presented in figure 2.3(c), where the pair of Kramers states denoted by blue
and red line degenerate with each other in all TRIM points. In the topologically non-trivial
system, such a continuous basis definition is impossible. The situation is schematically shown
in figure 2.3(d). Although the Kramers theorem is always satisfied, the pair of bands that
degenerate at a certain TRIM point Λa do not necessarily degenerate at the other TRIM
point Λb. Then we cannot construct a continuous basis as defined above, and the subsequent
discontinuity obstructs Stokes theorem and leads to a nonzero integer value of the topological
invariant ν. It is worth noting that a pair of such obstructions cancels out; this leads to the
definition of Z2 invariant, which can be understood as a parity of the integer value.
2.3 Three-dimensional topological insulators
Generalizing 2D invariant to three dimensions, Fu, Kane, and Mele obtained four invariants [7]
(ν0; ν1ν2ν3). Instead of four high symmetry points in the 2D system, the 3D system has eight
time-reversal invariant momentum points Λa. We will note them in a following way
Γn1n2n3 =
1
2
(n1b1 + n2b2 + n3b3) , nj = 0, 1, (2.28)
where bi are reciprocal lattice vectors. The strong invariant ν0 is the parity of the product of
all eight TRIM points as in formula (2.20)
(−1)ν0
=
8
a=1
δa. (2.29)
The other invariants are obtained as the product of only four TRIM points in the particular
surface 2D Brillouin zone. Since three possible independent surface orientations exist, we can
define three independent invariants. The invariant for surface perpendicular to x includes the
product of TRIM points with n1 = 1
(−1)ν1
=
n2,3=0,1
δ1n2n3 . (2.30)
The definition of the other two invariants is straightforward
(−1)ν2
=
n1,3=0,1
δn11n3 , (−1)ν3
=
n1,2=0,1
δn1n21. (2.31)
The selection of the TRIM points for the invariants ν1, ν2, and ν3 are shown in figure 2.5.
The ordinary insulator has trivial values of these invariants (0;000). Non-trivial topological
insulators are divided into the general class of strong topological insulators with ν0 = 1 and
weak topological insulator with ν0 = 0 but the nonzero value of at least one of the other
invariants ν1, ν2, ν3. The consequence of a topologically non-trivial state is the existence of
topologically protected surface states with Dirac cone dispersion.
Strong topological insulators have an odd number of Dirac cones present at any surface
orientation. Thus the strong topological insulator has topologically protected surface states
CHAPTER 2. TOPOLOGICAL INSULATORS 12
x
y
z
x
y
z
x
y
z
Figure 2.5: Schematic image one-eighth of Brillouin zone of the cubic lattice. Black and
red circles denote all eight TRIM points. Left: Red circles denote TRIM points selected for
invariant ν1 – in a plane perpendicular to x-axis. Center and right: TRIM points selection
for invariants ν2 and ν3, respectively.
insensitive to disorder as long as time-inversion symmetry is conserved. Breaking of timereversal
occurs with a magnetic field or magnetic order.
Weak topological insulators have an even number of Dirac points which can appear at
particular surface orientations. At the same time, at the other surface orientations, there is
only ordinary dispersion with a band gap. In a weak topological insulator, the Dirac cone-like
dispersion is not robust to any time-reversal perturbation. Specific perturbations, such as
coupling between two identical Dirac cones, can simultaneously open a band gap in a pair of
Dirac cones. Weak topological insulators have topological surface states, but they are not as
robust to impurities as strong topological insulators.
From the TFT point of view, the Chern number as a topological invariant exists in an
even number of spatial dimensions. The systems in lower dimensions can be seen as a projection
from higher dimension systems [6]. Then the Z topological invariant – Chern number
transforms into a lower dimension only as parity, i.e., Z2 topological invariant. The quantum
Hall effect exists in two dimensions, with the first Chern number as an integer topological
invariant. The next lowest system is the four-dimensional system described by the second
Chern number. Three-dimensional topological insulators and quantum spin Hall systems can
be seen as their projection to three or two dimensions, respectively. The topological invariant
is then just the parity of the second Chern number.
2.4 Properties of strong topological insulators
The surface states of the strong topological insulator can be evaluated with an effective
Hamiltonian with the surface perpendicular to z-axis
ˆHsurf = vf (σxky − σykx), (2.32)
up to the leading order in k [30, 31]. The dispersion of the surface states is linear Dirac
cone with spin locked perpendicular to the momentum. The topological properties of such
states are similar to edge states in QSH insulators; they resist perturbations, not breaking
time-reversal symmetry.
CHAPTER 2. TOPOLOGICAL INSULATORS 13
Surface states in topological insulators are not localized and should have quantized longitudinal
and Hall resistance. According [32], the Hall conductance of states with linear
dispersion has half-integer quantum Hall effect
σxy = N +
1
2
e2
h
. (2.33)
Since there are two surfaces of any imaginable sample expected total conductivity in the
experiment is an integer product of e2/h.
The spin-momentum locking directly leads to spin-related phenomena. For example,
charge fluctuations lead to spin fluctuations; novel excitation is present in topological insulators.
If a sample is irradiated by circularly polarized light, only electrons with specific
spin and momentum are excited, leading to spin-polarized photocurrent [33].
The surface quantum Hall effect also can be observed via a magnetic field induced by
surface currents. An electric field induces the magnetization, or a magnetic field electric
polarization [6,34]
M = P3
e2
h
E P = −P3
e2
h
B, (2.34)
where P3 = ±1/2 is the quantum of Hall conductance with sign according to the orientation
of magnetic field with respect to the topological insulator surface. The consequences of this
effect lead to a peculiar image magnetic monopole if a point charge is positioned close to a
boundary of the topological insulator and trivial insulator [35]. Another related effect is Kerr
and Faraday’s rotation of incident light due to surface states [36, 37], which can be used to
measure quantized value P3e2/h.
The topological insulator with incorporated ferromagnetic ordered atoms have quantum
anomalous Hall effect (QAHE), with quantized Hall conductivity and dissipation-less longitudinal
transport with zero resistance without applying an external magnetic field [38, 39].
Magnetic atoms inside the topological insulator induce the magnetic field. The first experimental
observation QAHE was done by Chang et al. [39] in vanadium doped (Bi,Sb)2Te3.
One of the most peculiar properties rises at the interface between a topological insulator
and superconductor [40]. Such interfaces can host Majorana fermion excitations. Several
proposed experimental configurations have several superconducting domains with different
phases on top of a single topological insulator [41]. Other proposed concepts were based
on the proximity of magnetic phase, and superconductor on topological insulator [42]. The
topological insulator in Josephson junction has been recently reported to form a hybrid qubit
as a promising structure for quantum computing [43].
2.5 Bi2Te3, Bi2Se3 and Sb2Te3 family of topological insulators
Bismuth and antimony chalcogenide materials Bi2Te3, Bi2Se3 and Sb2Te3 have been studied
for many years as low band gap materials and especially as materials with the highest thermoelectric
efficiency at room temperature [44]. They all have very similar hexagonal crystal
structures consisting of five atomic layers (quintuple layer – QL), which are weakly bound
at the so-called van der Waals gap. The crystal structure of Bi2Te3 is plotted in figure 2.6
(a). Crystal structure of Bi2Se3 and Sb2Te3 is almost identical to Bi2Te3 with only slightly
different interplanar distances. The van der Waals gap has substantial consequences on the
mechanical and structural properties. Crystal of bismuth chalcogenide very easily cleaves in
CHAPTER 2. TOPOLOGICAL INSULATORS 14
Figure 2.6: (a) Crystal structure of Bi2Te3. (b) Crystal structure of Bi1Te1 for comparison.
Black and green arrows show unit vectors of the hexagonal and rhombohedral unit cells,
respectively. Crystal structure of Bi2Se3 is very similar to Bi2Te3 structure with tellurium
atoms replaced by selenium and minor changes in interatomic distances.
the van der Waals gap, and clean surfaces can be easily prepared via Scotch tape technique
similar to the graphene preparation. The termination with anion (Se, Te) is also preferential if
the clean layer surface is prepared evaporating protection capping layer [45]. The weak bonds
also affect strain in the epitaxial layers; the van der Waals structure can release stress during
the growth, and the critical thickness to grow relaxed film is small. In other words, even
thin films grow as relaxed structures. The van der Waals gap is naturally strongly preferred
surface termination; the surface of the Bi2Te3 films shows steps with the thickness of 1 nm,
which is a thickness of a single QL motif [46].
The QL structure can be seen as a building block of compounds with different stoichiometry.
The most prominent example is the BiTe structure (stoichiometry Bi1Te1), which is
plotted in figure 2.6(b). It can be seen as a series of two QL and a bismuth bilayer – 2Bi2Te3
+ Bi2. A theoretical description of x-ray diffraction in this random system is presented in
section 3.1.2. More generally, with alternating changing such building blocks, it is possible to
achieve any chemical composition between Bi2Te3 and Bi4Te3 (1 QL + Bi2) [47,48]. In the
chapter 4, we present structural studies of Bi2Te3 and BiTe thin films [46] and homologous
series of general BixTey composition [49].
The structure of Bi2X3 is trigonal with fcc-type stacking of individual hexagonal layers
(ABCABC. . . ). The symmetry axis is only three-fold, and there is a high probability of
forming inverted twin domains. The twin domain ratio depends on the mismatch to the
substrate. While Bi2Te3 has a low mismatch (0.05 %) to the BaF2 the probability of twin
CHAPTER 2. TOPOLOGICAL INSULATORS 15
Figure 2.7: Experimental electronic structure of the Bi2Se3 and Bi2Te3 using ARPES.
domain formation is a couple of percents [46], for Bi2Se3 the mismatch reaches 2 % and the
twin domains form approximately half of the film. The size of the domains is approx 100 nm
as was shown by HRXRD [46] or low energy electron microscopy (LEEM) [45].
The non-trivial topology in Bi2Se3 was experimentally shown by Xia et al. [50]. All three
materials are strong topological insulators with Z2 topological invariants (1;000) [2]. The
experimental dispersions measured using ARPES are plotted in figure 2.7. From the bulk
band structure point of view, Bi2Se3 is a narrow band gap semiconductor with a direct band
gap in Γ point of 200 meV at 10 K. Topological surface states have excellent linear Dirac cone
shape with Dirac cone positioned well inside the bulk band gap 2.7. Bulk band structure of
Bi2Te3 is different; it has an indirect band gap with a conduction band minimum in Γ point
and another local minimum close to Z-F line. The maximum of the valence band also lies
close to Z-F line; it is an indirect band gap semiconductor with an indirect gap of 180 meV
but the direct band gap transition is only 200 meV at 10 K temperature. The band gap has
a maximum value for Se concentration of about 30 %.
Particular interest is given to magnetic doping with manganese to make a basis for the
quantum anomalous Hall effect. Manganese atoms form septuple layer structures MnBi2X4
(SL). The crystal structure is composed of randomly alternating QL and SL blocks forming
a natural heterostructure. The average number of the various blocks is determined by stoichiometry.
Two reprinted works are devoted to manganese doping in Bi2Se3 and Bi2Te3.
CHAPTER 2. TOPOLOGICAL INSULATORS 16
Another paper presents direct evidence of the gap opening in the Dirac point correlating with
out-of-plane magnetization in Mn-doped Bi2Te3. The last paper deals with the magnetic
structure of MnSb2Te4, which shows an unusually high Curie temperature of about 50 K.
These results are promising for possible observation of QAHE at temperatures above 10 K.
2.6 Topological crystalline insulators
Additional crystal symmetry can induce topologically protected states even in topologically
trivial materials. These materials have to possess an even number of Dirac cones (or obstructions
as defined in section 2.2) inside a Brillouin zone. In a specific case, the pair of
Dirac cones is protected via crystal symmetry. We will briefly present the crystal with mirror
symmetry, where a topological invariant mirror Chern number can be defined [51–53]. In a
system with half-integer spin, mirror symmetry operator ˆM squares as ˆM2 = −1 and has
two eigenvalues ±i. In the three-dimensional system, let us note Σ a surface in the Brillouin
zone which is invariant under mirror symmetry ˆM. For example, if the mirror plane is xyplane,
mirror invariant reciprocal planes Σ are planes with kz = 0, kz = π/c. The electronic
eigenstates at Σ plane decompose into two groups according to their mirror eigenvalue. Let
us note them as |u+
k,l and |u−
k,l with eigenvalues +i and −i, respectively. We can evaluate
the Chern number for each of the mirror subspace C+, C− using formula [53]
C± =
−i
2π Σ
dkxdkyTr ∂xA±
y (k) − ∂yA±
x (k) , (2.35)
where A±
a;l,l = u±
k,l|∂a|u±
k,l is Berry connection in the mirror subspace. In time-reversal
symmetric systems C+ +C− = 0 holds and the mirror Chern number Cm is defined analogous
to formula (2.24) as
Cm =
C+ − C−
2
. (2.36)
The mirror Chern number Cm can have odd or even values. When Cm is even, the surface
Dirac cones exist only on mirror-symmetric surfaces. The Dirac cones are in pairs located not
in the TRIM points but along mirror invariant lines in the surface Brillouin zone, which map
onto itself under mirror symmetry. On the other hand, odd Cm implies an odd number of
Dirac cones in any surface Brillouin zone. The material is a conventional topological insulator
with Dirac cones positioned in TRIM points.
One of the most studied topological crystalline insulators is narrow band gap semiconductor
(Pb,Sn)Se and (Pb,Sn)Te alloys. Lead compounds PbSe and PbTe are trivial insulators,
while tin compounds SnTe and SnSe have inverted band structures [54,55]. These materials
crystallize in a cubic rock salt structure, and they have a direct band gap in L point. In PbTe,
the valence band edge is formed by L+
6 states and the conduction band edge by L−
6 states,
while SnTe is inverted with L−
6 being valence edge states and L+
6 conduction band edge states.
At a certain concentration, the band gap closes, forming the Dirac cones. Band gap closing
occurs at 20–25% of Sn in selenide and around 40–50% of Sn in telluride, according to figure
2.8. Band gap size is also temperature dependent, and a transition from trivial insulator to
topological crystalline insulator can be induced by cooling. This effect was demonstrated by
Tanaka et al. for (Pb,Sn)Te [57] and Dziawa et al. in (Pb,Sn)Se [58]. The particular dispersion
of the surface states is surface orientation dependent. The rock salt structure has three
possible mirror symmetric surface orientations (001), (111), and (110) [59]. Most studied
CHAPTER 2. TOPOLOGICAL INSULATORS 17
Figure 2.8: Band gap in (Pb,Sn)Se and (Pb,Sn)Te alloys as a function of composition. Figure
reprinted from [56].
were (001) and (111) orientation; their surface Brillouin zones are plotted in figure 2.9. In
(001) orientation, four Dirac cones are in the vicinity of ¯X points. On the other hand, (111)
surfaces have four Dirac cones in ¯Γ and ¯M points [60]. An example of the band gap in ¯Γ
point temperature dependence in (Pb,Sn)Se alloys is presented in figure 2.10. One can get a
phase transition from topologically trivial into a topological crystalline insulator for a certain
alloy composition.
Figure 2.9: Surface Brillouin zones for (001) and (111) surface. Eight bulk L points project
into the four ¯X points in the case of (001) surface. At (111) surface the bulk L points project
into ¯Γ and three ¯M points.
The strain in [111] direction lifts the degeneracy of the ¯Γ and three ¯M points. This
leads to an odd number of Dirac cones with properties of a strong topological insulator [29].
Our experimental work has shown the degeneracy can be lifted by doping (Pb,Sn)Se with
bismuth [61]. The experiments were performed for tin concentration x = 28 %. We have
shown the band gap closes at ≈ 120 K without bismuth doping. If the bismuth concentration
CHAPTER 2. TOPOLOGICAL INSULATORS 18
Figure 2.10: Experimental temperature dependence of the band gap in two (Pb,Sn)Se samples
in topologically trivial (a) and transition to inverted band structure (b). The experiment was
performed at end-station ARPES 12 at synchrotron BESSY II.
overcomes 0.5 % band gap in ¯M points closes while in ¯Γ remains opened. The resulting case
has an odd number of Dirac cones which is Z2 topological insulator.
Chapter 3
Experimental methods
This chapter will briefly present several experimental methods in which the author has partially
participated in the experiment or data analysis. Special attention is devoted to the
x-ray diffraction analysis of thin films in the first section, which is the primary method used
by the author. The second section describes several other methods: synchrotron-based x-ray
absorption spectroscopy (XAFS), angle-resolved photoemission spectroscopy (ARPES), and
two methods that are available in CEITEC Nano core facility – low-temperature transport
measurement and high-resolution transmission electron microscopy (HR-TEM).
3.1 Structural analysis of thin films by X-ray scattering
In this chapter, we describe the primary method used for the structural characterization of
epitaxial thin films. X-ray scattering provides beneficial information about the crystalline
structure of samples. Another widely used method is electron microscopy, namely highresolution
transmission electron microscopy. The advantages of the x-ray diffraction are
the following (i) non-destructive method, (ii) no need for surface preparation, even samples
with protective cap layer can be studied, (iii) averaging the information over relatively large
sample volume (tens of mm2). On the other hand, x-ray diffraction is an indirect method,
and the structure has to be modeled. The usage of an incorrect model leads to incorrect
results. If an unknown structure is studied, selecting a proper model is critical. An example
of such a case is presented in this work. First studies of manganese doped Bi2Te3 assumed
manganese substitutional or interstitial incorporation of Mn atoms into Bi2Te3 lattice. The
disordered structure of Bi2Te3 layers was attributed to the stacking of Bi2Te3 quintuple layers
and Bi double layers. Nevertheless, it turned out the actual structure consists of alternating
quintuple layers Bi2Te3 with septuple layer structure of MnBi2Te4 – i. e., Te-Bi-Te-Mn-TeBi-Te
structure. The structure was confirmed by high-resolution TEM. A combination of
several experimental methods achieves the best results in structural characterization. That
is, of course, a general statement valid for all experimental science.
3.1.1 Basics of x-ray scattering from thin films
In this chapter, we will briefly describe the x-ray scattering theory with a focus on the model of
randomly alternating structural motifs. More detailed descriptions can be found, for example,
in the book by Pietsch et al. [62] The x-ray scattering from crystals can be described as a
19
CHAPTER 3. EXPERIMENTAL METHODS 20
quantum mechanical scattering model. In the following text, we will limit the description to
elastic photon scattering. The x-ray photon propagation is described using Maxwell equations
and derived wave equation
( + K2
)E(r) = ˆV (r)E(r), (3.1)
where we have already evaluated the time-dependent part of the electromagnetic wave E(r, t) =
E(r)e−iωt, K = 2π
λ is the magnitude of the vacuum wave vector, wavelength λ, frequency
ω = Kc, and ˆV is the scattering potential
ˆV (r) = −K2
χ(r) + grad div, (3.2)
where χ(r) is electric susceptibility. Since x-ray wavelength is comparable with interatomic
distance, spatial variation of electric susceptibility includes the atomic structure of matter.
Here we have also neglected magnetic response, which is at x-ray frequencies very well satisfied.
If the incident state is described with a state |E0 , total wave field |E and the scattering
potential as ˆV , scattering theory leads to the following formula
|E = |E0 + ˆG0
ˆV |E , (3.3)
where ˆG0 is Green’s operator of the wave equation. This equation can be rewritten as
|E = |E0 + ˆG0
ˆT|E0 , ˆT = ˆV + ˆV ˆG0
ˆV + ˆV ˆG0
ˆV ˆG0
ˆV + · · · (3.4)
The general solution to this formula is complicated. The simplest approximation is to take
only the first term in the infinite series, the so-called first Born approximation, known as a
kinematical approximation in the theory of x-ray scattering
|E ≈ |E0 + ˆG0
ˆV |E0 . (3.5)
In other words, the kinematical approximation describes the scattering process as a single
scattering process. The kinematical approximation also assumes that the intensity of the
incident wave is not affected by the scattering processes.
Thus the kinematical approximation can be used if the following conditions are satisfied
1. the intensity of the incident beam does not change within the scattering volume,
2. the scattered intensity is much lower than the incident beam intensity and
3. multiple scattering processes are negligible.
Those conditions are satisfied if
1. diffracting volume is small – comparable length-scale is coherence length of the x-ray
radiation, or
2. sample consists of many small incoherent domains (sometimes the term “crystallite” is
used instead of the more precise “coherently diffracting domain”), or
3. single crystal sample has very high defect density – effectively, it means the sample
consists of many small domains bound by the defects (dislocations, stacking faults,
among others).
CHAPTER 3. EXPERIMENTAL METHODS 21
In other cases (high-quality single crystals) dynamical theory of diffraction has to be used,
which solves the whole equation (3.3) [63].
The studied thin film samples always consisted of many domains with size in the order of
100–300 nm, being much smaller than the coherence length of 2 µm in a typical high-resolution
x-ray diffraction setup with Cu Kα source and Ge(220) two-bounce monochromator. Thus
kinematical approximation is used in the following. The equation (3.5) can be rewritten in a
space coordinates as
E(r) = E0 −
1
4π
d3
r
eiK|r−r |
|r − r |
ˆV (r )E0(r ). (3.6)
The incident wave is usually in the form of the plane wave E(r) = E0eiK0·r . Usually, we
observe the beam scatted into a direction far from the sample rather than intensity distribution
in real space. The phase in Fraunhofer approximation equals
K|r − r | ≈ Kr − Ks · r , (3.7)
where scattered wave vector Ks = kr/|r| is pointing from scattering volume towards detector.
The scattered wave field is then simply
Es(r) = −
1
4π
eiKr
r
E0 d3
r e−i(Ks−K0)r ˆV (r ), (3.8)
which means the scattered amplitude is proportional to the Fourier transform of scattering
potential. Usually scattering vector Q is defined as Q = Ks − K0 and the amplitude scatted
to the direction Ks then equals
Es(Q) = A d3
r e−iQ·r ˆV (r ), (3.9)
where A stands for a multiplication factor.
The susceptibility at x-ray frequencies is proportional to the electron density ρ(r)
χ(r) = −
λ2
π
reρ(r), (3.10)
where re = e2
4π 0m0c2 is the classical electron radius. It is worth noting that the formula is a
high-frequency limit of classical Drude response of free electrons.
The electron density inside a crystalline sample is the sum of the electron density of each
atom
ρ(r) =
N
n=1
M
j=1
ρj(r − Rn − rj), (3.11)
where the first sum runs over all N unit cells, each positioned at Rn and the second sum over
M atoms within the unit cell, rj is position of j-th atom within unit cell. It is advantageous
to evaluate Fourier transform of the electron density
ρFT
(Q) = F(Q)
n
e−iQ·Rn
, (3.12)
CHAPTER 3. EXPERIMENTAL METHODS 22
where the structure factor of the unit cell F is evaluated as
F(Q) = d3
rρcell(r)e−iQ·r
=
M
j=1
fj(Q)e−iQ·rj
, (3.13)
where fj(Q) is the atomic form factor of j-th atom equal to the Fourier transform of electron
density of the single atom.
The intensity of the scattered beam is proportional to the square of the magnitude of
scattered wave amplitude
I(Q) = |E(Q)|2
= E∗
(Q)E(Q). (3.14)
Putting formula (3.12) into the intensity we obtain
I(Q) = A|F(Q)|2
S(Q), S(Q) =
n,m
e−iQ·(Rn−Rm)
. (3.15)
where S(Q) is a geometric factor describing crystal structure and shape, and A is a multiplication
factor including experimental geometry, incident intensity, and detector aperture.
Usually, we measure only relative values, and the factor A is treated as an arbitrary fitting
parameter.
The natural materials have non-negligible x-ray absorption. The usual way to account
for absorption is to add photon energy-dependent dispersion corrections (H¨onl corrections)
to the atomic form factor
f(Q, E) = f0(Q) + f (E) + if (E), (3.16)
where f (E), f (E) are real and imaginary dispersion correction, respectively. The absorption
is proportional to the imaginary part. The real and imaginary parts of the form factor satisfy
Kramers-Kronig relations. The susceptibility χ and refractive index n =
√
1 + χ of any
material is then complex.
The simplest way to account for absorption correction is to correct the wave vector k
inside the material to match material refractive index n. The relationship is given by the
simple optical formula
k2
= n2
K2
= n2 ω
c
2
, (3.17)
by continuity of the in-plane component of vacuum wave vector K and wave vector in material
k = K . Instead of the scattering vector Q = Kf − Ki, we will use the corrected scattering
vector q = kf − ki.
3.1.2 X-ray scattering from the thin film with randomly alternating motifs
In this section, we will present the theoretical description of the x-ray scattering on the sample
with randomly alternating motifs. Non-stoichiometric crystals of van der Waals topological
insulators of Bi2X3 family often form crystalline structures with random stacking of two or
more building blocks. Systems with alternating structures were theoretically and experimentally
studied previously by Holstein, Croset, Kopp et al. [64–67].
We have used a similar model also derived from Pukite’s model of stepped surface [68].
Assume the layer consists of alternating motifs A and B. For example, it can be Bi2Te3
CHAPTER 3. EXPERIMENTAL METHODS 23
quintuple layer and bismuth bilayer [49] or Bi2Te3 quintuple layer and MnBi2Te4 septuple
layer [69]. Assume the layer consists of P segments, each with nA
j and nB
j elements of type A
and B, respectively. Here numbers nA
j and nB
j are random integer numbers different in every
segment. In such a way, we can describe any sample with alternating A and B motifs.
In the following, we will limit to the symmetric scattering, where vector Q is parallel with
surface normal axis z. Then only z component of the atomic positions plays a role.
Let us define the structure factor of motif A
FA(q) =
MA
t=1
ft(q)e−iqzt
, (3.18)
where the sum runs over MA atoms in motif A and the thickness of motif A is DA. Correspondingly
we define structure factor FB and thickness DB of motif B. The structure factor
of the j-th segment is then
Fj(q) =
nA
j
v=1
FA(q)e−iqDAv
+ e−iqDAnA
j
nB
j
v=1
FB(q)e−iqDBv
(3.19)
and its thickness
Dj = nA
j DA + nB
j DB. (3.20)
The amplitude of the scattered radiation then equals to
E(q) = A
P
j=1
Fj(q)e−iqzj
, zj =
j−1
k=1
Dk. (3.21)
The scattered intensity is the sample average of the square of the amplitude
I(q) = E∗
(q)E(q) = |A|2
P
i=1
P
j=1
F∗
i (q)Fj(q)e−i(qzj−q∗zi)
. (3.22)
The average can be divided into three terms: j < i, j = i and j > i:
I(q) = |A|2
P
i=1
|Fi(q)|2
e−2 Im (q)zi
+ (3.23)
+
P
i=1
i−1
j=1
F∗
i (q)Fj(q)e−i(qzj−q∗zi)
+
P
i=1
P
j=i+1
F∗
i (q)Fj(q)e−i(qzj−q∗zi)



.
Two later terms with j > i and j < i are complex conjugates of each other, so their sum is
its real part multiplied by two
I(q) = |A|2



P
i=1
|Fi(q)|2
e−2 Im (q)zi
+ 2 Re


P
i=1
i−1
j=1
F∗
i (q)Fj(q)e−i(qzj−q∗zi)





. (3.24)
CHAPTER 3. EXPERIMENTAL METHODS 24
To evaluate the averages, we have used a short-range order model – we assume the neighboring
segments are statistically independent
I(q) = |A|2
P
i=1
|Fi(q)|2
e−2 Im (q)(D1+···+Di−1)
+ (3.25)
+2 Re


P
i=1
F∗
i (q) e−2 Im (q)(D1+···+Di−1)
i−1
j=1
Fj(q)e−iq(Dj+···+Di−1)





.
Moreover, any couple of Di, Dj=i are also statistically independent. On the other hand, j-th
segment form factor Fj and its length Dj are strongly correlated. The averages can then
simplify into the form
I(q) = |A|2
|F(q)|2
P
i=1
e−2 Im (q)D
i−1
+ (3.26)
+2 Re

 F∗
(q)
P
i=1
e−2 Im (q)D
i−1
i−1
j=1
F(q)e−iqD
e−iqD i−j−1





.
Let us define a couple of new quantities
α = F∗
(q) , β = F(q)e−iqD
, γ = |F(q)|2
, ξ = e−iqD
, ζ = e−2 Im (q)D
.
(3.27)
The formula for scattered intensity is evaluated using well-known formulas of geometric series
summation
I(q) = |A|2
γ
1 − ζP
1 − ζ
+ 2 Re
αβ
ζ − ξ
1 − ζP
1 − ζ
−
1 − ξP
1 − ξ
. (3.28)
In the case of a very thick film, the sum can be calculated as a limit of P → ∞
I(q) = |A|2
γ
1
1 − ζ
+ 2 Re
αβ
(1 − ζ)(1 − ξ)
. (3.29)
An example of this model is presented in figure 3.1. The four figures show numerical
simulation using the formula (3.28) for bismuth telluride and bismuth selenide doped with
manganese. To simplify the simulation, each element consisted of just a single septuple
layer MnBi2X4 and a random number of quintuple layers Bi2X3. The random distribution is
described with its mean value NQL and its root mean square deviation (RMSD). The calculation
was performed for the constant value of relative RMSD (RMSD/ NQL ) (top panels)
or constant mean length NQL (bottom panels). The limiting cases are straightforward to
interpret.
The case of NQL = 50 in the top panels corresponds to a vast number of quintuples (in
average 50) with just one septuple layer structure. The system is then almost pure Bi2X3
system, and the peak positions correspond perfectly to a pure Bi2X3 system denoted by thin
vertical black lines. On the other hand, the case of NQL = 1 is in the average system with
alternating septuple and quintuple layers. The peak positions correspond to the sum lattice
parameter c = DQL + DSL.
CHAPTER 3. EXPERIMENTAL METHODS 25
100
10
2
104
106
10
8
1010
1012
10
14
a b
c d
<NQL> relative RMSD of NQL=0.5
1
2
5
10
20
50
3 6 9 12 15 18 21
Intensity(arb.u.)
Mn doped Bi2Se3
100
10
2
10
4
10
6
108
10
10
10
12
10
14
0 1 2 3 4 5
<NQL>=5
relative RMSD of NQL
1.0
0.7
0.5
0.3
0.2
0.1
Intensity(arb.u.)
Qz (Å
−1
)
100
10
2
104
106
10
8
1010
1012
10
14
<NQL> relative RMSD of NQL=0.5
1
2
5
10
20
50
3 6 9 12 15 18 21
Intensity(arb.u.)
Mn doped Bi2Te3
100
10
2
10
4
10
6
108
10
10
10
12
10
14
0 1 2 3 4 5
<NQL>=5
relative RMSD of NQL
1.0
0.7
0.5
0.3
0.2
0.1
Intensity(arb.u.)
Qz (Å
−1
)
Figure 3.1: Simulation of XRD profile of in symmetric scans.
The bottom panels show the dependence of distribution width. The curve with relative
RMSD 0.1 corresponds to an almost perfectly ordered multilayer of 5 quintuple layers and
a single septuple layer. The peaks correspond to a real space period of c = 5DQL + DSL.
Increasing RMSD, the peaks get smeared out to a broad diffraction curve. Interesting cases
are peaks at Qz ≈ 1.9 ˚A−1 and its second order at Qz ≈ 3.8 ˚A−1 which stay sharp even in a
case of very disordered structure. The reason is that the thickness of the septuple layer almost
coincides with 4/3 of the quintuple layer thickness DSL ≈ 4/3DQL. The third order diffraction
of quintuple layer structure (inter-planar distance d = DQL/3) thus corresponds to the fourth
diffraction order of septuple layers (inter-planar distance d = DSL/4). In other words, both
components share a mutual spatial frequency, and corresponding diffraction peaks do not
vanish in any random QL/SL stacking.
3.1.3 Substitutional and anti-site defects
The x-ray diffraction also allows us to study substitutional point defects in the positions of
the other atoms to a certain extent. The diffraction intensity is proportional to the square
of the structure factor. However, the most substantial effect is caused by heavy atoms, and
light atoms have only a minor contribution to the total scattering factor. For example, in the
case of manganese doped Bi2Te3, Mn is a very light element to bismuth or tellurium, and it
is generally not feasible to determine its position within the lattice.
CHAPTER 3. EXPERIMENTAL METHODS 26
100
102
104
106
10
8
1010
1012
1014
1016
1018
0 1 2 3 4 5 6 7 8 9
a
b
Intensity(arb.u.)
Qz (1/Å)
C1 C2
1.0 0.03
0.9 0.08
0.8 0.13
0.7 0.18
0.6 0.23
0.5 0.28
l=3 6 9 12 15 18 21 24 27 30 33 36 39 42 45
BaF2 BaF2 BaF2 BaF2
100
102
104
106
108
1010
10
12
10
14
1016
1018
1020
0 0.5 1 1.5 2
Intensity(arb.u.)
Qz (1/Å)
C1 C2
1.0 0.03
0.9 0.08
0.8 0.13
0.7 0.18
0.6 0.23
0.5 0.28
0.4 0.33
l=3 6 9 12
BaF2
Figure 3.2: Experimental (red) and simulated (black) symmetric scans of MnSb2Te4 thin film
grown on BaF2 (111).
On the other hand, particular diffractions are sensitive to the positions of light atoms.
We will present the example of MnSb2Te4 structure. The ideal structure of the septuple
layer MnSb2Te4 is supposed to be Te-Sb-Te-Mn-Te-Sb-Te. In reality, the manganese and
antimony atoms partially intermix, as is also confirmed by HRTEM in section 3.2.2. The
structure factor of the diffractions is given by formula (3.13). Since the atomic form factor
is proportional to the atomic number, the contribution of light elements is often negligible.
Thus the determination of light atoms inside a structure composed of heavy elements is very
uncertain and often almost impossible. However, in MnSb2Te4 diffraction 000 6 is sensitive
to the intermixing of Sb/Mn atoms. This diffraction is relatively weak because form factors
of Sb and Te atoms sum in structure factor with opposite phases; thus, their contribution
to the total structure factor is tiny. In such case, even small changes in structure factors
significantly impact the resulting intensity.
The simulation of MnSb2Te4 XRD profile with various intermixing values is plotted in
figure 3.2. The simulation was performed for several values of C1, which are the concentration
of manganese in central position Mn(Mn) and C2 manganese concentration in antimony
position Mn(Sb). The SL has a single manganese position and two antimony positions. The
CHAPTER 3. EXPERIMENTAL METHODS 27
stoichiometry of the structure is MnxSb2−xTe4, where x = C1 + 2C2. The set of simulations
was performed for the fixed total stoichiometry value x = 1.06, which was determined using
the Rutherford backscattering (RBS) experiment [70]. The figure shows that the antimony
and tellurium form factors do not cancel in the ideal structure; the simulated diffraction peak
vanishes close to total Sb/Mn intermixing C1 ≈ C2 ≈ 1/3. Our experimental data shows the
real intermixing is close to 10 % of the manganese position occupied by antimony (C1 = 0.9).
3.1.4 Reciprocal space mapping: lattice parameters and domain size
6.36
6.38
6.4
0 100 200 300 400
6.18
6.2
6.22
a(Å)
Temperature (K)
(a)
(Pb,Sn)Te
BaF2
90
90.1
0 100 200 300 400
α(deg)
Temperature (K)
(b)(b)
2.7 2.8 2.9
Q[1−10] (1/Å)
4.9
5
5.1
5.2
5.3
Q[111](1/Å)
10
0
10
1
102
10
3
PbSnTe
BaF2
T=295K
(c)
relaxed
strained
SnTe
PbTe
2.7 2.8 2.9
Q[1−10] (1/Å)
4.9
5
5.1
5.2
5.3
Q[111](1/Å)
10
0
10
1
102
10
3
PbSnTe
BaF2
T=80K
(d)
relaxed
strained
SnTe
PbTe
Figure 3.3: (a) Temperature dependence of (Pb,Sn)Te and BaF2 lattice parameters. (b)
Temperature dependence of (Pb,Sn)Te lattice angle. (c, d) Reciprocal space maps in the
vicinity of 513 reciprocal lattice points at 80 K and room temperature, respectively.
Another essential property studied by x-ray diffraction is strain and lattice in the epitaxial
layers. Most often, the epitaxial layer is grown on (001) or (111) surfaces of the cubic
substrate. Without any other preferential in-plane direction induced, for example, by miscut,
the symmetry along the out-plane axis is a four-fold or a three-fold rotational axis. For such
a case, the in-plane strain in any in-plane direction has the same value. That dramatically
simplifies the analysis since one needs to determine lattice parameters in arbitrary in-plane
and out-of-plane directions.
CHAPTER 3. EXPERIMENTAL METHODS 28
The lattice parameters are determined by measuring XRD reciprocal space maps in the
vicinity of two reciprocal lattice points. Usually, one symmetric diffraction is selected, and
the other has to be asymmetric. We can achieve higher precision using the substrate peak
as a reference. The symmetric diffraction is independent of the in-plane lattice parameter;
its position is used to determine the tilt between the substrate and layer lattice. The asymmetric
reciprocal space map is corrected for lattice tilt, and both in-plane and out-of-plane
lattice parameters are determined. An example of (Pb,Sn) lattice parameter determination
is presented in figure 3.3. Let us define the substrate lattice parameter asub, layer in-plane
lattice parameter a , out-of-plane a⊥, and unstrained lattice parameter of the layer a0. The
reciprocal space maps in figure 3.3(c,d) show several essential lines, the so-called relaxation
triangle. The vertical line parallel with Qz axis denotes the position of fully strained lattice,
also called pseudomorphic, when the in-plane lattice parameter matches the substrate one
a = asub. The relaxed line corresponds to the case of the layer holding its free unstrained
lattice parameter a⊥ = a = a0; this line connects the substrate peak position with the origin
of coordinates. Two other lines correspond to the lattice of SnTe and PbTe. In general, the
experimental peak should appear inside the relaxation triangle. The layer is fully relaxed
at room temperature shown in panel (c). However, at a temperature of 80 K in panel (d),
the layer peak is above the relaxation line, and the structure is over-relaxed. Differences in
thermal expansion coefficients can easily explain such a case; (Pb,Sn)Te layer has a bigger
thermal expansion coefficient than BaF2 substrate. During cooling down, the layer lattice
shrinks more than the substrate leading to an in-plane tensile strain in the layer.
The strain of cubic materials can be calculated from lattice parameters. For in-plane and
out-of-plane strain it holds
ε =
a − a0
a0
, ε⊥ =
a⊥ − a0
a0
. (3.30)
Solving linear theory of elasticity for stress-free surface, we obtain the strain components
constraint via Poisson’s ratio ν
ε⊥ = −2
ν
1 − ν
ε . (3.31)
Evaluating the preceding formula using lattice parameters, we obtain a formula for unstrained
lattice parameter
a0 =
(1 − ν)a⊥ + 2νa
1 + ν
. (3.32)
The formula is handy if we have to determine the composition of ternary alloy using Vegard’s
law. The Poisson’s ratio for (001) and (111) orientation of cubic lattice can be evaluated
using components of an elastic tensor as
ν001 =
C12
C11 + C12
, ν111 =
1
2
C11 + 2C12 − 2C44
C11 + 2C12 + C44
. (3.33)
In the case of (111) surface, the cubic lattice is deformed along [111] direction. The
lattice of the layer is not cubic anymore but rather rhombohedral. It can be helpful to
evaluate not out-of-plane a⊥ and in-plane a lattice parameters but rather to describe it
using rhombohedral lattice parameter ar and angle αr. The transformation formulas follow
from the geometrical correspondence
ar =
a2
⊥ + 2a2
3
, cos αr =
a2
⊥ − a2
a2
⊥ + 2a2 . (3.34)
CHAPTER 3. EXPERIMENTAL METHODS 29
Figure 3.4: Inner view of Rigaku SmartLab diffractometer in CEITEC Nano core facility. A
custom-built helium cryostat by ColdEdge company is mounted in the center of the goniometer.
The cryostat allows for measurement down to liquid helium temperature.
If angle α = 90◦ the lattice is cubic without any strain and a⊥ = a = a0. That is the case of
(Pb,Sn)Te/BaF2 at room temperature, as shown in figure 3.3.
Not only peak positions carry helpful information. The shape of the diffraction peak itself
can be fitted to obtain information about layer structure. The most common model is the
so-called mosaic block model. The crystal is assumed to be composed of a vast number of
small domains, each of them with random misorientation. The model parameters are average
radii of the domains in the in-plane (horizontal) Rh and out-of-plane (vertical) Rv directions
and average misorientation ∆ϕ. The simulation procedure was described in several preceding
works [62,71].
3.1.5 Temperature dependent XRD experiments
The temperature dependence of the lattice parameters and strain can be essential for the
interpretation of low-temperature experiments of the band structure. The structural analysis
laboratory at CEITEC was equipped with a high-temperature chamber up to 1100 ◦C, and a
liquid nitrogen cryostat. Later the low-temperature possibility was improved by purchasing
a liquid helium dome cryostat shown in figure 3.4.
We present several examples of low-temperature measurements of the lattice parameters
and strain. Figure 3.3 shows the temperature dependence of the lattice parameter of
(Pb,Sn)Te and BaF2 (111) substrate. The lattice angle of (Pb,Sn)Te increases with decreasing
temperature. This dependence is a direct consequence of the (Pb,Sn)Te thermal expansion
being larger than the expansion of BaF2 substrate.
Another example of (Pb,Sn)Se layers grown on various substrates is presented in figure 3.5.
The layers with 40 % Sn were grown on BaF2 (111), InP (111), and KCl (001). The thermal
expansion coefficient of InP is much smaller, the coefficient of BaF2 is slightly smaller, and
KCl is much bigger than the thermal expansion of (Pb,Sn)Se. The in-plane strain of the
layer is then compressive on KCl and tensile on BaF2 and InP. The BaF2 substrate with the
slightest difference in thermal expansion coefficient causes the smallest strain in the layer.
On the other hand, the layer’s electric field can be changed with the substrate choice due to
CHAPTER 3. EXPERIMENTAL METHODS 30
−0.008
−0.006
−0.004
−0.002
0
0.002
0.004
0.006
50 100 150 200 250 300
in−planestrain
Temperature (K)
Pb0.60Sn0.40Se
KCl (001)
InP (111)
BaF2 (111)
6.045
6.05
6.055
6.06
6.065
6.07
6.075
6.08
6.085
6.09
50 100 150 200 250 300
out−of−planelatticeparameter(Å)
Temperature (K)
Pb0.60Sn0.40Se
KCl (001)
InP (111)
BaF2 (111)
5.85
5.9
5.95
6
6.05
6.1
6.15
6.2
6.25
6.3
50 100 150 200 250 300
substratelatticeparameter(Å)
Temperature (K)
Pb0.60Sn0.40Se
KCl (001)
InP (111)
BaF2 (111)
6.05
6.055
6.06
6.065
6.07
6.075
6.08
6.085
50 100 150 200 250 300
unstrainedlayerlatticeparameter(Å)
Temperature (K)
Pb0.60Sn0.40Se
KCl (001)
InP (111)
BaF2 (111)
Figure 3.5: Temperature dependence of lattice parameters and strain of (Pb,Sn)Se layer
with 40% Sn content. (a) Substrate lattice parameter, (b) out-of-plane lattice parameter of
(Pb,Sn)Se, (c) unstrained bulk lattice parameter (Pb,Se)Se calculated from out-of-plane and
in-plane lattice parameters, (d) in-plane strain of (Pb,Sn)Se.
CHAPTER 3. EXPERIMENTAL METHODS 31
6.175
6.18
6.185
6.19
6.195
6.2
6.205
0 50 100 150 200 250 300 350
(a)
BaF2substratelatticeparameter(Å)
Temperature (K)
SnTe
Sn0.80Ge0.20Te
6.25
6.26
6.27
6.28
6.29
6.3
6.31
6.32
6.33
0 50 100 150 200 250 300 350
(b)
layerlatticeparameter(Å)
Temperature (K)
SnTe
Sn0.80Ge0.20Te
89
89.5
90
90.5
91
0 50 100 150 200 250 300 350
(c)
latticeangleα(o
)
Temperature (K)
SnTe
Sn0.80Ge0.20Te
0.001
0.01
0.1
1
10
0 50 100 150 200 250 300 350
(d)
Intensityratio333/444
Temperature (K)
SnTe
Sn0.80Ge0.20Te
Figure 3.6: Temperature dependence of SnTe and (Sn,Ge)Te lattice parameters, lattice angle,
and intensity ratio of 333 to 444 diffraction peaks.
the piezoelectric effect. The layers we have studied are conductive; the piezoelectric field is
screened in the bulk of the material, and close to surface space charge region is formed with
band bending.
Last we will present the phase transition observed in (Sn,Ge)Te layers. GeTe is ferroelectric
with a transition temperature of 700 K, while SnTe has a low ferroelectric transition
temperature below 100 K. Alloying SnTe with GeTe, one can tune the transition temperature.
The experimental results of SnTe and Sn0.80Ge0.20Te are presented in figure 3.6. The
layer’s lattice parameter shows a discontinuity in the thermal expansion and the lattice angle
at a temperature of 260 K. However, the most prominent signature of the ferroelectric
phase transition is the intensity change of 333 diffraction peaks. In the high-temperature
rock-salt phase, the structure factor of the odd-parity diffraction is proportional to the difference
between cationic (Sn,Ge) and anionic (Te) form factors. The form factor of Sn and
Te are almost identical, and the intensity of 333 diffraction peak is very small. In the lowtemperature
ferroelectric rhombohedral phase, anions and cations shift with respect to ideal
rock-salt positions. The structure factor of 333 diffraction peak drastically changes at the
phase transition. This effect is very well seen in figure 3.6(d); the relative intensity of 333
CHAPTER 3. EXPERIMENTAL METHODS 32
diffraction with respect to 444 diffractions rises by approximately one order of magnitude at
the phase transition temperature.
3.2 Other methods of structural analysis
In this section, we will briefly comment on two other methods we have used to characterize
the structure of the topological insulator films.
3.2.1 X-ray absorption spectroscopy
The measurement of the particular element at its x-ray absorption edge is often called the xray
absorption fine-structure (XAFS). It is an element-specific method that probes the optical
transition of an electron from the localized core level state into the empty state above the
Fermi level.
The XAFS spectra are usually divided into two regions: near vicinity of the absorption
edge called x-ray absorption near-edge structure (XANES) or near-edge x-ray absorption fine
structure (NEXAFS). In contrast, the spectra further above the edge are called Extended
x-ray absorption fine structure (EXAFS).
The standard XAFS analysis procedure is extracting the contribution of the studied absorption
edge. The absorption below the edge is subtracted, and the absorption coefficient is
normalized to the height of the absorption edge. The normalized absorption µN equals zero
below the edge, and its average above the edge equals one. This normalization is equivalent
to normalizing by the concentration of the studied atom. The oscillatory part above the edge
is usually denoted as χ = µN − 1.
The XANES part (spectral shape of absorption edge itself up to ≈ 20 eV above edge)
probes electronic states just above Fermi level in the position of the particular element. It
includes information on the particular element’s chemical state. The proper interpretation is,
however, quite complicated, and it is necessary to solve the material’s electronic structure.
Specialized computer programs are available; one of the most used is FDMNES code [72].
The EXAFS region further from edge ≥ 20 eV to 1 keV above the edge have a much more
straightforward interpretation. The electronic states far above the Fermi level can be well
approximated as free-electron states interacting with the neighboring atoms. Localized core
level electron is excited into free-electron wave function spreading as a spherical wave. The
spherical wave has a wave vector
k =
1
2me(E − Eedge), (3.35)
where E is photon energy, Eedge binding energy of the core level, and their difference is
electron kinetic energy above the Fermi level. The spherical wave scatters on the neighbor
atoms and interferes with an unscattered wave. The interference gives rise to the oscillatory
behavior of the absorption probability χ(k) with a period of ∆k = π/R, where R is the
distance of the neighbor atom. The period of the oscillation can be used to determine the
neighborhood of the particular atom. Often the simple analysis is performed as a Fourier
transform of χ(k) to the real space χFT (R). The real space function χFT (R) has maxima
in the distances of the neighbor atoms. The complete theory is rather complicated; we refer
to the existing literature [73]. The most often used software package for data analysis is
Demeter [74] and for simulation of EXAFS profile FEFF package [75,76].
CHAPTER 3. EXPERIMENTAL METHODS 33
−0.5
0.0
0.5
1.0
1.5
2.0
2.5
6.4 6.6 6.8 7 7.2 7.4
4%
6%
9%
13%
(a)
µ(arb.u.)
E (keV)
Bi2Te3: Mn
−0.5
0.0
0.5
1.0
1.5
2.0
2.5
6.4 6.6 6.8 7 7.2 7.4
6%
8%
10%
13%
(b)
µ(arb.u.)
E (keV)
Bi2Se3: Mn
Figure 3.7: Experimental normalized XAFS spectra of various concentration of Mn-doped
Bi2Te3 (a) and Bi2Se3 (b), respectively.
The experiment has to be carried out at synchrotron beamlines since no sufficient laboratory
sources with tunable photon energy exist. There are several possibilities for the
experimental setup. Bulk samples are most commonly measured in transmission regime using
two detectors – most often ionization chambers. The first ionization chamber is positioned
in front of the sample and measures the intensity of the incoming beam; the second chamber
is behind the sample and measures transmitted intensity. The transmission of the chamber
is optimally around 2/3; if the transmission is lower than 2/3, the absorption measurement
statistic worsens. On the other hand, the measured signal is proportional to the absorption in
the chamber, and too high transmission worsens the incoming beam measurement statistics.
The sample transmission is an exponential function of its thickness; the best statistics one
obtains with sample transmission of about 1/3 (1/e to be precise). Thus, the XAFS beamlines
are usually equipped with ionization chambers, allowing them to fill with arbitrary pressure
of selected noble gas to achieve optimal sensitivity for a wide range of chemical elements. The
fluorescence of the particular element is proportional to the photoelectric component of total
absorption corresponding to the particular edge. However, that is the only part important
for XAFS analysis.
For thin films, the most common method is to measure fluorescence instead of a transmission.
The incidence ionization chamber is still used similarly as in transmission mode, and
the sample is irradiated at low angle incidence to maximize the signal from the film. The
fluorescence signal is collected with an energy-dispersive x-ray detector.
In the following text, we show an example of XAFS used to characterize the positions of
manganese atoms inside the topological insulator lattice of Bi2Te3 and Bi2Se3. The measurement
was performed in the vicinity of Mn K edge at 6539 eV up to 7500 eV to cover sufficient
EXAFS range. The experiment was carried out at synchrotron ESRF beamline BM23. Figure
3.7 shows normalized absorption spectra collected at samples with various Mn concentrations.
The spectra have similar features independent of manganese concentrations.
CHAPTER 3. EXPERIMENTAL METHODS 34
0
0.5
1
1.5
2
2.5
3
3.5
6.5 6.55 6.6 6.65 6.7 6.75 6.8
septuple
substitutional
octahedral in vdW
tetrahedral in vdW
Te(1)
Te(2)
χ(arb.u.)
E (keV)
Mn doped Bi2Te3
measurement
calculation
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
6.5 6.55 6.6 6.65 6.7 6.75 6.8
septuple
substitutional
octahedral in vdW
tetrahedral in vdW
Se(1)
Se(2)
χ(arb.u.)
E (keV)
Mn doped Bi2Se3
measurement
calculation
Figure 3.8: Experimental data and simulation of EXAFS part for various manganese positions
in Bi2Te3 (a) and Bi2Se3 (b), respectively.
Mn doped Bi2Se3
position first shell distance(˚A) second shell distance (˚A)
center of septuple layer 6 Se 2.719
6 Bi 3.977
6 Mn 4.12
substitutional Bi
3 Se(1) 2.972
3 Se(2) 3.041
octahedral in vdW gap 6 Se 3.041
tetrahedral in vdW gap 4 Se 2.394
substitutional Se(1) 3 Bi 2.972
close to vdW gap 3 Se(1) 3.284
substitutional Se(2)
6 Bi 3.041
central position in Bi2Se3
quintuple layer (QL)
Mn doped Bi2Te3
position first shell distance(˚A) second shell distance (˚A)
center of septuple layer 6 Te 2.909
6 Bi 4.293
6 Mn 4.385
substitutional Bi
3 Te(1) 3.073
3 Te(2) 3.246
octahedral in vdW gap 6 Te 2.858
tetrahedral in vdW gap 4 Te 2.533
substitutional Te(1) 3 Bi 3.073
close to vdW gap 3 Te(1) 3.637
substitutional Te(2)
6 Bi 3.246
in center of QL
Table 3.1: Nominal distances of Mn neighbor atoms in various positions in Bi2Se3 and Bi2Te3
structures.
CHAPTER 3. EXPERIMENTAL METHODS 35
0.0
1.0
2.0
3.0
0 2 4 6 8 10 12
Mn doped Bi2Te3
x= 4%
x= 6%
x= 9%
x=13%
kχ(k)(Å
−1
)
k (Å−1
)
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0 1 2 3 4 5
x= 4%
x= 6%
x= 9%
x=13%
|χ(r)|
r (Å)
0.0
1.0
2.0
3.0
0 2 4 6 8 10 12
Mn doped Bi2Se3
x= 6%
x= 8%
x=10%
x=13%
kχ(k)(Å
−1
)
k (Å
−1
)
0.0
2.0
4.0
6.0
8.0
0 1 2 3 4 5
(a) (b)
(c) (d)
x= 6%
x= 8%
x=10%
x=13%
|χ(r)|
r (Å)
Figure 3.9: (a), (c) Extracted oscillatory part χ(k) of the absorption spectra above edge multiplied
by wave vector k and its fit. (b), (d) Fit of the Fourier transform of the oscillatory part
χ(r). Top row presents data of Mn doped Bi2Te3 samples, the bottom of Bi2Se3, respectively.
CHAPTER 3. EXPERIMENTAL METHODS 36
Mn doped Bi2Se3
Mn concentration 6 Se (˚A) 6 Bi (˚A) 6 Mn (˚A)
4 2.75±0.08 not fitted not fitted
6 2.67±0.04 3.97±0.14 4.02±0.12
8 2.71±0.04 4.10±0.11 4.04±0.08
10 2.72±0.03 4.14±0.09 4.02±0.06
13 2.71±0.04 3.97±0.15 4.2±0.2
Mn doped Bi2Te3
Mn concentration 6 Te (˚A) 6 Bi (˚A) 6 Mn (˚A)
4 2.90±0.09 not fitted not fitted
6 2.92±0.04 4.3±0.2 4.0±0.2
9 2.92±0.04 4.3±0.2 4.0±0.2
13 2.91±0.06 4.3±0.2 4.2±0.2
Table 3.2: Fitted distances of neighbor atoms in the first coordination (Se/Te) and second
coordination shell (Bi and Mn) of Mn-doped Bi2Se3 and Bi2Te3.
0
0.5
1
1.5
2
6530 6540 6550 6560 6570 6580
Bi2Se3:Mn
energy (eV)
experiment 4% Mn
experiment 8% Mn
Mn in septuple
substitutional Mn
0
0.5
1
1.5
2
6530 6540 6550 6560 6570 6580
Bi2Te3:Mn
energy (eV)
experiment 3% Mn
experiment 10% Mn
Mn in septuple
substitutional Mn
Figure 3.10: Near edge part of absorption spectra.
CHAPTER 3. EXPERIMENTAL METHODS 37
First, we will discuss the EXAFS part above the absorption edge. The absorption spectra
are normalized to the height of the absorption edge (the height of the absorption edge is
1). The oscillatory part above the absorption edge was simulated using FEFF9 code [75]
for various theoretical manganese positions in the structure of topological insulators, and
comparison is shown in figure 3.8. Distances of the nearest neighbors are presented in table
3.2.1. The best fit to the experimental data has a central position in the septuple layer.
However, in Bi2Te3 structure, the interstitial octahedral position inside the van der Waals
gap has very similar distances to the nearest neighbor atoms as the central position of the
septuple layer.
The fitting of the EXAFS oscillatory part is shown in figure 3.9, and the resulting distances
are presented in table 3.2.1. The agreement of the fitted distances with nominal distance in
the central position in the septuple layer is excellent. The agreement in the distances of the
second coordination shell is acceptable within experimental error bars. The fitting of Mn
atoms is difficult; the scattering power of Mn atoms is much weaker than bismuth, tellurium,
or selenium. Their contribution to the experimental curve is small to heavier atoms.
The last analysis was done by calculating the shape of the edge using FDMNES code with
a multiple scattering approach on a muffin-tin potential. The calculation of the exact energy
of 3d-4f orbitals is incorrect, leading to incorrect pre-edge structure of the calculated spectra
in figure 3.10. However, the main shape of the absorption edge structure is correct. Our
calculations show that the most significant peak at the absorption edge is at higher energy
for Mn in the central septuple position than for Mn in the substitutional position. The
experimental spectra show a double peak structure indicating a specific manganese amount
in the substitutional position. The substitutional peak is significantly higher in low manganese
doped Bi2Se3 (4% Mn). This observation agrees with XRD analysis where Bi2Se3 samples
with such Mn doping do not include sufficient septuples to accommodate all manganese atoms.
Also, similar mixing was observed in MnSb2Te4 as discussed in section 3.1.3.
3.2.2 Transmission electron microscopy
The structural analysis by XRD was justified using transmission electron microscopy. The
high-resolution transmission electron microscope FEI Titan Themis 60–300 is available in the
CEITEC Nano core facility. The lamellae were prepared using a focused ion beam also in the
CEITEC Nano core facility using FEI Helios dual beam scanning electron microscope. The
lamellae thickness was in the range of 50–100 nm.
We have used chiefly a high-angle annular dark field (HAADF) detector and a highresolution
scanning transmission electron microscopy (STEM) regime. The focus of the
incoming electron beam limits the spatial resolution. The STEM resolution of FEI Titan
at 300 keV energy is about 1.4 ˚A allowing for resolution of individual atoms. The HAADF
detector collects electrons scattered at higher angles. FEI Titan uses an angular range of
70–200 mrad. The theoretical interpretation of contrast in HAADF detector is relatively
straightforward; heavier elements are stronger scatterers than light elements.
The example of analysis of MnSb2Te4 layer is presented in figure 3.11. The distribution
of particular elements was further studied using energy dispersive x-ray spectroscopy (EDX).
Panel 3.11(d) shows the spatial distribution of the HAADF signal, and panels 3.11(e-g) present
the same area EDX signal of elements Mn, Sb, and Te, respectively. Extracted line profiles
of HAADF and Mn EDX in the vertical direction are presented in panel 3.11(c). The EDX
signal was collected for the lengthy exposition of about 30 minutes with higher flux than
CHAPTER 3. EXPERIMENTAL METHODS 38
Figure 3.11: (a), (b), (d) HRSTEM of MnSb2Te4 sample with HAADF detector. (a), (b) Raw
HAADF image and Fourier filtered HAADF image, respectively. (d) Smaller area HRSTEM
and corresponding EDX elements map of Mn (e), Sb (f), and Te (g). (c) Extracted line profiles
from panels (d) and (e) show the highest Mn concentration in the center of the septuple layer.
CHAPTER 3. EXPERIMENTAL METHODS 39
Figure 3.12: (a) HRSTEM experiment of MnSb2Te4 layer. (b), (c), (d) Panels show simulation
with different concentrations of manganese in central and antimony positions. (b)
Nominal MnSb2Te4 structure (C1 = 1, C2 = 0), (c) fully random occupation of Sb/Mn positions
(C1 = C2 = 1/3). (d) partial intermixing of Mn/Sb (C1 = 0.8, C2 = 0.15). (e)
comparison of extracted line profiles from the experiment (red) and simulation in panel (d)
(blue), respectively.
usual HRTEM images. The resolution of EDX is thus about 0.5 nm. However, the Mn
signal distribution suggests the manganese atoms concentrate in the septuple layer structure’s
central position in agreement with the XRD analysis presented in section 3.1.3.
Further quantitative analysis was done by simulating HAADF images in a specialized
software µSTEM [77]. We have simulated several mixing conditions similar to the values
obtained in section 3.1.3. The results compared to the experiment are shown in figure 3.12.
Panel (a) shows the experimental image, and panels (b-d) show the simulated image with
various Mn/Sb intermixing levels. Panel (b) shows the nominal structure of MnSb2Te4 with
a central position occupied only by Mn atoms (C1 = 1, C2 = 0 in notation explained in
section 3.1.3). The simulated HAADF signal in the central septuple layer position is too
dark in simulation for the experiment. Simulated intensities of Sb and Te atoms are almost
indistinguishable since Sb and Te differ just by one in atomic number. Panel (c) shows entirely
random Sb/Mn intermixing (C1 = C2 = 1/3). The experimental intensity of the central
septuple position is smaller than in Sb positions, indicating a not entirely random case. Panel
(d) shows intermixing with C1 = 0.8, C2 = 0.15, which corresponds to a conclusion in section
3.1.3. The extracted intensity profile of the experimental and simulated HAADF intensity
are shown in panel (e).
CHAPTER 3. EXPERIMENTAL METHODS 40
000000000000000000000000000000000000000000000000000000000000000000000000
000000000
000000000000000000000000000000000000
111111111111111111111111111111111111111111111111111111111111111111111111
111111111
111111111111111111111111111111111111
x
y
z
Electron
analyzer
θ
(a)
(b)
E
E
φ
f
F
E B
E kin
h
h ν
ν
ϕ
φB
Sample Vacuum
A
Spectrometer
Figure 3.13: (a) schematic of the ARPES experiment. (b) Schematics of energy levels.
3.3 Angle-resolved photoemission spectroscopy
We have used angle-resolved photoemission spectroscopy (ARPES) to study the electronic
band structure. The author participated in several ARPES experiments, but his scientific
specialization is more focused on structural analysis. Therefore this chapter will be brief,
covering only the basics of the ARPES method. For a more precise overview, we suggest
further literature [78–81].
The principle of the method is to excite the electron system with the photon in ultraviolet
to soft x-ray range (6–1000 eV). The excited electron can escape the sample; the electron
optical system detects its momentum and kinetic energy. The schematics of the experimental
setup are in figure 3.13. The simplest photoemission model is called the three-step model:
1. Excitation of the electron by photon absorption from the bound state to the excited
state above the Fermi level.
2. Diffusion of the excited electron to the surface.
3. electron escapes from the material to the vacuum.
The three-step model is a significant simplification; we assume the initial and final states in
the material are single particle states neglecting correlations with other electrons. The initial
state has wave-vector ki and final state kf . Let us assume the electron’s initial state has
binding energy EB measured with respect to the Fermi level. The energy of the excited state
is
Ef = hν − EB, (3.36)
where hν is the energy of the incoming photon. The incoming photon’s momentum is usually
negligible concerning the size of the Brillouin zone. Momentum of photon with energy of
100 eV is 0.05 ˚A−1, which approximately 2 % of the typical Brillouin zone. During the excitation
process, the electron crystal momentum is conserved up to any reciprocal lattice vector
G
kf = ki + G. (3.37)
The probability per unit time of the transition from initial to final state wfi can be calculated
using Fermi’s golden rule
wfi =
2π
ψf | ˆHi|ψi
2
δ (Ef − EB − hν) , (3.38)
CHAPTER 3. EXPERIMENTAL METHODS 41
where ˆHi is the photon interaction Hamiltonian. Usually, the dipole approximation is sufficient
to describe the interaction
ˆHi = · p, (3.39)
where is the polarization vector of incoming light.
The electron then diffuses towards the surface. The probability of reaching the surface
exponentially decreases with the distance from the sample by an inelastic mean free path. A
wave describes the electron state in a vacuum outside the sample with the kinetic energy of
Ekin = hν − EB − φ, where φ is a work function. The components of electron wave vector K
in a vacuum are described as
Kx =
√
2mEkin
sin θ cos ϕ, Ky =
√
2mEkin
sin θ sin ϕ, Kz =
√
2mEkin
cos θ. (3.40)
During the electron transition through the sample surface, the in-plane component of the
electron momentum is conserved
K = k . (3.41)
The out-of-plane component kz can be determined by approximating the final state to be
nearly free electron state. The wave vector of the final state is given by
Ef = E0 +
2k2
f
2m
, (3.42)
where E0 is the energy level corresponding state with zero wave vector. Usually, this level can
be approximately assigned to the bottom of the valence band. Combining the above formulas,
one can obtain the relation for the out-of-plane component of the wave vector
2
2m
(k2
z + k2
) = Ef − E0, (3.43)
kz =
2m
2
(Ef − E0) − K2 =
2m
2
(Ekin + V0), (3.44)
where inner potential V0 is the energy of the bottom of the valence band with respect to the
vacuum level outside the sample V0 = |E0| + φ.
We want to emphasize the following aspects of the ARPES technique:
• At a given photon energy, one measure only a particular two-dimensional cut through
the complete band structure. The experiment will measure the photoelectron intensity
as a function of electron kinetic energy and exit angles I(Ekin, θ, ϕ). Out-of-plane
component of the wave vector kz depends on kinetic energy and angle θ.
• The whole three-dimensional band structure has to be measured by changing photon
energy in a range covering the whole Brillouin zone in kz.
• bulk band states have energy dispersion with changing photon energy. The surface
states are localized in z direction and do not disperse with kz. This effect can be used
to distinguish bulk and surface states.
Most of the above formulas were determined in the approximative three-step photoemission
model. The better description of ARPES is a one-step model calculation whole transition
process at once [82]. The final stage in the one-step model is a state combining free-electron
wave in a vacuum with a damped state in the material.
CHAPTER 3. EXPERIMENTAL METHODS 42
Figure 3.14: Superconducting magnet up to 9 T and cryostat down to 2 K made by Cryogenics
company. The instrument is located in the CEITEC Nano core facility and can provide
magnetic and transport measurements. The photo shows the setup with a vibrating sample
magnetometer (VSM).
A D
C
B
A D
CB
Figure 3.15: Schematics of four sample contacts in van der Pauw geometry. Left: ideal sample
shape, Right: the real case for rectangular sample. The contacts have to be in corners, not
inside the sample.
3.4 Electrical transport measurements
Transport measurements accompanied the structural analysis. In most cases, we have used
van der Pauw geometry with four contacts in the corners of the thin rectangular sample. The
sample resistivity and Hall conductivity are determined by measuring several current and
voltage contact commutations [83].
Let’s denote the resistance RAB,DC = VDC/IAB measured with current IAB flowing between
contacts A, B and voltage VDC measured between contacts D and C. From the sym-
CHAPTER 3. EXPERIMENTAL METHODS 43
metry it follows RAB,DC = RBA,CD = RDC,AB = RCD,BA. The sample resistivity can be
determined from two commutations using the van der Pauw formula
exp (−πRAB,DC/RS) + (−πRBC,AD/RS) = 1, RS =
ρ
t
, (3.45)
where RS is a sheet resistivity of the film, ρ resistivity of the sample and t sample (layer)
thickness. The Hall coefficient RH can be determined by measurement in the magnetic field
B perpendicular to the sample plane
RH =
RAC,DB + RBD,AC
2
t
B
. (3.46)
The average of two commutations will suppress the ohmic voltage contributions in case the
contacts are not exactly symmetric. The concentration of majority charge carriers can be
calculated as
n =
rH
e0RH
, (3.47)
where we have neglected the contribution of minority carriers, e0 is the elementary charge,
and rH is the Hall coefficient, usually close to 1.
The samples were measured in a Cryogenics device equipped with a closed-cycle helium
cryostat, superconducting magnet up to 9 T magnetic field, and temperature down to 2 K,
see figure 3.14. The contacts were made using conductive silver paste.
The ferromagnetic samples are known to have an anomalous Hall effect in addition to the
ordinary Hall effect. The simple (naive and incorrect) theory would attribute the anomalous
Hall effect to the magnetic field inside the sample as a sum of the external magnetic field and
magnetization. The detailed theory is quite complicated [84]. In explaining the Hall effect in
3d metal, one has to consider the contribution of 3d and 4s electrons close to the Fermi level.
Each of those bands has a different density of states and scattering rate, which also depends
on the material’s magnetic state, domain boundaries, and other properties. Thus, we did not
analyze the anomalous Hall effect in detail, and we only used its presence as a measure of
ferromagnetic order.
Chapter 4
Reprinted papers
The selected reprinted papers are divided into three groups: (i) papers describing properties
of Bi2Te3, Bi2Se3 and Bi2(SexTe1−x)3 topological insulator films (1 – 3), (ii) papers dealing
with magnetically doped topological insulators (4 – 7), and (iii) papers describing properties
of Bi-doped topological crystalline insulators (Pb,Sn)Se and (Pb,Sn)Te.
1. Growth, Structure, and Electronic Properties of Epitaxial Bismuth Telluride Topological
Insulator Films on BaF2 (111) Substrates,
O. Caha, A. Dubroka, J. Huml´ıˇcek, V. Hol´y, H. Steiner, M. Ul-Hassan, J. S´anchezBarriga,
O. Rader, T. N. Stanislavchuk, A. A. Sirenko, G. Bauer, and G. Springholz,
Crystal Growth and Design 13, 3365 (2013).
Share 40 %
author’s contribution XRD experiment and analysis, transport and thermoelectric
experiment, manuscript writing
The paper analyzes epitaxially grown bismuth telluride layers of stoichiometry Bi2Te3
and BiTe. The analysis is focused on structural analysis using the XRD technique. We
have studied the size of the domains, strain lattice parameters, and twinning of the
crystalline structure. Also, optical spectroscopy, Raman spectroscopy, transport, and
ARPES results are included. The structure of the epitaxial layer can be controlled via
the flux of particular compounds. The film grown using Bi2Te3 compound evaporation
cell only tends to reach the stoichiometry of BiTe. To grow Bi2Te3, an additional Te
flux is needed.
2. Structure and composition of bismuth telluride topological insulators grown by molecular
beam epitaxy,
H. Steiner, V. Volobuev, O. Caha, G. Bauer, G. Springholz, and V. Hol´y, J. Appl.
Crystallography 47, 1889 (2014).
Share 15 %
author’s contribution part of XRD experiment and analysis
The non-stoichiometric alloy layers of Bi2Te3−δ were grown with varying tellurium flux.
We have achieved stoichiometry within the range δ =0–1. The structure of thin films was
analyzed using x-ray diffraction. The diffraction pattern was described by a model of
random stacking of Bi2Te3 quintuple layer and Bi2 bilayer. The non-linear stoichiometry
dependence of the in-plane lattice parameter and average lattice spacing was determined.
44
CHAPTER 4. REPRINTED PAPERS 45
3. Interband absorption edge in the topological insulators Bi2(Te1−xSex)3,
A. Dubroka, O. Caha, M. Hronˇcek, P. Friˇs, M. Orlita, V. Hol´y, H. Steiner, G. Bauer,
G. Springholz, and J. Huml´ıˇcek, Phys. Rev. B 96, 235202 (2017).
Share 15 %
author’s contribution XRD experiment and analysis, contribution to manuscript writing
The Bi2(SexTe1−x)3 alloy layers were prepared using molecular beam epitaxy. The alloy
layers were studied using ellipsometry and reflectivity in the far-infrared to near-UV
range (0.06 eV to 6.5 eV) at low and room temperatures. The band gap of the layers was
determined, considering the Burstein-Moss shift in highly doped semiconductors. The
compositional of the band gap is non-linear with the maximum at about xSe = 30 %. The
alloy is a direct band gap semiconductor for higher selenium concentrations xSe > 30 %.
More tellurium-rich material xSe < 30 % has an indirect band gap with maxima of the
valence band slightly off Γ-point.
4. Non-magnetic band gap at the Dirac point of the magnetic topological insulator (Bi1−xMnx)2Se3,
J. S´anchez-Barriga, A. Varykhalov, G. Springholz, H. Steiner, R. Kirchschlager, G. Bauer,
O. Caha, E. Schierle, E. Weschke, A. A. Uenal, S. Valencia, M. Dunst, J. Braun,
H. Ebert, J. Minar, E. Golias, L. V. Yashina, A. Ney, V. Hol´y, and O. Rader, Nature
Communications 7, 10559 (2016).
Share 8 %
author’s contribution XRD experiment and analysis, contribution to ARPES
and XMCD measurements, contribution to manuscript writing
The (Bi,Mn)2Se3 layers on BaF2 were prepared and analyzed. The ARPES analysis
has shown a band gap in Dirac point to be large ≈ 100 meV, and temperature independent.
The ferromagnetic Curie temperature of about 10 K was determined by SQUID
magnetometry and XMCD. The magnetic easy axis direction is in-plane. The band gap
surviving up to room temperature is of non-magnetic origin.
5. Structural and electronic properties of manganese-doped Bi2Te3 epitaxial layers,
J. R˚uˇziˇcka, O. Caha, V. Hol´y, H. Steiner, V. Volobuiev, A. Ney, G. Bauer, T. Duchoˇn,
K. Veltrusk´a, I. Khalakhan, V. Matol´ın, E. F. Schwier, H. Iwasawa, K. Shimada, and
G. Springholz, New J. Phys. 17, 013028 (2015).
Share 20 %
author’s contribution XRD, X-ray absorption spectroscopy
manuscript writing
The magnetic alloy layers of (Bi,Mn)2Te3 were grown on BaF2. The manganese positions
were analyzed using x-ray absorption spectroscopy. The manganese positions
were identified as an octahedral interstitial in the van der Waals gap. The crystalline
structure is increasingly disordered with increasing manganese content. The ARPES
measurements lack sufficient resolution and low enough temperature to observe magnetic
band gap opening. However, we were unaware that Mn atoms occupy the septuple
layers MnBi2Te4 at the time of publication. The structural analysis interpretation is
not entirely correct.
6. Large magnetic gap at the Dirac point in Bi2Te3/MnBi2Te4 heterostructures,
E. D. L. Rienks, S. Wimmer, J. S´anchez-Barriga, O. Caha, P. S. Mandal, J. R˚uˇziˇcka,
CHAPTER 4. REPRINTED PAPERS 46
A. Ney, H. Steiner, V. V. Volobuev, H. Groiss, M. Albu, G. Kothleitner, J. Michaliˇcka,
S. A. Khan, J. Min´ar, H. Ebert, G. Bauer, F. Freyse, A. Varykhalov, O. Rader, and
G. Springholz, Nature 576, 423 (2019).
Share 12 %
author’s contribution XRD experiment and analysis, x-ray absorption spectroscopy,
transport measurement, preparation of some TEM samples,
contribution to manuscript writing.
The Mn-doped samples were grown and analyzed using magnetic measurements, XRD,
XAFS, HRTEM, and other methods. The structure was composed of random stacking
of Bi2Te3 quintuple layers and MnBi2Te4 septuple layers. The concentration of septuple
layers increases with manganese doping. The Curie temperature was found to be approximately
20 K, and the magnetization easy-axis is out-of-plane. The low-temperature
ARPES and spin-resolved ARPES experiments have shown a band gap opening in the
Dirac point with a size of 90 meV. The temperature dependence of the band gap size
correlates with remanence magnetization. The paper presented the first direct observation
of a magnetic band gap in the topological surface state. Bismuth selenide, on
the contrary, does not show a magnetic band gap since its magnetization easy-axis is
in-plane.
7. Mn-Rich MnSb2Te4: A Topological Insulator with Magnetic Gap Closing at High Curie
Temperatures of 45–50 K,
S. Wimmer, J. S´anchez-Barriga, P. Kuppers, A. Ney, E. Schierle, F. Freyse, O. Caha,
J. Michaliˇcka, M. Liebmann, D. Primetzhofer, M. Hoffman, A. Ernst, M. M. Otrokov,
G. Bihlmayer, E. Weschke, B. Lake, E. V. Chulkov, M. Morgenstern, G. Bauer, G. Springholz,
and O. Rader, Advanced Materials 2021, 2102935 (2021).
Share 8 %
author’s contribution XRD experiment and analysis, x-ray absorption spectroscopy
transport measurement, preparation of TEM samples,
and contribution to TEM analysis and manuscript writing.
The layers of MnSb2Te4 with a slight excess of Mn were studied. We have found the
concentration of Mn in the substitutional and central septuple layer positions. The
magnetic Currie temperature is relatively high for a magnetic topological insulator,
almost 50 K. Contrary to bismuth selenide and bismuth telluride, antimony telluride is
p-doped. Thus photoemission study of the band gap. Instead, we have used scanning
tunneling spectroscopy to show magnetic band gap opening correlating with magnetic
order.
8. Topological quantum phase transition from mirror to time reversal symmetry protected
topological insulator,
P. S. Mandal, G. Springholz, V. V. Volobuev, O. Caha, A. Varykhalov, E. Golias,
G. Bauer, O. Rader, and J. S´anchez-Barriga, Nature Communications 8, 968 (2017).
Share 10 %
author’s contribution XRD experiment and analysis
contribution to ARPES experiments,
contribution to manuscript writing.
CHAPTER 4. REPRINTED PAPERS 47
This paper deals with (Pb,Sn)Se topological crystalline insulator. Topological crystalline
insulators are merely protected by individual crystal symmetries and exist for
an even number of Dirac cones. We demonstrated that Bi-doping of (Pb,Sn)Se (111)
epilayers induces a quantum phase transition from a topological crystalline insulator to
a Z2 topological insulator. The transition occurs because Bi-doping lifts the fourfold
valley degeneracy and induces a gap at Γ, while the three Dirac cones at the ¯M points
of the surface Brillouin zone remain intact. We interpret this new phase transition
as caused by a lattice distortion. Our findings extend the topological phase diagram
enormously and make strong topological insulators switchable by distortions or electric
fields.
9. Giant Rashba Splitting in Pb1−xSnxTe (111) Topological Crystalline Insulator Films
Controlled by Bi-Doping in the Bulk,
V. V. Volobuev, P. S. Mandal, M. Galicka, O. Caha, J. S´anchez-Barriga, D. Di Sante,
A. Varykhalov, A. Khiar, S. Picozzi, G. Bauer, P. Kacman, R. Buczko, O. Rader, and
G. Springholz, Advanced Materials 29, 1604185 (2017).
Share 10 %
author’s contribution XRD experiment and analysis,
contribution to ARPES experiment,
contribution to manuscript writing.
The topological properties of lead-tin chalcogenide topological crystalline insulators can
be tuned by temperature and composition. We have shown that bulk Bi doping of
epitaxial (Pb,Sn)Te (111) films induce a giant Rashba splitting at the surface that the
doping level can tune. Tight binding calculations identify their origin as Fermi-level
pinning by trap states at the surface.
CHAPTER 4. REPRINTED PAPERS 48
4.1 Properties of thin films of topological insulators Bi2Te3
and BiTe
The paper analyzes epitaxially grown bismuth telluride layers of stoichiometry Bi2Te3 and
BiTe. The analysis is focused on structural analysis using the XRD technique. We have
studied the size of the domains, strain lattice parameters, and twinning of the crystalline
structure. Also, optical spectroscopy, Raman spectroscopy, transport, and ARPES results
are included. The structure of the epitaxial layer can be controlled via the flux of particular
compounds. The film grown using Bi2Te3 compound evaporation cell only tends to reach the
stoichiometry of BiTe. To grow Bi2Te3, an additional Te flux is needed.
Growth, Structure, and Electronic Properties of Epitaxial Bismuth
Telluride Topological Insulator Films on BaF2 (111) Substrates
O. Caha,†
A. Dubroka,†
J. Humlíček,†
V. Holý,‡
H. Steiner,§
M. Ul-Hassan,§
J. Sánchez-Barriga,∥
O. Rader,∥
T. N. Stanislavchuk,⊥
A. A. Sirenko,⊥
G. Bauer,§
and G. Springholz*,§
†
Department of Condensed Matter Physics and CEITEC, Masaryk University, Kotlářská 2, 61137 Brno, Czech Republic
‡
Department of Electronic Structures, Charles University, Praha, Czech Republic
§
Institut für Halbleiter- und Festkörperphysik, Johannes Kepler Universität, Altenbergerstrasse 69, 4040 Linz, Austria
∥
Helmholtz-Zentrum Berlin für Materialien und Energie, Elektronenspeicherring BESSY II, Albert-Einstein-Straße 15, 12489 Berlin,
Germany
⊥
Department of Physics, New Jersey Institute of Technology, Newark, New Jersey 07102, United States
*S Supporting Information
ABSTRACT: Epitaxial growth of topological insulator
bismuth telluride by molecular beam epitaxy onto BaF2
(111) substrates is studied using Bi2Te3 and Te as source
materials. By changing the beam flux composition, different
stoichiometric phases are obtained, resulting in high quality
Bi2Te3 and Bi1Te1 epilayers as shown by Raman spectroscopy
and high-resolution X-ray diffraction. From X-ray reciprocal
space mapping, the residual strain, as well as size of coherently
scattering domains are deduced. The Raman modes for the
two different phases are identified and the dielectric functions
derived from spectroscopic ellipsometry investigations.
Angular resolved photoemission reveals topologically protected
surface states of the Bi2Te3 epilayers. Thus, BaF2 is a
perfectly suited substrate material for the bismuth telluride compounds.
■ INTRODUCTION
Recent discovery of a new class of materials, called topological
insulators, has opened up a whole new research arena.1−5
Topological insulators behave in the bulk like ordinary
insulators but support in addition a conducting two-dimensional
topological surface state with linear energy-momentum
dispersion shaped like a Dirac cone.2,6,7
Because of strong
spin−orbit coupling, the electron momentum in these surface
states is locked to the spin orientation and spin-flip scattering is
prohibited by time reversal symmetry.1,8
As a result, spin
polarized currents can be produced without the needs of
external magnetic fields, which offers great advantages for
spintronic or quantum computation applications.1,5,9
The
helical spin structure of the topological surface states also
provides a basis for fundamental new physics such as magnetic
monopoles and Majorana fermions.1,2
Among the new materials exhibiting three-dimensional
topological insulating properties, the bismuth chalcogenides
Bi2Te3 and Bi2Se3 have attracted most attention because a
single Dirac cone is formed at the Γ-point of the Brillouin zone
within the bulk band gap, as has been revealed by angular
resolved photoemission6,7
and scanning tunneling spectroscopy
studies.10,11
Bi2Te3 is also a superior thermoelectric material for
energy harvesting applications, since it exhibits the highest
thermoelectric figure of merit at room temperature among all
bulk materials.12,13
Up to now, most studies of the topological
properties of Bi2Te3 have been performed on bulk single
crystals cleaved under ultrahigh vacuum conditions.3,7,14
For
practical device applications, however, epitaxial layers are
desired15
for monolithic integration in multilayers and gated
heterostructures that would allow tuning of the Fermi level to
the Dirac point and control spin polarized currents in
devices.15,16
Considerable efforts have been made to grow
Bi2Te3 epitaxially on substrates like Si17−21
or GaAs,22−26
which, however, exhibit a very large lattice mismatch of up to
14% to Bi2Te3.
Bismuth telluride can crystallize in several different crystal
structures in dependence of its stoichiometric composition. The
crystal structure of the most common Bi2Te3 phase consists of
of three Te1
−Bi−Te2
−Bi−Te1
quintuplet layers (QL) as
fundamental building block (see Figure 1a). These are stacked
on top of each other in an ABCABC stacking sequence. In
addition, several alternative phases with lower Te concentration
exist, including Bi1Te1 (called tsumoite), as well as Bi3Te4 and
Received: January 9, 2013
Revised: May 15, 2013
Published: July 12, 2013
Article
pubs.acs.org/crystal
© 2013 American Chemical Society 3365 dx.doi.org/10.1021/cg400048g | Cryst. Growth Des. 2013, 13, 3365−3373
Reprinted page 1 of paper [46] “Structure and properties of Bi2Te3 and BiTe thin films”.
Bi4Te3 (pilsenite) among others.27
The different phases share
the same hexagonal structure of R3̅m space group symmetry,
but show a different stacking of the Bi and Te layers.28,29
The
Bi1Te1 structure, depicted in Figure 1b, consists of twelve
atomic Te1
−Bi1
−Te2
−Bi2
−Te3
−Bi3
−Bi3
−Te3
−Bi2
−Te2
−Bi1
−
Te1
lattice planes30
that can be split into two mirrored hextuple
layers (HL). The unit cells of Bi4Te3 and Bi3Te4 consist even of
21 lattice planes grouped in three blocks of septuplet layers,
comprising each of seven lattice planes. While Bi2Te3 has been
intensely studied over the past few years, the properties of the
other phases have remained rather unexplored. In particular,
BiTe has been available only in the form of bulk crystals30
or
polycrystalline films,31
that is, to the best of our knowledge no
work on epitaxial BiTe layers has been published so far.
In the present work, we report on molecular beam epitaxy
(MBE) of single phase Bi2Te3 and BiTe epilayers and we
provide detailed insight in their structural and electronic
properties. Contrary to most previous studies, epitaxial growth
is carried out on BaF2 (111) substrates,32
which exhibit an
almost perfect matching of the in-plane lattice constant to those
of the bismuth telluride compounds (see Table 1). In fact, the
lattice-misfit to Bi2Te3 of Δa||/a = 0.04% is particularly small,
that is, BaF2 is practically lattice-matched. BaF2 also features
several additional advantages. First of all, BaF2 is highly
insulating and optically transparent, which is favorable for
transport measurements and optical spectroscopy. Second,
because of the perfect (111) orientation, cleaved BaF2
substrates are virtually step free over tens of square micrometer
surface areas, contrary to the usual miscut steps with spacing
smaller than 100 nm present on standard Si or GaAs substrate
surfaces. As the lattice plane stacking and the height of these
steps differs from those of the bismuth tellurides, these steps act
as sources for stacking faults and antiphase domain boundaries
in epilayers. BaF2 also shows a better matching of the in-plane
thermal expansion coefficient of 18.7 × 10−6
K−1
to that of
Bi2Te3 of 14 × 10−6
K−1
at 300 K33
compared to Si (2.6 × 10−6
K−1
) or GaAs (5.73 × 10−6
K−1
). As shown in this work, this
leads to rather low values of thermal stress within the epilayers.
The thermal expansion coefficient of bulk BiTe has not been
reported so far, but one can assume that it is similar to that of
Bi2Te3.
In terms of growth, we show that by tuning of the beam flux
composition, that is, the tellurium to bismuth flux ratio, single
phase Bi2Te3 and BiTe epilayers are obtained. Their excellent
structural perfection is demonstrated by high resolution X-ray
diffraction and the optimum growth conditions for the different
phases are derived. Quantitative evaluation of reciprocal space
maps yields the strain as well as size of coherently scattering
domains and by Raman scattering the active phonons in both
compounds are identified. Raman experiments carried out in
backscattering geometry from the surface as well as from the
layer/substrate interface show that the entire epilayers are
single phase even for thicknesses as large as 830 nm. By infrared
and far-infrared spectroscopy we determine the plasma
frequencies and thus, the free carrier concentrations of the
Figure 1. Hexagonal unit cell of (a) Bi2Te3 and (b) BiTe with the base
vectors indicated by the black arrows. For Bi2Te3, the unit cell consist
of 15 atomic lattice planes that are grouped in three quintuple layers
(QL) with Te1
−Bi−Te2
−Bi−Te1
stacking. The quintuple layers are
van der Waals bonded to each other by a Te−Te double layer (van der
Waals gap). For BiTe, the unit cell consists of 12 atomic lattice planes
with Te1
−Bi1
−Te2
−Bi2
−Te3
−Bi3
−Bi3
−Te3
−Bi2
−Te2
−Bi1
−Te1
stacking
sequence that can be split in two hextuple layer (HL) blocks. The
green arrows indicate an alternative definition of the crystal structure
using rhombohedral base vectors. The lattice parameters of Bi2Te3 and
BiTe are listed in Table 1.
Table 1. Structural Properties of the BiTe and Bi2Te3 Epilayers Grown on BaF2 (111) Substrates Determined by X-ray
Reciprocal Space Mapping Compared to Results for Bulk Materials Reported in Literaturea
composition sample d (nm) a (Å) c (Å) RL (nm) RV (nm) Δϕ (deg)
Bi2Te3-epilayers M2780 830 4.3804 30.53 6000 200 0.08
M2704 250 4.382 30.51 1300 80 0.05
Bi2Te3-bulk ref 34 4.3835 30.487
ref 35 4.386 30.497
ref 36 4.3852 30.483
BiTe-epilayers M2777 400 4.402 24.202 200 40 0.18
M2732 250 4.400 24.229 100 40 0.2
BiTe-bulk ref 30 4.423 24.002
ref 37 4.422 24.052
ref 38 4.40 23.97
BaF2 (111) ref 39 4.384 10.739
a
Also listed are the in- and out-of-plane lattice constant of the (111) BaF2 substrates, with cubic lattice constants of a0 = 6.200 Å. The average lateral
and vertical mosaic block sizes RL,V and the root mean square angular lattice misorientation Δϕ of the epilayers were obtained from Figure 4.
Crystal Growth & Design Article
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layers. By angular resolved photoemission, the surface band
structure of the Bi2Te3 epilayers is established, showing a wellresolved
Dirac cone with pronounced hexagonal warping. Thus,
these layers are very well suited for further studies of the
topological properties of this material.
■ EXPERIMENTAL SECTION
Bismuth telluride epilayers were grown by molecular beam epitaxy in a
Riber 1000 system under ultrahigh vacuum conditions at a background
pressure of 5 × 10−10
mbar. The molecular beams were generated
using a compound bismuth telluride effusion cell (nominal
composition of Bi2Te3) operated at around 500 °C, and a separate
tellurium cell operated at 280−330 °C for stoichiometry control. The
flux rates were 1−2 Å/s for bismuth telluride and 0−2 Å/s for excess
tellurium, which was controlled by a quartz crystal microbalance. The
layers were deposited on cleaved BaF2 (111) substrates at substrate
temperatures between 300−400 °C measured with an infrared optical
pyrometer. The surface structure of the films was monitored by in situ
reflection high-energy electron diffraction as well as atomic force
microscopy (AFM). X-ray diffraction experiments were performed
using a high-resolution X-ray diffractometer equipped with a Cu tube,
parabolic mirror and four-bounce Ge (220) Bartels monochromator
on the primary side, and a channel-cut Ge (220) analyzer on the
secondary side. Unpolarized Raman spectra were acquired with a
Renishaw InVia spectrometer at room temperature in backscattering
geometry. The exciting beam of a 632.8 nm HeNe laser was focused
either on the front side surface or backside of the films through the
transparent BaF2 substrate. The spot size was about 2 μm and the laser
power was low enough to avoid local heating.
The optical properties were determined by ellipsometric measurements
using a home-built ellipsometer attached to a Bruker IFS55
EQUINOX mid-infrared Fourier spectrometer. In the near-infrared,
visible, and ultraviolet range, ellipsometric spectra were acquired with a
Woollam M-2000 and Jobin Yvon UVISEL ellipsometer. This was
complemented by reflectance measurements in the 0.01−0.2 eV range
using a Bruker IFS 66v/S spectrometer as well as far-infrared
ellipsometric measurements at the NSLS synchrotron light source in
Brookhaven. The Hall conductivity was determined by van der Pauw
measurements. The electronic structure was determined by angle
resolved photoemission spectroscopy (ARPES) at the UE112-PGM2a
beamline of BESSY II, Berlin using a Scienta R8000 electron analyzer
and linearly polarized light with 21 eV photon energy. For these
measurements, the epilayers were protected after growth by a Te
capping layer deposited in the MBE system. This layer was desorbed in
the ultrahigh vacuum ARPES chamber just before the photoemission
experiments.
■ RESULTS AND DISCUSSION
Molecular Beam Epitaxy. Epitaxial growth of bismuth
telluride onto (111) BaF2 substrates proceeds in a 2D growth
mode at substrate temperatures above 300 °C independent of
the beam flux composition, i.e., independent of the excess Te
flux. This is evidenced by the streaked RHEED diffraction
patterns observed during growth presented in Figure 2 for two
samples grown with a Te flux of (a) 2 and (b) 0 Å/s,
respectively. At substrate temperatures below 300 °C, a
significant roughening of the surface due to limited surface
diffusion occurs. For high excess Te flux greater than 2 Å/s,
which is a factor of 2 larger compared to the bismuth telluride
flux, the stoichiometric composition of the epilayers corresponds
to Bi2Te3 as proven by the X-ray analysis described
below. Without or with only very small excess Te flux, the Te
content of the epilayers is reduced such that more Bi rich
epilayers are formed with a stoichiometry close to the Bi1Te1
phase. For both types of samples, atomic force microscopy
measurements reveal smooth, that is, atomically flat surfaces as
shown by Figure 2c and d, respectively. On the Bi2Te3 layers,
surface steps of predominantly one quintuple unit thickness,
that is, 10.1 Å height, are found, meaning that the surface is
tellurium terminated at the van der Waals gaps, in agreement
with previous studies.40
For the BiTe layers, a broader variation
of step heights from 4 Å corresponding to single BiTe bilayers,
up to 24 Å equivalent to the 12 atomic layers of the hexagonal
unit cell are observed. This arises from the fact that the unit cell
of BiTe includes only one weakly bonded van der Waals Te−
Te double layer (DL), that is repeated only every 12 atomic
lattice planes (see Figure 1b). On a 10 μm length scale, the
root-mean-square roughness of the epilayers is less than a few
nm in both cases.
Apart from single phase Bi2Te3 and BiTe layers obtained
with high, respectively, low excess Te flux, epilayers with mixed
bismuth telluride phases are formed at intermediate Te flux
rates. These layers show multiple X-ray diffraction peaks arising
from several bismuth telluride phases and were not considered
for further analysis. The RHEED patterns of these layers,
however, are almost indistinguishable from those of the single
phase layers as the different bismuth telluride phases differ only
in their Bi−Te layer stacking sequence, whereas the overall
hexagonal in-plane lattice structure and lattice constant is nearly
preserved.27
The AFM images of such layers exhibit a broader
range of step heights because of the variation of the vertical
lattice plane stacking of the different regions. This indicates that
the coexistence of the different phases is mainly accommodated
by stacking faults in the layers. In order to study and compare
in detail the structural and electronic properties of the two main
bismuth telluride phases, only single phase epilayers consisting
of pure BiTe and Bi2Te3 were employed for further analysis.
The corresponding sample parameters are indicated in Table 1
and the layer thicknesses ranged from 250 to 830 nm.
Structure Analysis. The crystal structures of the bismuth
tellurides with the R3̅m space group can be described by two
Figure 2. Reflection high-energy electron diffraction patterns observed
in situ during molecular beam epitaxy of (a) Bi2Te3 and (b) Bi1Te1
along the [11̅00] azimuth direction. Corresponding atomic force
microscopy surface images of 400 nm thick epilayers are shown in
panels c and d, respectively. The growth conditions differ only in the
excess Te flux supplied during growth of 2 and 0 Å/s for panels a and c
and panels b and d, respectively. The substrate temperature was 350
°C.
Crystal Growth & Design Article
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Reprinted page 3 of paper [46] “Structure and properties of Bi2Te3 and BiTe thin films”.
equivalent definitions of the base vectors in rhombohedral or
hexagonal axes, as indicated by the black and green arrows in
Figure 1, respectively. In this paper, we use the hexagonal
definition of the base vectors a and c perpendicular,
respectively, parallel to the hexagonally ordered atomic
(Te,Bi) planes, where the c-axis is equivalent to the [0001]
hexagonal or [111] rhombohedral direction. As illustrated by
Figure 1, the structures of Bi2Te3 and BiTe mainly differ by
their different stacking sequence. For Bi2Te3, the hexagonal unit
cell consists of three quintuple layers, that is, five atomic Te1
−
Bi−Te2
−Bi−Te2
planes stacked on top of each other,
corresponding in total to 15 lattice planes per unit cell. The
quintuple layers are weakly bonded together by van der Waals
forces between the Te−Te double layer, for which the lattice
plane spacing is increased by ∼36% compared to the average
value of 2.032 Å = c/15. The unit cell of BiTe consists of a
single block of twelve atomic planes with Te1
−Bi1
−Te2
−Bi2
−
Te3
−Bi3
−Bi3
−Te3
−Bi2
−Te2
−Bi1
−Te1
stacking sequence.30
As
shown by Figure 1, it contains only one weakly bonded Te−Te
van der Waals double layer, but an additional metallic Bi−Bi
double layer in the middle of the cell that joins together two
hextuplet layers with inverse stacking sequence. The nominal
lattice parameters of Bi2Te3 are a = 4.384 Å and c = 30.487
Å,34−36
and for BiTe, they are around 4.423 and 24.002 Å with
some variation in literature30,37,38
(see Table 1). Thus, the inplane
atomic distances in BiTe are slightly larger and the
average vertical lattice-plane spacing slightly smaller compared
to Bi2Te3. For both compounds, the in-plane hexagonal lattice
parameter a fits well to the in-plane lattice constant a∥ = 4.384
Å = a0/√2 of (111) BaF2 substrates. In fact, Bi2Te3 is
practically lattice matched to BaF2 with a lattice misfit Δa∥/a <
0.04%. For BiTe, the lattice-mismatch is somewhat larger, but it
is still less than 0.9%, depending on the used bulk lattice
parameter.
Phase analysis of the samples was assessed using X-ray
diffraction along the symmetric truncation rod perpendicular to
the epilayer surface. The resulting diffraction curves of Bi2Te3
and BiTe epilayers are presented in Figure 3 in red and blue
color, respectively. Evidently, the layers show only the (000l)
Bragg peaks of Bi2Te3 and BiTe as indicated by the vertical red
and blue lines. Thus, the layers grow in c-axis orientation on the
BaF2 substrates for which the (111) and (222) peaks are
indicated by the black dotted lines. For Bi2Te3, because of the
3-fold quintuple layer stacking, only the Bragg peaks with l = 3,
6, 9, 12, ... appear in the diffraction spectra, whereas no such
simple selection rule exists for BiTe due to its twelve atomic
layer stacking. As indicated by the crosses and triangles, for
both samples the positions and intensities of the diffraction
peaks correspond very well to the calculated values, and no
other secondary phases are observed. This demonstrates that by
appropriate choice of the MBE growth conditions single phase
epilayers can be obtained.
Detailed structural information of the epilayers were derived
by X-ray diffraction reciprocal-space mapping.41
In this
technique, the diffusely scattered intensity is measured as a
function of the scattering vector Q = Kfinal − Kincident in the
vicinity of various reciprocal-lattice vectors h (diffraction
vector). For a structurally perfect layer, the reciprocal-space
map (RSM) consists of a narrow vertical rod of lateral width
ΔQx determined only by the experimental resolution. Its width
along Qz is inversely proportional to the layer thickness d
according to ΔQz ≈ 2π/d. On the contrary, a layer with
structural defects produces a broader RSM maximum, the shape
of which depends on the nature and density of defects whereas
its position depends on the composition and strain state of the
layer.
For all samples, reciprocal space maps were recorded around
the symmetric and asymmetric reciprocal lattice points (RLP)
hsym = (00012) and hasym = (11̅016) for BiTe and hsym =
(00015) and hasym = (11̅020) for Bi2Te3. The results are
presented in Figure 4a−d, respectively. For the two phases, the
chosen RLPs are approximately at the same positions in
Figure 3. Symmetric X-ray diffraction scans along qz perpendicular to
the surface of Bi2Te3 (red line, sample M2780) and BiTe (blue line,
sample M2777) epilayers grown on BaF2 (111) substrates. The vertical
lines denote the calculated (hkl) Bragg positions of the layer and
substrate peaks, and the crosses and diamonds the intensity, that is,
structure factors computed for the Bi2Te3, respectively, BiTe lattice
structures shown in Figure 1. The sample parameters are listed in
Table 1.
Figure 4. Reciprocal space maps of the 400 nm BiTe epilayer M2777
(top) and 800 nm Bi2Te3 epilayer M2780 (bottom) on BaF2 (111),
measured around the symmetric (00012) (a) and (00015) (c) as well
as asymmetric (11̅016) (b) and (11̅020) (d) reciprocal lattice points.
The simulation of the measured intensity distributions using a mosaicblock
model is represented by the black contour lines and the resulting
structure parameters are listed in Table 1.
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reciprocal space, which allows a direct comparison of the
scattered intensity distributions. Evidently the intensity
distribution is considerably broader for the BiTe compared to
the Bi2Te3 epilayer, but in both cases the widths are larger than
for a perfect epilayer. For the BiTe layer (upper part of Figure
4) the vertical and lateral full width at half-maximum (fwhm) is
ΔQx = 0.1299 nm−1
and ΔQz = 0.0823 nm−1
, respectively, and
for the Bi2Te3 layer (lower part of Figure 4) ΔQx = 0.0328
nm−1
and ΔQz = 0.0397 nm−1
. To account for this broadening,
the defect structure was approximated by a mosaic model in
which the layers consist of randomly placed and randomly
rotated coherent domains (mosaic blocks).41,42
For simulation
of the reciprocal space maps, the coherent domains are
assumed as uniaxial ellipsoids with mean lateral and vertical
radii RL and RV, respectively, and root-mean square (rms)
angular lattice misorientations Δϕ. The domain size is random
and the radii are distributed according to the Gamma
distribution with order mR, so that the rms deviations of the
radii are σL,R = RL,V/√mR.
The calculated reciprocal space maps for both samples are
represented as solid iso-intensity contour lines in Figure 4 that
are superimposed on the measured data and the best fit
structure parameters are listed in Table 1. Evidently, the
simulations are in nice agreement with both the symmetric and
asymmetric RSMs for both phases. For the BiTe layer, the
mosaic block parameters are derived as RL = (200 ± 10) nm, RV
= (40 ± 5) nm, and Δϕ = (0.18 ± 0.02)°. The simulations are
not much sensitive to the order mR in the range between 5 and
20. We have performed a similar analysis also on the thinner d
= 250 nm BiTe layer and the resulting parameters are RL =
(100 ± 10) nm, RV = (40 ± 5) nm, and Δϕ = (0.20 ± 0.02)° as
listed in Table 1. The values are very similar for both samples
except for the lateral size of coherent domains, which in both
cases roughly equals half of the layer thickness, whereas the
lattice misorientations Δϕ and vertical coherent domain size RV
are independent of thickness. From the fit of the diffraction
maxima, we obtain the BiTe lattice parameters as a = (4.401 ±
0.002) Å and c = (24.21 ± 0.01) Å, which are identical for both
samples within the experimental precision. The lattice
parameters differ somewhat from the bulk values listed in
Table 1. This may arise from a residual epitaxial strain in the
epilayers due to the nominal 0.9% mismatch to the BaF2
substrate. However, given the uncertainty in the bulk lattice
parameters, this could also be due to a deviation from the exact
stoichiometric composition that also influences the lattice
parameters.29
The same analysis was performed for the Bi2Te3 samples.
The resulting fit of the symmetric and asymmetric RSMs are
displayed in Figure 4c and d, which yields a mean vertical and
lateral radius of coherent domains of RV = (100 ± 30) nm and
RL ≈ (6000 ± 200)nm, where the latter exceeds the ∼1 μm
coherence width of the primary X-ray beam. The rms domain
misorientation of Δϕ = (0.08 ± 0.02)° is significantly smaller
than for the BiTe epilayers, and the same result was also found
for the thinner 250 nm Bi2Te3 layer (see Table 1) with domain
radii of RL = (130 ± 50) nm and RV = (80 ± 30) nm and an
rms misorientation of Δϕ = (0.05 ± 0.03)°. This evidences a
higher structural perfection of the Bi2Te3 layers resulting from
the almost perfect lattice matching to the BaF2 substrates.
Similar results were recently obtained for Bi2Se3,43,44
where a
significant improvement of the structural quality was found for
growth on nearly lattice matched InP (111) substrates
compared to Si (111).
From the fit of the RSMs, the lattice parameters of the Bi2Te3
epilayers were determined as a = (4.380 ± 0.001) Å and c =
(30.53 ± 0.01) Å, which are identical to the bulk values (see
Table 1) with a deviation of less than −0.08%, respectively,
+0.14%. Essentially the same was also obtained for the thinner
epilayer. Considering the bulk lattice constant of a = 4.3835 Å
reported by Wyckoff,34
a minute residual in-plane strain of
−0.08% is inferred in the epilayers, corresponding to an inplane
stress of ∼40 MPa using the elastic coefficients of Jenkins
et al.45
The ratio between the in-plane and out-of-plane strain
values also agrees with the reported Poisson’s ratio of Bi2Te3.45
It is noted that the residual strain has actually the opposite sign
of the +0.04% layer/substrate lattice mismatch. This can be
explained by the thermal expansion coefficient mismatch
between BaF2 and Bi2Te3 of 18.7 × 10−6
K−1
versus 14 ×
10−6
K−1
, which induces a small compressive in-plane strain of
−0.15% in the layers upon cooling from 350 °C to room
temperature after growth. For thin Bi2Te3 epilayers on Si (111)
a significantly larger out-of-plane strain value of −1% was
recently reported.21
The epitaxial relationship of the samples was determined by
azimuthal scans at the asymmetric (11̅016) and (11̅020)
reciprocal lattice points of Bi2Te3, respectively, BiTe, where the
samples were rotated around the surface normal vector at fixed
X-ray incidence and exit angles. The results are displayed in
Figure 5, where the azimuth angle ϕ is measured relative to the
[112̅] surface direction of the (111) BaF2 substrate. Evidently,
for both samples the main layer peaks denoted by “A” appear at
azimuths angles ϕ = 0°, 120°, 240°, and 360°, indicating that
the [11̅00] direction of the hexagonal layer lattice is parallel to
the [112̅] substrate direction. The appearance of equivalent
peaks in azimuth directions differing by 120° is in agreement
with the 3-fold R3̅m symmetry of the BiTe and Bi2Te3 lattice
structures. However, the azimuthal scans also show weak
additional secondary peaks denoted by “B” at azimuthal
positions of 60°, 180° and 300°, indicating the presence of a
small number of twinned domains for which the [11̅00]
Figure 5. Azimuthal diffraction scans in the asymmetric diffraction
maxima at h = (11̅020) for the Bi2Te3 epilayer (upper curve) and at h
= (11̅016) for the BiTe layer (lower curve) on BaF2 (111) substrates.
The azimuthal angle φ is measured relative to the in-plane [112̅]
substrate direction. The major peaks in the positions ϕ = 0°, 120°, and
240° denoted by “A” correspond to the 3-fold symmetry along the caxis
with alignment of the [11̅00] crystallographic direction of the layer
to the [112̅] direction of the BaF2 substrate. The hundred times
weaker secondary peaks at the intermediate azimuthal directions
denoted by “B”, correspond to twinned domains rotated by 180°.
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direction is antiparallel to the [112̅] substrate direction, that is,
the domain lattice is rotated by 180°. Reciprocal space maps
measured in the vicinity of the secondary domain peaks show
that the peak widths do not differ from those of the untwinned
domains, i.e., the coherent size and rms misorientation is the
same as that of the untwinned ones. Moreover, the intensity
ratio of the twinned peaks does not show any dependence on
the epilayer thickness. This indicates that the formation of the
secondary twin domains occurs already in the early nucleation
stage of growth. Since the intensity of the twinned domain
peaks is only about 1/100 of the untwined ones, the probability
of twin formation on BaF2 (111) is very low for both Bi2Te3
and BiTe epilayers, which is contrary to the growth on Si (111)
where a much higher twinning ratio was reported.19
This is
another indication for the superior quality of our layers.
Raman Scattering. For further assessment of the layer
properties, Raman spectra were measured in the backscattering
geometry both from the front side as well as back side of the
layers through the transparent BaF2 substrate. The penetration
depth of the exciting 632.8 nm HeNe laser light was obtained
from ellipsometric measurements and amounts to about 28 nm
for Bi2Te3 and 25 nm for BiTe. The back side and front side
Raman spectra of the 830 nm Bi2Te3 epilayer are shown in
Figure 6a and b, respectively. Very similar spectra were
measured at different spots of the sample as well as on the
layer with smaller thickness. The Raman spectra show three
strong bands, corresponding to the normal modes of A and E
symmetry.46
The peaks were fitted by convolution of Gaussian
and Lorentzian lineshapes represented by the dashed lines in
Figure 6a using an additional weak linear background.
Evidently, the model spectra are in excellent agreement with
the measured spectra, that is, the difference between the
experimental and fitted spectra (open squares in Figure 6a) is
very small and indicates only a slight asymmetry of the bands.
The frequencies and widths (fwhm) of the two Ag and one Eg
vibrations of Bi2Te3 obtained from the fits of several
independent measurements on different position and samples
are listed in Table 2, together with literature values, correcting
for the 1.5 cm−1
-wide Gaussian profile of our instrument. The
small fwhm values confirm the excellent quality of our epilayers.
Identical Raman spectra, i.e., peak positions and fwhm values
were obtained from the front side and back side of the layers
(see Table 2 and Figure 6b and a). This demonstrates that the
epilayers are highly uniform in strain and composition both in
the lateral as well as vertical direction and that the lattice
perfection is already very high at the layer/substrate interface.
This is a clear indication for pseudomorphic growth because of
the near-perfect substrate lattice-matching. The only minor
difference is the appearance of very weak additional bands in
the front side Raman spectra, such as those labeled by arrows in
Figure 6b, which we attribute to surface degradation in humid
air and are not present in the Raman spectra collected from the
backside from the layer/substrate interface. Detailed studies on
the oxidation process of Bi2Te3 and Bi2Se3 have been presented
elsewhere.49
Raman measurements were also performed for the BiTe
epilayers and the result is shown in Figure 6b by the open
circles. All BiTe samples exhibit six pronounced bands above 50
cm−1
, with slightly larger widths when excited through the
substrate side. The latter is a signature of the less good lattice
matching to the substrate in this case. Table 3 lists the
frequencies and widths obtained from the fit of the Raman
spectra, together with the only reported literature data obtained
from a polycrystalline BiTe film grown by pulsed laser
deposition (PLD) on silicon substrate.31
Since 12 different
Raman−active bands are expected for the rather complex BiTe
structure31
in a fairly narrow frequency interval, the relatively
small widths of the Raman peaks of our samples (see Table 3)
confirm the high quality of the layers found by our x−ray
studies. The additional weak features at 72 and 75 cm−1
of
variable strength in the spectrum from the film surface (arrows
in Figure 6b) are again attributed to surface oxidization.
Figure 6. (a) Backside Raman spectrum (full squares) of the 830 nm
Bi2Te3 epilayer measured through the transparent BaF2 substrate from
the Bi2Te3/BaF2 interface. The dashed lines represent the
deconvolution of the spectrum by the sum of three Gauss-Lorentzians
and a linear background. The difference between measured and model
spectra is represented by the open squares. (b)Front side Raman
spectra of the Bi2Te3 (squares) and the 400 nm BiTe (open circles)
epilayer. The dashed lines represent the model fits and the detected
peak positions are labeled by the red and black numbers in units of
cm−1
. The weak Raman bands highlighted by the arrows are attributed
to surface oxidation.
Table 2. Measured Raman Frequencies and Widths (fwhm)
of the Bi2Te3 Epilayers in Units of cm−1
Derived from Figure
6 and Their Comparison with Literature Values from
Epilayers,26,25
Bulk Crystals,46,47
as well as Microcrystals48
Bi2Te3 sample type A1g
1
/fwhm Eg
2
/fwhm A1g
2
/fwhm
front side epilayers/BaF2 60.9/3.0 101.2/3.7 133/9
back side epilayers/BaF2 60.6/3.1 100.8/4.0 133/10
ref 26 epilayer/GaAs −/− 102/− 134/−
ref 25 epilayer/GaAs −/− 99.8/− 132/−
ref 46 bulk 62.5/− 103/− 134/−
ref 47 bulk 62.0/5 102.3/6 134/10
ref 48 microcrystals 61/3.5 101/4.5 133/−
Crystal Growth & Design Article
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Optical and Electronic Properties. The optical constants
of the Bi2Te3 and BiTe epilayers were determined over a wide
spectral range from the far-infrared to the ultraviolet (UV),
combining spectroscopic ellipsometry and reflectivity measurements
including synchrotron data acquired at NSLS
Brookhaven. The near-normal incidence infrared reflectivity
was analyzed with the standard model of coherent interferences
within a layer on a substrate,50
assuming the dielectric function
of the layer in the Drude-Lorentz form as described in detail in
the Supporting Information.
Figures 7a and b show the real part of the optical
conductivity σ1(ω) = −iωε0(ε(ω) − 1) derived for the BiTe
(black solid lines) and Bi2Te3 epilayers (blue dash-dotted
lines), and Figure 7c and d the real part of the dielectric
function ε1(ω). The dispersion of the optical constants was
obtained by the combination of reflectivity in the far-infrared,
and ellipsometry at higher frequencies, using the variational
dielectric function approach.51
The Bi2Te3 sample is transparent
in the energy range below about 0.2 eV and from the
resulting interference fringes the layer thickness was
determined as 830 nm. The BiTe epilayer is only slightly
transparent below 0.2 eV because of much stronger free carrier
absorption. The corresponding thickness was obtained as (390
± 5) nm close to the nominal value of 400 nm. The derived
pseudodielectric function of Bi2Te3 in the 0.6−6 eV range did
not exhibit any detectable angular dependence. Consequently,
it represents the in-plane response E⃗ ⊥ c. At these photon
energies the reported anisotropy of bulk Bi2Te3 is small.52
The
characteristic energies of the spectral features seen in Figure 7b
are in good agreement with those of bulk Bi2Te3 reported in ref
52.
For BiTe, the absorption above 0.3 eV is due to interband
transitions, dominated by the strong band at 1.35 eV, and side
bands at 0.42 and 2.7 eV as indicated by the arrows in Figure
7b. This structure is similar to that of Bi2Te3, which is
represented by the blue dash-dotted line for comparison. The
interband transitions are likely related to the Bi−Te bilayer,
which is the basic building block of both the Bi2Te3 and BiTe
structure (see Figure 1). The weaker band at 0.18 eV in BiTe
(see Figure 7a) is related to the 0.15 eV structure in Bi2Te3
reported in ref 52. At lower energies, the increase of the real
part of conductivity and the decrease of the real part of the
dielectric function with the decreasing photon frequency arises
from the strong contribution of conducting electrons. The
analysis of the spectra using the Drude model yields ωpl = 1.58
± 0.04 eV and γ = 0.09 ± 0.01 eV. Using
ω
ε
=
*
nq
m
pl
2
2
0 (1)
where n is the carrier concentration and q and m* the charge
and effective mass, the free carrier concentration in BiTe is
found to be about 20 times larger than in Bi2Te3, assuming the
effective masses are roughly the same. Since our X-ray and
Raman measurements have revealed a high crystalline
perfection of the samples and no signatures of increased
broadening is found in the optical spectra, this high carrier
concentration in BiTe is probably not caused by extrinsic effects
like vacancies but rather by a metal-like band structure,
involving a band that crosses the Fermi level. This conclusion is
supported by the analysis of the second BiTe sample that
yielded also a large value of the plasma frequency (1.45 eV). To
our knowledge, no calculations of the BiTe band structure have
been available; however, calculations of the isostructural BiSe
compound53
show several bands crossing the Fermi level in the
direction perpendicular to the c-axis, which supports our
conclusion.
To confirm the large difference in the carrier concentration
of the BiTe and Bi2Te3 layers, we have measured the DC
electric and Hall conductivities by the Van der Pauw method.
The DC conductivity of BiTe amounts to 3700 ± 200 ω−1
cm−1
. The Hall effect measurement revealed n-type conductivity
with a carrier concentration of 7 ± 1 × 1020
cm−3
using a Hall factor of unity. From this carrier concentration and
the measured plasma frequency, we derive the effective electron
mass to be about 0.37 ± 0.05 me in BiTe. Since the Hall effect
measurement on the Bi2Te3 samples were hampered by the
Ettingshausen effect, we have measured the thermoelectric
Seebeck coefficient instead, giving S = 170 ± 20 mV K−1
at 300
K, which yields a free electron concentration of 1.3 ± 0.3 ×
1019
cm−3
(see ref 54), which is more than 1 order of
magnitude lower than for the BiTe epilayer, in agreement with
Table 3. Measured Raman Frequencies and Widths (fwhm) of the Bi1Te1 Epilayers in Units of cm−1
Derived from Figure 6b
Compared to Literature Values Obtained for Polycrystalline Pulsed Laser Deposited (PLD) Films31
BiTe sample type ν/fwhm ν/fwhm ν/fwhm ν/fwhm ν/fwhm ν/fwhm
front side epilayers/BaF2 60.0/3.3 83/2.8 92.3/4.7 101.6/9 122/6 128/7
back side epilayers/BaF2 59.0/4.5 83/10 90.8/6 101.9/11 120/7 126/17
ref 31 PLD films 88/− 117/−
Figure 7. Real part of conductivity (top) and real part of the dielectric
function (bottom) of BiTe (black solid lines) and of Bi2Te3 (blue
dash-dotted lines) added for comparison. For clarity the spectra for the
far-infrared (left) and near-infrared−ultraviolet ranges (right) are
displayed on different scales. The dots in panel a correspond to the
measured dc conductivity measured in van der Pauw geometry.
Crystal Growth & Design Article
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Reprinted page 7 of paper [46] “Structure and properties of Bi2Te3 and BiTe thin films”.
the optical data. The DC conductivity of Bi2Te3 amounts to
160 ± 30 ω−1
cm−1
. The DC conductivities derived from the
electrical measurements are indicated in Figure 7a by the black,
respectively, and blue dot on the ordinate axis. Clearly, the
values agree well with the low-energy extrapolation of the
infrared conductivity measurements, demonstrating a good
consistency of our data.
To further assess the quality of the epilayers, we have
performed angle resolved photoemission (ARPES) measurement
of the electronic dispersion at the UE112-PGM2a
beamline of BESSY II in Berlin under ultrahigh vacuum
conditions at room temperature. For protection of the samples,
the surface was capped in situ after by a 100 nm Te capping
layer, which was desorbed in the photoemission chamber at
BESSY just before the ARPES experiments. The resulting
three-dimensional band dispersion is presented in Figure 8 for
Bi2Te3 grown under the same conditions as described above.
Identical ARPES spectra were obtained from different places of
the sample, indicating a high uniformity of the samples in the
lateral direction. The topologically protected surface state
(TSS) indicated by the dashed line in Figure 8b shows the
expected linear dispersion with the Dirac point overlapping
with the bulk valence band (BVB). The dispersion of the
surface state deviates from the simple isotropic Dirac cone of
Bi2Se3,6
showing a significant hexagonal warping of the band
dispersion at the Fermi level, as can be seen at the top of the
ARPES map displayed in Figure 8a. According to the ARPES
measurements, the bottom of the bulk conduction band (BCB)
lies about ∼130 meV below the Fermi level (see Figure 8b),
which compares very well to the value of 120 meV calculated
from the bulk electron concentration 1.3 × 1019
cm−3
. This
indicates that the free electron concentration at the surface
assessed by ARPES does not differ significantly from the bulk
concentration. Therefore, the Se capping and subsequent
preparation of the clean surface for ARPES measurement by
annealing does not produce a charge density on the surface.
The ARPES results are in nice agreement with previous
theoretical and experiments on the electronic band structure of
Bi2Te3.7
This demonstrates that the structural quality of the
epitaxial bismuth telluride layers is very well suited for studies
of the band structure of both bulk and topological surface
states. Preliminary ARPES measurements on BiTe epilayers do
not show a 2D surface state, which is an indication that BiTe is
not a topological insulator.
■ CONCLUSION
In summary, we have demonstrated heteroepitaxial growth of
different bismuth telluride phases onto BaF2 (111) substrates
using molecular beam epitaxy. The stoichiometric composition
of the layers was adjusted by control of the Te flux provided
during growth and single phase hexagonal BiTe and Bi2Te3
epilayers were obtained at low and high excess Te flux,
respectively. The layers grow with their c-axis perpendicular to
the surface and due to the good lattice matching to the BaF2
substrate, a high structural perfection was obtained. The strain,
size and tilts of the coherently scattering domains were
determined by high resolution X-ray reciprocal space mapping,
revealing a better structural perfection of Bi2Te3 compared to
BiTe due to the almost perfect substrate lattice matching. This
is supported by Raman measurements that show a low defect
concentration and high crystalline quality present at the
Bi2Te3/BaF2 interface. This suggests that the layer/substrate
lattice-mismatch is an important parameter for heteroepitaxial
growth of bismuth telluride epilayers, in spite of the van der
Waals bonding present in the crystal structure.
For both bismuth telluride phases, the Raman modes,
electronic structure, and optical properties were derived from
spectroscopic measurements and the plasma frequency of free
electrons as well as the interband transitions were deduced. By
angular resolved photoemission spectroscopy, the three-dimensional
dispersion of the topologically protected surface state
was measured for Bi2Te3 epilayers, revealing the Dirac point at
the top of the bulk valence band and a strong hexagonal
warping of the surface state at higher energies. The position of
the Fermi level probed by photoelectron spectroscopy was
found to be in good agreement with the carrier concentration
in the bulk derived from transport measurements. Thus, the
employed sample preparation produces very clean surfaces for
photoemission studies. Infrared and transport measurements
indicate a bulk metallic character of the BiTe material with a
more than one order of magnitude higher carrier concentration
as compared to Bi2Te3. To the best of our knowledge, the
growth of epitaxial layers and infrared optical measurements of
the BiTe phase was demonstrated for the first time. The small
lattice mismatch between BiTe and Bi2Te3 provides good
conditions for fabrication of heterostructures and superlattices
of the two phases. This may open a new pathway for realization
of topological insulator structures.
■ ASSOCIATED CONTENT
*S Supporting Information
Additional information and figures showing optical properties,
This material is available free of charge via the Internet at
http://pubs.acs.org.
■ AUTHOR INFORMATION
Corresponding Author
*E-mail: gunther.springholz@jku.at.
Figure 8. Band dispersion of the Bi2Te3 epilayers measured by angular
resolved photoemission (ARPES). Panel (a) on the left shows the
three-dimensional map of the photoemission intensity in the vicinity of
the Γ point. The Fermi level is at 0 eV, and the kx axis corresponds to
the Γ−K direction in the hexagonal two-dimensional surface Brillouin
zone and the ky axis to Γ−M direction. Panel b shows the 2D
dispersion (first derivative of the photoemission intensity with respect
to energy) in the kx direction. The dashed line indicates the
topologically protected surface state (TSS). BCB denotes the bulk
conduction band and BVB the bulk valence band. The measurements
were performed using ℏν = 21 eV photons for excitation.
Crystal Growth & Design Article
dx.doi.org/10.1021/cg400048g | Cryst. Growth Des. 2013, 13, 3365−33733372
Reprinted page 8 of paper [46] “Structure and properties of Bi2Te3 and BiTe thin films”.
Funding
The work was supported by the CSF grant P204/12/0595. Use
of the National Synchrotron Light Source, Brookhaven
National Laboratory, was supported by the U.S. Department
of Energy, Office of Science, Office of Basic Energy Sciences,
under Contract No. DE-AC02-98CH10886. Near-IR-VIS
ellipsometry measurements at the Center for Functional
Nanomaterials, Brookhaven National Laboratory, have been
supported by DOE DE-AC02-98CH10886.
Notes
The authors declare no competing financial interest.
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Crystal Growth & Design Article
dx.doi.org/10.1021/cg400048g | Cryst. Growth Des. 2013, 13, 3365−33733373
Reprinted page 9 of paper [46] “Structure and properties of Bi2Te3 and BiTe thin films”.
Supplementary Material
Growth, Structure and Electronic Properties of Epitaxial Bismuth
Telluride Topological Insulator Films on BaF2 (111) Substrates
O. Caha, A. Dubroka, J. Humlíček, V. Holý, H. Steiner, M. Ul-Hassan, J. Sánchez-Barriga,
O. Rader, T. N. Stanislavchuk, A. A. Sirenko, G. Bauer, and G. Springholz
(Dated: January 9, 2013)
PACS numbers:
1
Reprinted supplement page 1 of paper [46] “Structure and properties of Bi2Te3 and BiTe thin film”.
OPTICAL PROPERTIES
The optical constants of the Bi2Te3 and BiTe epilayers were determined by combining
spectroscopic ellipsometry and reflectivity measurements. For this purpose a mid-infrared ellipsometer
attached to a Bruker IFS55 EQUINOX Fourier spectrometer as well as a Woollam
M-2000 and Jobin Yvon UVISEL ellipsometer for the near-infrared, visible and ultraviolet
range were employed. Reflectance measurements in the 0.01–0.2 eV range were done using
a Bruker IFS 66v/S spectrometer and far-infrared ellipsometric measurements at the NSLS
synchrotron in Brookhaven. Figure 1(a) presents the near-normal incidence infrared reflectivity
of the Bi2Te3/BaF2 sample (solid line). Since the layer is transparent in this energy
range, the spectrum exhibits also features from the substrate – for example the structure
near 0.02 eV is due to the substrate phonon. The sequence of minima and maxima at higher
energies corresponds to the interference in the layer. We have analyzed the spectrum with
the standard model of coherent interferences within a layer on a substrate [1] assuming the
dielectric function of the layer in the Drude-Lorentz form
(ω) = ∞ −
ω2
pl
ω(ω + iωγ)
+
k
Ω2
pl,k
Ω2
0,k − ω2 − iωΓk
(1)
where ∞ stands for the electronic interband contribution, ωpl and γ denotes the plasma
frequency and broadening of the Drude term and Ωpl,k, Ω0,k and Γk the plasma frequency,
frequency and broadening of the Lorentz terms, respectively. The dielectric function of the
BaF2 was determined by fitting the reflectivity of a bare substrate in the far-infrared range
assuming the 3–term Lorentz model similar to Eq. (1), from which we obtain in units of
cm−1
except for ∞: ∞ = 2.16, Ω0,1 = 186, Ωpl,1 = 402, Γ1 = 6.1, Ω0,2 = 270, Ωpl,2 = 57,
Γ2 = 51, Ω0,3 = 330, Ωpl,3 = 52, Γ3 = 53 at T = at 300 K
The model spectrum of the whole layer–substrate structure presented as dashed line
in Figure 1(a) fits very well to the measured data up to the energy of about 0.1 eV. At
higher energies, the substrate is transparent and the quantitative analysis of the spectra is
complicated due to the incoherent reflections from the backside of the sample. The model
dielectric function involved also a Lorentz oscillator at Ω0 = 5.6 meV corresponding to
the so-called alpha phonon [2], which lies outside the frequency range of our spectrometer.
The resulting best–fit parameters for the epilayer are: ∞ = 45 ± 2, ωpl = (0.33 ± 0.02) eV,
γ = (0.07±0.01) eV. In addition, we obtained the thickness of the layer as d = (830±40) nm.
2
Reprinted supplement page 2 of paper [46] “Structure and properties of Bi2Te3 and BiTe thin film”.
1
0
20
40
60
80
0.8 65430.60.4
ε
photon energy [eV]
ε1
ε2
0.3 2
Bi
2
Te
3
b)
0.00 0.05 0.10 0.15 0.20
0.3
0.4
0.5
0.6
0.7
0.8
R
photon energy [eV]
data
model
Bi
2
Te
3
/BaF
2
a)
FIG. 1: (a) Far-infrared reflectivity of the Bi2Te3/BaF2 epilayer (solid line) and a model spectrum
(dashed line) for electric vector perpendicular to the c-axis, E ⊥ c. (b) Real and imaginary part of
the dielectric function of Bi2Te3 obtained from ellipsometric measurements up to 5 eV.
Since the reflectivity was measured at near-normal incidence, the retrieved dielectric function
corresponds to the in-plane direction, E ⊥ c. The derived dielectric constants were included
in the dielectric functions depicted in Fig. 7 of the manuscript.
Figure 1(b) displays the real and imaginary part of the dielectric function of the Bi2Te3
layer above 0.2 eV, where the layer is opaque. The spectra were obtained from the ellipsometric
measurements at the angle of incidence of 70 degrees (0.6–6) eV, and at 75 degrees
(0.2–0.6) eV. The displayed (pseudo)dielectric function was obtained assuming that the layer
is isotropic. As usual, the pseudo-dielectric function very close to the in-plane contribution.
This is particularly true for spectra acquired at low angles of incidence, and for large values
of the index of refraction, with the in–plane orientation of the electric vector inside the
layer. The pseudo-dielectric function measured in the 0.6–6 eV range did not exhibit any
detectable angular dependence. Consequently, it represents the in-plane response, E ⊥ c. At
these photon energies the reported anisotropy of bulk Bi2Te3 is small [3]. The characteristic
energies of the spectral features seen in Fig. 1(b) are in good agreement with those of bulk
reported in Ref. [3]. However, the magnitude of our spectra is by a factor 1.5-2 smaller and
our value ∞ = 45±2 is smaller by a factor of ∼2 than that obtained in Ref. [2]. The discrepancy
is probably caused by errors in the absolute values of the measured reflectivity in the
3
Reprinted supplement page 3 of paper [46] “Structure and properties of Bi2Te3 and BiTe thin film”.
0.02 0.03 0.04 0.05 0.06 0.07 0.08
2
3
4
5
6
σ1
[mΩ
-1
cm
-1
]
photon energy [eV]
9 K
300 K
240
150
90
FIG. 2: Temperature dependence of the real part of conductivity of the BiTe epilayer in the far–
infrared regime determined by ellipsometry at the NSLS synchrotron in Brookhaven.
cited works, or by the errors induced by extrapolations necessary for the Kramers-Kronig
analysis.
As indicated in Fig.7 of the manuscript(a), the infrared conductivity of BiTe exhibits two
bands near 0.02 and 0.05 eV that are superimposed on the Drude contribution. In order to
inspect these bands in a greater detail, we have have performed low-temperature far-infrared
ellipsometric measurements at the NSLS synchrotron in Brookhaven. Figure 2 displays the
resulting real part of conductivity from 9 to 300 K. The sharper structures in the spectra are
artefacts due to the inhomogeneity of the polarizer. Both bands at around 0.02 and 0.05 eV
gradually sharpen and soften with decreasing temperature.
[1] R. M. A. Azzam and N. M. Bashara, Ellipsometry and polarized light (Elsevier Science Publisher
B. B., 1987).
[2] W. Richter, H. Kohler, and C. Becker, Phys. Status Solidi B 84, 619 (1977).
[3] D. L. Greenaway and G. Harbeke, J. Phys. Chem. Solids 26, 1585 (1965).
4
Reprinted supplement page 4 of paper [46] “Structure and properties of Bi2Te3 and BiTe thin film”.
CHAPTER 4. REPRINTED PAPERS 62
4.2 Structure of BixTey thin films with general stoichiometry
The non-stoichiometric alloy layers of Bi2Te3−δ were grown with varying tellurium flux. We
have achieved stoichiometry within the range δ =0–1. The structure of thin films was analyzed
using x-ray diffraction. The diffraction pattern was described by a model of random stacking
of Bi2Te3 quintuple layer and Bi2 bilayer. The non-linear stoichiometry dependence of the
in-plane lattice parameter and average lattice spacing was determined.
research papers
J. Appl. Cryst. (2014). 47, 1889–1900 doi:10.1107/S1600576714020445 1889
Journal of
Applied
Crystallography
ISSN 1600-5767
Received 10 June 2014
Accepted 11 September 2014
# 2014 International Union of Crystallography
Structure and composition of bismuth telluride
topological insulators grown by molecular beam
epitaxy
Hubert Steiner,a
Valentine Volobuev,a
Ondrˇej Caha,b
Gu¨nther Bauer,a
Gunther
Springholza
and Va´clav Holy´c
*
a
Institut fu¨r Halbleiter- und Festko¨rperphysik, Johannes Kepler Universita¨t, Altenbergerstrasse 69,
4040 Linz, Austria, b
Department of Condensed Matter Physics and CEITEC, Masaryk University,
Kotla´rˇska´ 2, 61137 Brno, Czech Republic, and c
Department of Condensed Matter Physics, Charles
University in Prague, Ke Karlovu 5, 121 16 Prague, Czech Republic. Correspondence e-mail:
holy@mag.mff.cuni.cz
The structure and composition of Bi2Te3À topological insulator layers grown by
molecular beam epitaxy is studied as a function of beam flux composition. It is
demonstrated that, depending on the Te/Bi2Te3 flux ratio, different layer
compositions are obtained corresponding to a Te deficit  varying between 0 and
1. On the basis of X-ray diffraction analysis and a theoretical description using a
random stacking model, it is shown that for  ! 0 the structure of the epilayers is
described well by a random stacking of Te–Bi–Te–Bi–Te quintuple layers and
Bi–Bi bilayers sharing the same basic hexagonal lattice structure. The random
stacking model accounts for the observed surface step structure of the layers and
compares very well with the measured X-ray data, from which the lattice
parameters a and c as a function of the chemical composition were deduced. In
particular, the in-plane lattice parameter a is found to continuously increase and
the average distance of the (0001) hexagonal lattice planes is found to decrease
from the Bi2Te3 to the BiTe phase. Moreover, the lattice plane distances agree
well with the linear interpolation between the Bi2Te3 and BiTe values taking the
strain in the epilayers into account. Thus, the chemical composition Bi2Te3À can
be directly determined by X-ray diffraction. From analysis of the X-ray
diffraction data, quantitative information on the randomness of the stacking
sequence of the Bi and Te layers is obtained. According to these findings, the
layers represent random one-dimensional alloys of Te–Bi–Te–Bi–Te quintuple
and Bi–Bi bilayers rather than a homologous series of ordered compounds.
1. Introduction
Bismuth telluride has attracted tremendous interest in the past
few years because it not only represents one of the best
thermoelectric materials (Tritt, 1999; Snyder & Toberer, 2008)
but is also an outstanding member of a new class of materials
called topological insulators (Hasan & Kane, 2010; Zhang et
al., 2009; Hsieh et al., 2009; Qu et al., 2010; Qi & Zhang, 2011).
These materials exhibit striking new physical properties owing
to the existence of topologically protected two-dimensional
surface states that display an energy momentum dispersion
shaped like a Dirac cone (Zhang et al., 2009; Xia et al., 2009;
Chen et al., 2009). In these surface states, the electron
momentum is locked to the spin direction (Hasan & Kane,
2010; Roushan et al., 2009; Sanchez-Barriga et al., 2014) and
therefore, spin polarized currents can be induced without the
needs of external magnetic fields. This offers interesting
possibilities for novel spintronic devices (Hasan & Kane, 2010;
Moore, 2010; Qi & Zhang, 2011) and may provide a basis for
fundamentally new physics such as magnetic monopoles and
Majorana fermions (Hasan & Kane, 2010; Zhang et al., 2009).
In contrast to conventional III–V, II–VI or IV–VI
compound semiconductors, bismuth telluride (as well as
bismuth selenide) can exist in multiple phases with different
chemical compositions, including Bi2Te3, Bi3Te4, Bi5Te6 and
BiTe (Yamana et al., 1979), among others (Massalski &
Okamoto, 1996). These compounds constitute a homologous
series of structures (Stasova, 1967; Kim et al., 2001; Bos et al.,
2007) that share the same basic hexagonal lattice, formed by
ABCABC . . . stacking of hexagonally ordered alternating Bi
and Te layers, with additional Te–Te or Bi–Bi double layers
inserted at certain distances to accommodate the differences
in composition, i.e. the Te/Bi content. According to the Bi–Te
phase diagram (Massalski & Okamoto, 1996), stoichiometric
Bi2Te3 is the compound with the highest Te content, with a Te/
Bi ratio of 1.5. For the other phases, this ratio is reduced as
denoted by Bi2Te3À, where  > 0 defines the Te deficit in the
material compared with Bi2Te3.
Reprinted page 1 of paper [49] “Structure of Bi2Te3−x films”.
For Bi2Te3, the basic building blocks of the lattice are Te–
Bi–Te–Bi–Te quintuple layers (QLs) that are van der Waals
bonded to each other through the facing Te–Te double layers
(DLs). This gives rise to the well known threefold quintuple
layer stacking described by a hexagonal unit cell containing
three QLs (see Fig. 1a). As the Te content decreases
(increasing the Te deficit ), additional Bi–Bi double layers are
inserted between the quintuple layers which, if inserted at
regular distances, give rise to a homologous series of ordered
compounds that can be regarded as adaptive natural superlattices
(Stasova, 1967; Kim et al., 2001; Bos et al., 2007; Cava et
al., 2013). For example, for Bi2Te2 a Bi–Bi DL is inserted after
every second QL, for Bi5Te6 after every fourth QL, for Bi4Te5
after every fifth QL and so forth. The corresponding stacking
of the two-dimensional arrays in Bi2Te3, Bi4Te5, Bi1Te1 and
Bi4Te3 is shown schematically in Fig. 1. A further overview of
other ordered BimTen phases [denoted (mn) in the following]
can be found in papers by Kim et al. (2001), Bos et al. (2007)
and Cava et al. (2013). It is noted that a similar homologous
series also exists in the Bi–Se system, in which analogous
phases occur (Lind & Lidin, 2003; Lind et al., 2005; Valla et al.,
2012).
For practical applications of topological insulator materials,
high-quality epitaxial layers with well controlled properties
are of key importance (He et al., 2013). Owing to the existence
of different stoichiometric phases, however, the structure and
composition of bismuth chalcogenide layers grown by molecular
beam epitaxy (MBE) (Peranio et al., 2006; Liu et al.,
2010; Chen et al., 2011; Krumrain et al., 2011; Borisova et al.,
2012; Fukui et al., 2012; Li et al., 2010; Plucinski et al., 2011; Liu
et al., 2011; Zhang et al., 2012; Cao et al., 2012; Caha et al.,
2013) or other vapor phase methods are much less well defined
than those of the usual binary semiconductors such as GaAs,
InAs, ZnSe, PbTe etc., where only one single well defined
stoichiometric phase with 1:1 composition exists. As a result,
the structure and composition of bismuth telluride epilayers
are expected to strongly depend on the MBE growth conditions,
but no detailed studies on this have been reported up to
now.
To resolve this issue, we have investigated here the growth
and structure of bismuth telluride layers as functions of the
beam flux composition. We show that, although two-dimensional
growth occurs for any composition, a continuous series
of Bi2Te3À layers with arbitrary  is obtained under conditions
of reduced Te flux during growth. We developed a description
of the structure of the Bi2Te3À layers based on the model of a
stochastic sequence of QLs and DLs, which enables us to
simulate the diffraction curves averaged over a statistical
ensemble of all sequences. We demonstrate by the comparison
of the measured and simulated diffraction curves that the
resulting layer structure is formed by randomly incorporated
Bi–Bi double layers after random numbers of quintuple layers
rather than by ordered superstructures. Thus, only from the
average distance of the Bi–Bi double layers is the actual
stoichiometry  defined. The average atomic layer spacing in
the c direction is found to decrease with increasing  value,
roughly following the Vegard law connecting the limiting cases
of Bi2Te3 and Bi2Te2 with  = 0 and 1, respectively. As this
average lattice plane spacing can be directly deduced from the
position of selected Bragg diffraction maxima, the layer
compositions can be unambiguously obtained. The composition
has a profound influence not only on the step structure of
the surface but also on the background carrier concentration
and mobility, which is important for device applications.
Similar effects are also expected for bismuth selenide layers.
2. Sample growth
Bismuth telluride layers were grown by molecular beam
epitaxy using a compound bismuth telluride effusion source
with nominal Bi2Te3 composition, yielding a beam flux with an
overall Te/Bi flux ratio of approximately one. An additional
tellurium source is used to tune the beam flux composition and
to obtain a Te-rich beam flux composition, as needed to get the
2:3 stoichiometry in the growing layer or any other composition
in between. To systematically study the effect of beam flux
composition, a series of samples were grown in which the Te
flux was varied between 0 and 2.4 A˚ sÀ1
($1.25 monolayers
per second), while keeping the bismuth telluride flux rate
constant at $1 A˚ sÀ1
(0.1 QL sÀ1
). It is to be noted, however,
that a large portion of the excess Te flux re-evaporates from
the surface, and thus only a small fraction of Te atoms are
actually incorporated, meaning that the composition of the
layers differs from the impinging beam flux composition. The
flux rates and beam flux ratios were determined by a quartz
crystal microbalance moved into the substrate position. The
research papers
1890 Hubert Steiner et al.  Structure and composition of Bi–Te topological insulators J. Appl. Cryst. (2014). 47, 1889–1900
Figure 1
Stacking sequence of two-dimensional Bi and Te lattice planes in ordered
homologous BimTen (Bi2Te3À) structures with different compositions: (a)
Bi2Te3, (b) Bi4Te5, (c) Bi1Te1 and (d) Bi4Te3, with the corresponding Te
deficits  = 0, 0.5, 1 and 1.5, respectively. The black rectangles denote the
crystallographic unit cells; the Bi–Bi DLs are emphasized by shaded
areas. The numbers 1; . . . ; 7 in panels (a) and (c) refer to the distances of
the ð0001Þ lattice planes Áz1 to Áz7 as used for the model simulations
(see the text).
Reprinted page 2 of paper [49] “Structure of Bi2Te3−x films”.
layer thickness was 350 nm and the growth temperature was
613 K for all samples, and a background pressure of $5 Â
10À10
mbar was maintained during growth. Cleaved BaF2(111)
was used as substrate material. It is essentially lattice matched
to Bi2Te3 (Caha et al., 2013) because its in-plane lattice
constant of að111Þ
sub = asub(3)À1/2
= 0.4384 nm is practically equal
to the hexagonal lattice constant a = 0.4385 nm of Bi2Te3
(Nakajima, 1963; Wyckoff, 1964), i.e. the lattice mismatch Áa/
a is only 0.04%. For BiTe, a = 0.4423 nm (Yamana et al., 1979;
Shimazaki & Ozawa, 1978; Stasova, 1967) is slightly larger, but
the lattice mismatch to BaF2 is still below 1% (Caha et al.,
2013).
The surface evolution during growth was monitored using in
situ reflection high-energy electron diffraction (RHEED).
Figs. 2(a)–2(d) show representative RHEED patterns for four
samples grown with different excess Te fluxes, JTe, increasing
from 0 to 1.4 A˚ sÀ1
; there is no difference in the RHEED data
for higher fluxes between 1.4 and 2.4 A˚ sÀ1
. The streaked
RHEED patterns are practically indistinguishable, evidencing
that two-dimensional growth occurs in all cases, resulting in a
locally smooth terraced surface with atomic scale surface
steps. For all layers, the resulting surface structure was
determined by atomic force microscopy (AFM), and the
results are presented in the middle panels of Fig. 2. All layers
exhibit smooth surfaces, but the characteristic surface step
structure drastically differs for the different samples. Whereas
the sample grown with a high excess Te flux (Fig. 2h) shows a
well defined terrace structure with rather smooth and straight
step edges preferably aligned along three h1"1100i directions, for
the other samples grown with lower excess Te flux (Figs. 2e–
2g) much rougher step edges and a rather irregular step
structure are formed.
A closer inspection of the AFM images reveals that a
uniform, i.e. constant, step height h exists only for the high
excess Te flux sample, where h = 1 nm is the height of one Te–
Bi–Te–Bi–Te quintuple layer. In contrast, a variety of step
heights is observed for the other samples, h ranging from $0.4,
0.6, 1 and even 1.2 nm, corresponding to the height of one
bilayer (BL), trilayer (TL), quintuple layer as well as a
septuple (SL) layer. This is demonstrated by the surface
profiles depicted in the bottom panel of Fig. 2, where the
different step heights are labeled according to the corresponding
number of atomic planes. This is clear evidence that
the crystal structure, i.e. the layer stacking, strongly differs for
the different samples. For the pure Bi2Te3 phase, the lattice is
formed exclusively of QL blocks, which are weakly van der
Waals bonded by the Te–Te layers of the adjacent QLs. Thus,
there is a strong tendency to complete each QL before a new
research papers
J. Appl. Cryst. (2014). 47, 1889–1900 Hubert Steiner et al.  Structure and composition of Bi–Te topological insulators 1891
Figure 2
Top: RHEED patterns recorded during Bi2Te3À growth with different excess Te flux rates (JTe) from 0 to 1.4 A˚ sÀ1
, from (a) to (d), respectively,
indicating two-dimensional growth in all cases. The main growth flux is provided from a compound Bi2Te3 effusion cell, giving a growth rate of 1 A˚ sÀ1
.
Middle: AFM images of the resulting 350 nm-thick Bi2Te3À layers on BaF2(111) with the Te-deficit values  indicated as determined by X-ray diffraction
(image size 3 Â 3 mm). Bottom: measured surface profiles for the different layers, with the different steps heights corresponding to double (2), triple (3),
quintuple (5) and septuple (7) atomic lattice planes indicated by the numbers and by the vertical scale bars in view (k). The horizontal dashed lines
represent the normal quintuple layer spacing of Áh = 1 nm expected for the pure Bi2Te3 phase.
Reprinted page 3 of paper [49] “Structure of Bi2Te3−x films”.
QL nucleates on the surface, which results in a surface structure
that exclusively features QL layer steps (Teweldebrhan et
al., 2010). This is a first indication that only the epitaxial layers
grown with high excess Te flux, JTe ! 1.4 A˚ sÀ1
, grow in the
pure Bi2Te3 phase. Further inspection also reveals that the QL
layer steps tend to be straight and aligned along the h1"1110i
surface directions, whereas the other types of steps observed
for the samples grown with less excess Te flux do not show a
clear preferred step direction, causing a much higher stepedge
roughness as seen in Figs. 2(f)–2(g).
When reducing the Te flux during epitaxial growth, at some
point there is not sufficient Te present on the surface to
complete each quintuple layer and to maintain a fully Teterminated
surface state. As a result, with decreasing Te flux,
more and more stacking faults are introduced in the QL layer
stacking, leading to incomplete QL layers as well as to the
introduction of additional Bi–Bi double layers into the Bi2Te3
lattice. This corresponds exactly to the structural motif of the
Bi2Te3À phases with reduced Te content (Te deficit  > 0), in
which such Bi–Bi double layers are introduced to decrease the
overall Te/Bi ratio (see Fig. 1). As a result, surface steps with
smaller as well as larger step heights are formed on the surface
where, for example, an additional Bi–Bi–Te layer on top of a
QL layer corresponds to a trilayer step height, whereas an
additional Bi–Te layer leads to a DL surface step. Thus, the
surface structure observed for the low Te flux samples is a
clear indication that Bi2Te3À layers with significant Te deficit
 > 0 are formed. However, it is evident that the addition of a
Bi–Bi DL during growth does not occur synchronized over the
whole layer surface but rather with considerable statistical
variation at different locations. Therefore, disordered atomic
layer stackings will be formed rather than well ordered
superstructures. Under such conditions, domain boundaries
between regions of different stackings are formed, resulting in
a significantly increased defect density in the layers.
3. X-ray diffraction
To clarify in detail the structural properties of the samples
with different compositions, X-ray diffraction measurements
were performed using a Seifert diffractometer equipped with a
primary Ge monochromator and parabolic mirror for Cu K1
radiation and a pixel detector on the secondary side.
Symmetric diffraction scans of various samples from the series
are shown in Fig. 3, with the excess Te flux increasing from the
top to the bottom. The diffraction curves were measured in the
symmetric geometry, i.e. they represent the distributions of the
diffracted intensity along the Qz axis normal to the surface. All
layers only show ð000LÞ diffraction maxima, indicating growth
with the hexagonal c axis perpendicular to the BaF2 (111)
surface independent of the beam flux composition.
For the layer grown with the highest excess Te flux
(!1.4 A˚ sÀ1
) (lowest curve in Fig. 3), only diffraction peaks
with L equal to a multiple of three, i.e. L = 3, 6, 9, . . ., appear.
This indicates that only the pure Bi2Te3 phase is formed, in
which this selection rule arises from the fact that the unit cell is
nonprimitive and it is composed of three quintuple layers
stacked on top of each other and that these three QLs are
identical in the symmetric diffraction geometry. As we discuss
in detail below, the intensities of the (0009) and (00012)
reflections are very low owing to the vanishingly small structure
factor of a single QL.
With decreasing excess Te flux the diffraction peaks shift
and broaden, and some even split into peak pairs as indicated
by the short black arrows in Fig. 3. For the sample grown
without excess Te flux (upmost curve in Fig. 3), the intensity
and position of the diffraction peaks correspond to those
expected for the Bi1Te1 phase (Caha et al., 2013), exhibiting a
unit cell composed of 12 atomic layers [two QLs plus one Bi–
Bi DL, see Fig. 1(c)]. Thus, in contrast to Bi2Te3, the unit cell of
Bi1Te1 is primitive. Therefore, all diffractions ð000LÞ are
allowed and more diffraction peaks appear for Bi1Te1 than for
Bi2Te3, in spite of its smaller unit cell. For the samples with
intermediate Te fluxes, i.e. intermediate compositions (middle
curves in Fig. 3), there is no indication of the formation of
research papers
1892 Hubert Steiner et al.  Structure and composition of Bi–Te topological insulators J. Appl. Cryst. (2014). 47, 1889–1900
Figure 3
Symmetric diffraction curves for the Bi2Te3À sample series grown with
different excess Te fluxes, increasing monotonically from zero for the
topmost curve to JTe = 3 A˚ sÀ1
for the lowest curve. The curves were
measured in symmetric diffraction geometry along the ð000LÞ rod
perpendicular to the surface and for clarity are shifted vertically with
respect to each other. The numbers in blue and red denote the L indexes
of the diffraction maxima of the pure Bi2Te3 and Bi1Te1 phases,
respectively; the color of the curves indicates a gradual change of the
structure from Bi2Te3 (blue) to Bi1Te1 (red) with decreasing excess Te
flux. The short vertical arrows indicate the splitting of the weak (00012)
maximum of the (23) phase into two peaks with decreasing excess Te flux.
The BaF2 substrate diffraction peaks are labeled by S and the green
circles mark the Umweganregung peaks (see text).
Reprinted page 4 of paper [49] “Structure of Bi2Te3−x films”.
ordered superstructures as expected for the homologous series
of ordered BimTen phases, in which case additional peaks
should appear. Instead, we only find a continuous shift of the
diffraction peaks as a function of composition, i.e. the peaks of
Bi2Te3 smoothly evolve into those of BiTe. Strikingly, with
decreasing Te content, the diffraction peaks shift in various
directions. For example, the (0006) peak of the Bi2Te3 phase
shifts to the right, i.e. to higher Qz, and seamlessly transforms
into the (0005) peak of the Bi1Te1 phase, whereas in contrast
the (00018) peak of Bi2Te3 shifts to the left to evolve into the
(00014) diffraction maximum of Bi1Te1. Other peaks seem to
stay nearly at a constant position [e.g. the (00015) peak of
Bi2Te3] or split up or even disappear, as is seen, for example,
for the (0009) and (00010) peaks of Bi1Te1 (denoted by the
short black arrows in Fig. 3). With increasing Te content, these
peaks move closer and closer to each other and eventually
merge for the highest Te excess fluxes ( < 0:2), creating the
(00012) diffraction peak of the Bi2Te3 phase. It is noted that
several diffraction maxima denoted by S in Fig. 3 stem not
from the layer but from the substrate or are created by the
Umweganregung effect (denoted by green circles), i.e. the
wave being previously diffracted by the substrate is diffracted
by the layer, or the substrate diffracts the wave diffracted by
the layer. These additional diffraction maxima are, therefore,
ignored in the subsequent data analysis.
The diffraction data in Fig. 3 clearly demonstrate that there
is a rather continuous evolution of the lattice structure as a
function of composition, contrary to the picture of a discrete
series of distinct homologous structures with different
arrangements of unit cells. This means that the layer material
resembles more a random one-dimensional alloy of Bi and Te
lattice planes that can accommodate any arbitrary composition
with a quasi-continuous adoption of the average lattice
parameters. This assumption is also supported by the observation
that the diffraction peaks for the intermediate
compositions show a significant broadening as is common for
disordered alloy materials.
To determine the lateral lattice parameter a of the hexagonal
lattice of the samples, we have measured reciprocalspace
maps of the diffracted intensity in the vicinity of the
asymmetric reciprocal lattice point (313) of the substrate and
of the ð1 "11 0 20Þ one of Bi2Te3. As shown in Fig. 4, the two
diffraction maxima occur close to each other in the same
reciprocal plane perpendicular to the sample surface
ð111Þcubic k ð000 1Þhexagonal, and their lateral reciprocal coordinates
along ½1"221Šcubic k ½1"1100Šhexagonal are given by
HðsubÞ
k ¼
2
asub
ð8=3Þ1=2
; HðmnÞ
k ¼
2
amn
ð4=3Þ1=2
: ð1Þ
As asub ’ amn(2)1/2
[amn denotes the a parameter of the (mn)
phase], the substrate and layer diffraction maxima have almost
the same lateral positions. In Figs. 4(a) and 4(b), we show the
reciprocal-space maps of the samples with the highest and
lowest excess Te flux rates [(23)-like and (11)-like, respectively].
In the maps, the diffraction maxima of the substrate
and the layer are denoted by S and L, respectively. The
maxima occur at practically the same in-plane positions owing
to the nearly identical in-plane lattice constants. For the
samples with lower Te content grown under low excess Te
conditions, the layer peak gradually moves to somewhat lower
Qx and higher Qz values, indicating a continuous increase of
the in-plane lattice parameter a and a concomitant decrease of
the average distance of the hexagonal (0001) basal atomic
planes (referred to here as inter-plane distances) as described
in detail in x4.
4. Theory of X-ray diffraction from a random stack of
layers
For the analysis of the measured diffraction data, we developed
a theoretical description of X-ray diffraction from a
random stack of layers based on the statistical theory of
diffraction from randomly layered systems (Holstein, 1993).
An elegant matrix formulation of this problem was proposed
by Croset & de Beauvais (1997, 1998) and used for the
description of X-ray diffraction from epitaxial layers with a
random sequence of layers by Kopp et al. (2012). As we stated
above, the structure of every trigonal (hexagonal) BimTen
phase can be described by the face-centered cubic like
stacking of two-dimensional hexagonal (0001) arrays of Bi and
Te atoms with different stacking sequence including Te–Bi–
Te–Bi–Te quintuples as well as Bi–Bi double layers.
Depending on the Te flux used during MBE deposition, the
number of quintuplets nj between the (j À 1)th and jth Bi–Bi
double layers can vary. In the following, we assume that nj are
random and the values nj, nk, j 6¼ k, are statistically independent.
For the genuine (i.e. ideally periodic) Bi2Te3 and Bi1Te1
phases nj ! 1 and nj = 2 hold, respectively (see Fig. 1). We
assume that the measured intensity of diffracted X-rays is
averaged over the statistical ensemble of all possible
sequences of numbers nj. This assumption is justified because
research papers
J. Appl. Cryst. (2014). 47, 1889–1900 Hubert Steiner et al.  Structure and composition of Bi–Te topological insulators 1893
Figure 4
Asymmetric reciprocal-space maps of two Bi2Te3À layers grown with the
highest (a) and lowest (b) excess Te flux rates and Te deficit  ’ 0 and  ’
1, respectively, showing the (313) diffraction peaks of the substrate
(denoted by S) and the ð1 "11 0 20Þ maxima of the layer (L). The step of the
iso-intensity contours is 100:2
.
Reprinted page 5 of paper [49] “Structure of Bi2Te3−x films”.
in our diffraction experiment the irradiated sample area is, by
many orders of magnitude, larger than the coherence width of
the primary X-ray beam (which lies below 1 mm). Using
kinematical approximation of X-ray diffraction and restricting
ourselves to symmetric diffraction only, the amplitude EðQÞ of
the wave diffracted from a given sequence of two-dimensional
arrays (characterized by the given sequence of nj values) is
given by
EðQÞ ¼ A
PM
k¼1
fkðqÞ expðÀiqzkÞ: ð2Þ
Here, A is the constant containing the primary intensity and
polarization factor, Q ¼ 4= sinðiÞ is the length of the
scattering vector (i is the incidence angle), q is the complex
length of the scattering vector corrected for refraction and
absorption, m is the total number of two-dimensional atomic
layers in the coherently irradiated volume, zk is the coordinate
of the kth layer along [0001], and fk is the atomic scattering
factor of the atoms in layer k consisting either of Bi or Te
atoms (fTe or fBi).
The sequence of the coordinates zk is constructed from a
given set of nj values using the following rules:
(1) The inter-plane distances in the quintuplet not adjacent
to a Bi–Bi doublet (i.e. in the layer sequence of . . . TekTe–Bi–
Te–Bi–TekTe . . . ) are given by Áz1, Áz2, Áz3, Áz2, Áz1, where
Áz1 is the distance of the van der Waals bonded Te–Te layers
and Áz2;3 are the Te–Bi distances with the QL.
(2) If a quintuplet adjoins a Bi–Bi doublet (i.e. for the layer
sequence . . . TekBi–BikTe–Bi–Te–Bi–TekTe . . . ), the interplane
distances are Áz6, Áz7, Áz6, Áz5, Áz4, Áz3, Áz2, Áz1,
where the corresponding inter-plane distances are indicated in
Fig. 1.
(3) If both ends of a quintuplet are attached to Bi–Bi
doublets (sequence . . . TekBi–BikTe–Bi–Te–Bi–TekBi–Bik
Te . . . ), the inter-plane distances are Áz6, Áz7, Áz6, Áz5, Áz4,
Áz4, Áz5, Áz6, Áz7, Áz6.
(4) A Bi–Bi doublet cannot adjoin another doublet; at least
one quintuplet must occur between two doublets.
In this notation, Áz2;3 correspond to the Te–Bi inter-plane
spacings within a QL not adjacent to a Bi–Bi DL and Áz1 is
the inter-plane distance in the van der Waals bonded Te–Te
double layer adjoining two QLs. If a QL adjoins a Bi–Bi DL,
its inter-plane distances are modified from Áz2;3;3;2 to Áz2;3;4;5.
Áz6 is the inter-plane distances between the last Te layer of a
QL and the first Bi layer in the DL, and Áz7 is the distance
between the Bi layers in the Bi–Bi DL. From our simulations it
turned out, however, that the results are almost insensitive to
the distances Áz4;5. Therefore, we replaced these values by the
corresponding distances Áz3;2 within the quintuplets in the
pure Bi2Te3 phase.
Using the rules listed above, we calculated directly the
diffracted intensity averaged over the statistical ensemble of
all random sequences fnj; j ¼ 1; . . . ; P; hnji ¼ Ng of the
numbers of QLs between two Bi–Bi DLs; P is the total
number of structure units in the layer stack (i.e. the total
number of Bi–Bi DLs); the jth unit comprises nj QLs and one
Bi–Bi DL. The formula for the ensemble-averaged intensity is
quite cumbersome and it is presented in Appendix A.
The diffracted intensity exhibits rapid oscillations caused by
the fixed length of the layer stack; the period of the oscillations
is roughly 2/[(5N + 2)hÁzi], where hÁzi is the mean interplane
distance and N  hnji is the mean number of QLs
between subsequent Bi–Bi DLs. In order to suppress these
nonphysical oscillations we performed a numerical convolution
of the calculated diffraction curve with a suitable peak
function (we used a standard Gaussian function) corresponding
to the limited coherence width Lcoh of the incoming
X-ray beam. The full width at half-maximum of this function is
2=Lcoh. In the simulations we assumed Lcoh = 0.2 mm (i.e.
much longer than the QL length) and chose the number P of
the structure units so large that the total thickness of the layer
stack fairly exceeds Lcoh. The value of Lcoh affects only the
widths of the diffraction peaks. The nominal layer thickness of
350 nm slightly exceeded Lcoh; however, structure defects not
included in the stacking model broadened the measured
diffraction maxima.
The simulation model used here is similar to the statistical
models of layered systems based on the Markow chain of the
first order and published previously by Kopp et al. (2012).
Both models can be directly compared, if we use nj quintuple
layers and one Bi–Bi double layer as the structure unit used in
these works. As the number of nj values could be large, our
system is a ‘many-state system’ in the terminology used by
Kopp et al. (2012). The matrix formalism used in the cited
works is rather complicated for such many-state systems, and
the direct averaging described in Appendix A can be used
instead.
In Figs. 5, 6 and 7, we present illustrative results of the
numerical simulations of the diffracted intensity along the
ð000LÞ direction for different lattice structures. First, let us
consider ideally periodic BimTen phases [denoted by (mn)]
with various N. The corresponding diffraction curves are
shown in Fig. 5, where the curve N ! 1 corresponds to the
ideal (23) phase, and N = 1, 2, 3, 5 refer to the (43), (11), (67)
and (45) phases, respectively. As stated above, the diffraction
maxima of Bi2Te3 along the ð000LÞ rod appear only for L = 3p
(p is an integer), because the three quintuplets occurring in the
unit cell are identical in symmetric ð000LÞ diffraction, and
therefore a three-times smaller structure unit (one QL) acts as
the unit cell for symmetrical diffraction. We emphasize that
the (00012) diffraction is almost forbidden in Bi2Te3, as its
position nearly coincides with a sharp minimum of the structure
factor of one QL, which is represented by the superimposed
blue dashed curve in Fig. 5. Therefore, the intensity
of the (00012) maximum is extremely sensitive to the interplane
distances Áz1;2;3 in the QL. Most notable, for N ! 2, i.e.
large distances of the Bi–Bi double layers, the diffraction
curves of the ordered phases exhibit rather closely spaced
diffraction peaks arising from the natural superlattice period
produced by the periodically inserted Bi–Bi DLs, where the
satellite spacing decreases inversely proportionally to N.
For the analysis of the positions of the diffraction peaks of
the ideally ordered phases, let us assume for the moment that
research papers
1894 Hubert Steiner et al.  Structure and composition of Bi–Te topological insulators J. Appl. Cryst. (2014). 47, 1889–1900
Reprinted page 6 of paper [49] “Structure of Bi2Te3−x films”.
the inter-plane distances Ázi are identical and equal to the
mean inter-plane distance hÁzi of the actual structure. If the
layers contain identical atoms (a virtual ‘mixture’ of Bi and Te
atoms, for instance), the diffraction peaks of such a virtual
crystal (VC) will appear at the following points on the (000L)
rod,
QðVCÞ
L ¼
2
hÁzi
L; ð3Þ
where L is an integer. The diffraction curve of such a virtual
structure is plotted in Fig. 5 (bottom green line). Now, let us
replace the virtual atoms in the layers by a sequence of Bi and
Te atoms corresponding to an ideally ordered (mn) phase,
keeping the same average inter-plane distance hÁzi. This
chemical modulation results in additional peaks that can be
considered as modulation (superlattice) maxima accompanying
the main mean maxima in equation (3). If the
elementary unit cell of the ideally ordered (mn) phase consists
of NQ (Te–Bi–Te–Bi–Te) QLs and ND (Bi–Bi) DLs, the
maxima will appear at the points
research papers
J. Appl. Cryst. (2014). 47, 1889–1900 Hubert Steiner et al.  Structure and composition of Bi–Te topological insulators 1895
Figure 7
ð000LÞ diffraction curves simulated for disordered BinTem structures: (a)
diffraction curves for Bi1Te1 with a constant number of QLs N = 2 but
increasingly random positions of the Bi–Bi DLs in the crystal, as
described by the different orders m of the 
 distribution of the random
numbers of QLs between two DLs; (b) shows the effect of disorder for
different values of N from N = 1 [which corresponds to the disordered
(11) phase] to N ! 1 [(23) phase] and constant m = 10. The red
numbers in (a) and the blue numbers in (b) denote the positions of the
diffraction maxima and their indexes L of the (11) and (23) phases,
respectively. The arrows denote the diffraction peaks of the virtual crystal
(see text); the curves are shifted vertically for clarity.
Figure 6
Details of the diffraction curves along the ð000LÞ rod in the vicinity of the
ð0 0 0 12Þð23Þ
maximum, calculated for various values of N of QLs between
the Bi–Bi DLs for perfectly ordered phases, i.e. m ! 1 (dotted lines),
and for disordered phases with m = 10 (full lines). The values of N are
indicated; the curves are shifted vertically for clarity. The vertical dotted
lines and the blue numbers denote the theoretical positions and L values
of the diffraction maxima of the (23) phase.
Figure 5
Diffraction curves calculated along the symmetric ð000LÞ direction for
ideally periodic, i.e. perfectly ordered, BimTen phases with different (mn)
numbers, corresponding to different numbers of quintuplets N = 1, 2, 3, 5
and N ! 1 between two Bi–Bi doublets (see Fig. 1) from top to bottom.
The blue and red numbers denote the diffraction indexes L of the (23)
and (11) phases, respectively. The bottom green line represents the
diffraction curve of a ‘virtual’ crystal having constant inter-plane
distances and containing identical atoms. The blue and red dashed
curves superimposed on the diffraction curves for the (11) and (23)
phases are the structure factors of one QL and of one unit cell of the (11)
phase, respectively. The curves are shifted vertically for clarity.
Reprinted page 7 of paper [49] “Structure of Bi2Te3−x films”.
QðmnÞ
L ¼
2
ð5NQ þ 2NDÞhÁzi
L; ð4Þ
if we still assume constant inter-plane distances hÁzi.
Obviously ðm : nÞ ¼ ð2NQ þ 2NDÞ : ð3NQÞ must hold. For
instance, in the (23) phase NQ ¼ 3 and ND ¼ 0 and, thus, the
diffraction maxima appear at the points
Qð23Þ
L ¼
2
15hÁzi
L 
2
5hÁzi
p; ð5Þ
because only the maxima with L = 3p (p is an integer) are
allowed. In the (11) phase, NQ ¼ 2 and ND ¼ 1, i.e. the
diffraction maxima are at
Qð11Þ
L ¼
2
12hÁzi
L: ð6Þ
Let us now compare the positions of the diffraction maxima
of different (mn) phases assuming the same value of hÁzi in
all phases. From equations (3)–(6), it follows that only the
maximum ð0 0 0 15tÞð23Þ
(t is an integer) of the (23) phase
coincides with the maxima of other phases; these maxima
correspond to the averaged structure used in equation (3) and
their distance is ÁQ = 2/hÁzi. If t = 1, for instance, the
maximum ð0 0 0 15Þð23Þ
coincides with the maxima ð0007Þð43Þ
,
ð0 0 0 12Þð11Þ
, ð0 0 0 17Þð67Þ
and ð0 0 0 27Þð45Þ
of the phases (43),
(11), (67) and (45), respectively; this maximum is equivalent to
the first diffraction peak ð0001ÞðVCÞ
of the VC. Analogously, all
maxima ð0 0 0 15tÞð23Þ
are equivalent to the VC diffraction
maxima ð000tÞðVCÞ
. Because, as we show later, the average
inter-plane distance hÁzi gradually decreases with decreasing
N, these maxima move to larger Q with decreasing N, i.e. when
moving from (23) towards the pure (11) phase. On the other
hand, however, the positions of other maxima move in
different ways with decreasing N. For instance, the maximum
ð0 0 0 18Þð23Þ
does not correspond to any maximum of other
(mn) phases, which is obvious from Fig. 5. In fact, with
decreasing N, this maximum splits up into two maxima, with a
separation that increases with decreasing N. In the case N = 2,
however, only the left maximum from this pair appears [which
corresponds to the ð0 0 0 14Þð11Þ
peak], as the right one coincides
with a local minimum of the structure factor of the (11)
phase (the red dashed curve in Fig. 5). Therefore, the
maximum ð0 0 0 18Þð23Þ
seems to move to smaller Q with
decreasing N. In the position of the almost forbidden
maximum ð0 0 0 12Þð23Þ
a similar splitting occurs, converting to
the diffraction maxima ð0009Þð11Þ
and ð0 0 0 10Þð11Þ
of the (11)
phase.
From this analysis it follows that only the diffraction
maxima ð0001ÞðVCÞ
 ð0 0 0 15Þð23Þ
! ð0 0 0 12Þð11Þ
! ð0007Þð43Þ
and ð0002ÞðVCÞ
 ð0 0 0 30Þð23Þ
! ð0 0 0 24Þð11Þ
! ð0 0 0 14Þð43Þ
can be used for the determination of the dependence of hÁzi
on N. Fig. 6 demonstrates in detail the various types of the
maxima described above. The VC maximum ð0 0 0 15Þð23Þ
moves to larger Q if we decrease N. This behavior corresponds
to a decrease of hÁzi with decreasing N. On the other hand,
the maximum ð0 0 0 12Þð23Þ
splits into a pair of maxima and,
conversely, ð0009Þð23Þ
and ð0 0 0 18Þð23Þ
move to smaller Q. As
we explained above, this shift of the maxima does not correspond
to an increase of hÁzi.
A comparison of the measured diffraction curves of Fig. 3
with the curves simulated for perfectly periodic (mn) phases
shown in Fig. 5 reveals that only the diffraction curve of the
sample with the highest Te excess flux is similar to the calculated
diffraction curve of the perfect (23) phase. The other
experimental curves exhibit far fewer diffraction maxima than
the simulated ones. Thus, the experimental results can only be
explained if we assume a certain statistical disorder in the
layer sequence. The strong effect of disorder on the simulated
diffraction curves for the case of a constant mean number
hni  N = 2 of QLs between two Bi–Bi DLs, corresponding to
an average composition equal to the (11) phase, with the
different degrees of disorder accounted for by the order m of
the 
 distribution of the numbers n of QLs between two
adjacent Bi–Bi DLs, is seen in Fig. 7(a). The curve m = 1
corresponds to the ideally ordered (11) phase. When
decreasing the order m, evidently the diffraction maxima
become broadened and gradually disappear, except for the
VC maxima ð0001ÞðVCÞ
 ð0 0 0 12Þð11Þ
and ð0002ÞðVCÞ

ð0 0 0 24Þð11Þ
which correspond to the ð0 0 0 15Þð23Þ
and
ð0 0 0 30Þð23Þ
peaks of the (23) phase. In Fig. 7(b) we demonstrate
the dependence of the simulated diffraction curves on
N, keeping the degree of disorder constant at m = 10. It is
obvious that for small m (i.e. large N) only a few modulation
peaks persist: for instance, the pair of maxima that originates
from the splitting of the ð0 0 0 12Þð23Þ
maximum is observed,
whereas most other modulation peaks (cf. Fig. 5) disappear.
This is also demonstrated by Fig. 6, where zoomed-in
diffraction spectra are shown for the ordered (dotted curves)
and disordered (solid curves) structures. However, the
persisting splitting of the ð0 0 0 12Þð23Þ
maximum makes it
possible to determine the mean number of QLs N also for
disordered structures. The blue and red arrows in Figs. 7(a)
and 7(b) denote the positions of the VC diffraction peaks
ð0001ÞðVCÞ
 ð0 0 0 15Þð23Þ
 ð0 0 0 12Þð11Þ
and ð0002ÞðVCÞ

ð0 0 0 30Þð23Þ
 ð0 0 0 24Þð11Þ
. As the mean inter-plane distance
hÁzi in the (23) phase is larger than that in the (11) phase, the
VC maxima move to larger Q with decreasing N, i.e. when
moving from the (23) phase towards (11). It is emphasized that
this tendency is preserved also in disordered structures,
meaning that the positions of the VC peaks can be used indeed
for the determination of hÁzi in random structures.
5. Quantitative results
To determine the real structure of the Bi2Te3À epitaxial layers,
the measured diffraction curves of all samples were fitted with
the above described model, treating the inter-plane distances
Áz1;2;3;6;7 (assuming Áz4 ¼ Áz3 and Áz5 ¼ Áz2) as well as the
mean number of quintuplets N between the Bi–Bi DLs and
the order m of the 
 distribution of the random numbers n as
fit parameters. The fitted diffraction curves are presented as
solid lines in Fig. 8, together with the experimental data
(points).
research papers
1896 Hubert Steiner et al.  Structure and composition of Bi–Te topological insulators J. Appl. Cryst. (2014). 47, 1889–1900
Reprinted page 8 of paper [49] “Structure of Bi2Te3−x films”.
Evidently, the fits of the measurements are satisfactory; the
regions around the substrate and Umweganregung peaks were
excluded from the fitting. The remaining discrepancies
between the experimental data and the calculated diffraction
curves may be caused by sample inhomogeneities both within
the layers and on the surfaces.
As a result from the fits, we obtain for each sample the
stacking sequences of Bi and Te layers as well as the interplane
distances Áz1;2;3;6;7 between the individual lattice planes,
and by averaging over all Ázk, the average inter-plane
distance hÁzi is deduced. In addition, we obtain the overall Te
deficit  of the samples simply by summing up the total
number of Te and Bi layers in a given stacking sequence. The
composition is also directly related to the average number N
of QLs between subsequent Bi–Bi DLs according to
 ¼ 3=ðN þ 1Þ: ð7Þ
As expected, the mean inter-plane distances hÁzi obtained
from the fit agree with the values directly derived from the
ð0001ÞðVCÞ
 ð0 0 0 15Þð23Þ
! ð0 0 0 12Þð11Þ
and ð0002ÞðVCÞ

ð0 0 0 30Þð23Þ
! ð0 0 0 24Þð11Þ
; . . . peak positions in the diffraction
curves. The latter method yields the hÁzi values with
better accuracy because of the limited quality of the fit of the
whole diffraction curves and because the former approach is
independent of the model. Through the order parameter m,
obtained from the fits, we also get information on the
randomness of the stacking sequence, i.e. degree of deviation
of the actual from the perfectly ordered structures.
In Fig. 9, all derived structure parameters of the samples are
plotted as a function of the Te deficit  calculated using the
above equation. Fig. 9(a) shows the in-plane hexagonal lattice
parameter a deduced from the reciprocal-space maps (cf.
Fig. 4) and Fig. 9(b) shows the mean vertical inter-plane
distance hÁzi (black filled circles) obtained from the simulations
as functions of the Te deficit . Evidently, a gradually
increases from a = 0.438 to $0.44 nm when  increases from 0
to 1, i.e. when the composition changes from (23) to (11). This
can be described by a polynomial of aðÞ of the second order
(see below). Conversely, the mean inter-plane distance
decreases almost linearly from hÁzi = 0.2035 to 0.201 nm for
the same change in composition. This means that with
increasing Te deficit, i.e. an increasing number of inserted Bi–
Bi DLs, the average inter-plane distance hÁzi shrinks and the
lateral lattice parameter a expands.
According to literature data for bulk samples of various
ordered (mn) phases, represented by the colored circles in
Fig. 9(a) (Brebrick, 1968; Shimazaki & Ozawa, 1978; Yamana
et al., 1979; Korzhuev et al., 1992; Feutelais et al., 1993; Safarov,
1994; Bos et al., 2007), the dependence of abulk of bulk BimTen
on  can be expressed by a polynomial of the second order,
too. On the basis of this observation, we interpolate the
tabulated values of abulk to obtain the expected lateral lattice
parameters abulk of the bulk materials having the same Te
deficit  as in our layers. These values, denoted by empty
circles in Fig. 9(a), are assumed as relaxed lattice parameters
of our Bi2Te3À layers (arelaxed). The deviations between our
values of a obtained for the epilayers [black circles in Fig. 9(a)]
and those extrapolated from the bulk literature data are
ascribed to a partial strain in the investigated samples due to
the BaF2 substrate, where with increasing Te deficit  and a
corresponding increase of in-plane lattice parameter a, a small
but increasing lattice misfit develops.
In order to compare our values of the mean inter-plane
distances hÁzi (black filled circles in Fig. 9b) with the
published data for bulk material, we calculated the corresponding
relaxed inter-plane distances hÁzirelaxed using the
elastic equilibrium formula
hÁzirelaxed ¼ hÁzi 1 þ
2C13
C33
a À arelaxed
arelaxed
 
; ð8Þ
where C13;33 are the elastic constants of Bi2Te3 taken from the
paper by Jenkins et al. (1972) (we neglected their dependence
on ). Fig. 9(b) shows the relaxed mean inter-plane distances
of our layers (empty circles) in comparison with the distances
reported for ideally ordered (mn) phases (Bos et al., 2007)
(colored circles). Clearly, after the strain correction the mean
inter-plane distances agree very well with the published values
for ideally ordered phases.
From this analysis, we obtain the following relations
between the lattice parameters a and mean inter-plane
distances hÁzi of the Bi2Te3À epitaxial layers as functions of
the Te deficit :
a ¼ 0:0026 ð5Þ 2
þ 0:43764 ð8Þ ðnmÞ;
hÁzi ¼ À0:0027 ð2Þ  þ 0:2037 ð1Þ ðnmÞ:
ð9Þ
If we correct these values for the partial strain relaxation by
equation (8), we obtain the values for the corresponding
relaxed lattices
research papers
J. Appl. Cryst. (2014). 47, 1889–1900 Hubert Steiner et al.  Structure and composition of Bi–Te topological insulators 1897
Figure 8
Measured (points) and simulated (lines) diffraction curves for the
Bi2Te3À epitaxial layers grown using various excess Te flux rates,
resulting in various Te deficits  as obtained from the fitting procedure.
The vertical dotted lines denote the positions of the diffraction peaks
ð000LÞð23Þ
of the (23) phase with corresponding L values indicated above.
The colors of the lines denoting the fitted curves range from blue [(23)
phase,  = 0] to red [(11) phase,  = 1]. The BaF2 substrate peaks are
marked by S; the curves are shifted vertically for clarity. The green circles
mark the Umweganregung peaks.
Reprinted page 9 of paper [49] “Structure of Bi2Te3−x films”.
arelaxed ¼ À0:0023 ð1Þ 2
þ 0:0075 ð1Þ  þ 0:43828 ð2Þ ðnmÞ;
hÁzirelaxed ¼ 0:0019 ð1Þ 2
À 0:0052 ð3Þ  þ 0:2032 ð1Þ ðnmÞ:
ð10Þ
The numbers in the parentheses in equations (9) and (10)
denote the statistical errors of the last digits. From these
relations, the composition, i.e. Te/Bi content, in any Bi2Te3À
samples can be deduced simply by measuring their in-plane
lattice parameter a and/or the mean inter-plane distance hÁzi
as described above. In particular, the inter-plane distances
hÁzi (Fig. 9b) show a linear dependence on the Te deficit ,
nicely following the Vegard law in the range of  from 0 to 1,
i.e. between the pure Bi2Te3 and BiTe phases. This continuous
dependence is an indication that the samples with intermediate
compositions can be regarded as one-dimensional
random alloys of these two phases. Furthermore, Figs. 9(a) and
9(b) indicate that the (43) phase deposited onto the BaF2(111)
substrate should be stress-free, as both a; arelaxed and
hÁzi; hÁzirelaxed coincide if we extrapolate their values to
 ! 3=2.
From the fits, we also obtain the  dependences of the
individual inter-plane distances Áz1;2;3;6;7 between the lattice
planes (see Fig. 1), and the results are presented in Fig. 9(c).
Evidently, the inter-plane distances Áz2;3 within the QLs and
Áz1 between adjacent quintuplets (black circles) are almost
independent of the Te deficit , i.e. on the mean number N of
QLs between the Bi–Bi DLs. In addition, the values agree well
with the published ones for bulk Bi2Te3 (blue circles) (Safarov,
1994). This indicates that the QL building blocks of the
Bi2Te3À compounds are practically unaffected by the insertion
of additional Bi–Bi DLs. Conversely, the inter-plane
distances inside the Bi–Bi DL (Áz7) and between the DL and
the first Te layer of the adjacent QL (Áz6) (open symbols in
Fig. 9c) strongly change on changing the Te deficit ; namely
Áz7 inside the Bi–Bi DL decreases with increasing , and the
separation between the DL and adjacent QL (Áz6) increases.
It is also noted that, while our values for Ázj agree well with
literature values for  ¼ 0 (i.e. for Bi2Te3), a significant
deviation is found when  ¼ 1 (i.e. Bi2Te2  Bi1Te1 phase)
(Yamana et al., 1979), represented by the blue and red circles
in Fig. 9(c), respectively. The latter observation may be
explained by the fact that the lattice parameters a and hÁzi of
our epitaxial layers have already deviated from the bulk
literature values.
Fig. 9(d) shows the degree of stacking disorder as a function
of the Te deficit , quantified in terms of the relative r.m.s.
deviation N=N of the number of QLs between two DLs. The
r.m.s. deviations are very small for  ¼ 0 and  ! 1, i.e. for
composition close to the pure (23) and (11) phases, meaning
that well ordered structures are formed in these cases.
Between these limiting cases,
however, the structures are highly
disordered, and the maximum
disorder is present for the sample with
 ’ 0.15, i.e. N ’ 19. In this case,
N ’ N and therefore the random
numbers n of the QLs between two
Bi–Bi DLs are distributed according
to a geometrical distribution. This
distribution is ‘memoryless’, i.e. the
sequence of doublets and quintuplets
can be described by the Markow chain
of the first order with one QL and
one DL as two states. In such a chain,
the probability that a quintuplet is
followed by a doublet does not
depend on the position of the
previous doublet in the sequence. This
is quite reasonable because, for very
large average distances N between
consecutive Bi–Bi doublets, it is
rather unlikely that a sufficiently
strong interaction exists that can
mediate any ordering process.
Finally, we have also investigated
the influence of the chemical composition
on the carrier concentration
and carrier mobilities of the layers.
From Hall-effect measurements, we
find for the samples with composition
very close to Bi2Te3 ( < 0:08), an ntype
conduction with an electron
research papers
1898 Hubert Steiner et al.  Structure and composition of Bi–Te topological insulators J. Appl. Cryst. (2014). 47, 1889–1900
Figure 9
(a) Measured lateral lattice parameters a (black circles) of our Bi2Te3À epitaxial layers and calculated
relaxed lateral lattice parameters (open circles) obtained by interpolation of the literature data plotted
as a function of the Te deficit  obtained from the fit. (b) Mean inter-plane distances hÁzi determined
from the positions of the ð0 0 0 15Þð23Þ
and ð0 0 0 30Þð23Þ
diffraction maxima (black circles) as a function
of . Open circles denote the relaxed values of hÁzi obtained after correction for the lateral strain
using equation (8). Colored circles labeled with (mn) represent published lattice parameters a [in (a)]
and inter-plane distances [in (b)] for ideally ordered bulk BimTen phases (Bos et al., 2007). (c) Interplane
distances Áz1;2;3;6;7 determined from the fit of the diffraction curves versus . The inter-plane
distances for bulk Bi2Te3 and Bi1Te1 (Safarov, 1994; Yamana et al., 1979) are denoted by blue and red
circles, respectively. (d) The relative r.m.s. deviation N=N of the numbers of QLs between two Bi–Bi
DLs, quantifying the degree of disorder in the samples, plotted versus . In all panels, the vertical
black, red and green lines denote the values for the (23), (11) and (43) phases with  = 0, 1 and 1.5,
respectively. The black lines in (a), (b) and (c) represent the linear and parabolic fits of the measured
data.
Reprinted page 10 of paper [49] “Structure of Bi2Te3−x films”.
concentration of about n = 2–10 Â 1018
cmÀ3
and electron
mobilities around 900 cm2
VÀ1
sÀ1
at room temperature and
of 1500 cm2
VÀ1
sÀ1
at 77 K. For all other samples, the electron
concentration is well above 1020
cmÀ3
, i.e. two orders of
magnitude larger, and it tends to increase up to 1021
cmÀ3
with
increasing Te deficit . This indicates that the Bi–Bi DLs act as
electron donors. In fact, for Bi2Te3 epitaxial layers grown with
very high excess Te flux containing exclusively QLs, we can
also obtain p-doped layers. For the Te-deficit layers with high
electron concentration and  ! 0:1, the mobilities drop to
around 30 cm2
VÀ1
sÀ1
, practically independent of temperature
and composition. This agrees well with the high degree of
structural disorder in these samples, not only vertically but
also laterally as shown in Fig. 2. The latter is due to the
asynchronous incorporation of the Bi–Bi doublets across the
surface during growth, which gives rise to a high density of
domain boundaries in the lateral direction. Thus, the growth
conditions and composition play a crucial role not only for the
structure of the samples but also for the electronic transport
properties, which are crucial for device applications.
6. Summary
In summary, we have determined the structural and growth
properties of topological insulator Bi2Te3À layers grown by
molecular beam epitaxy on BaF2(111) substrates. We have
demonstrated that, depending on the excess Te flux employed
during deposition, the actual chemical composition Bi2Te3À
varies from  = 1 with no excess Te flux up to  = 0 for the
highest excess flux. The Te content of the epilayers has a
profound influence on their surface morphology as well as on
the structural and transport properties. A detailed analysis of
the X-ray diffraction curves using a statistical model of the
layer stacking revealed that the actual stacking of the twodimensional
Bi and Te layers consists of a random sequence of
Te–Bi–Te–Bi–Te quintuple layers and Bi–Bi double layers.
From the fits of the diffraction data, we determined the 
dependencies of the in-plane lattice parameters and the mean
inter-plane distances, revealing that these values continuously
change as functions of composition, as expected for random
alloys between Bi2Te3 ( = 0) and BiTe ( = 1). However, as the
change in composition is accommodated by insertion of a
larger or smaller number of two-dimensional Bi–Bi double
layers in between the quintuple layers, exclusively absent only
for Bi2Te3, these structures must be regarded as one-dimensional
random alloys rather than as three-dimensional alloys
with statistical occupancy of individual lattice sites by Te or Bi
atoms. The relaxed lattice parameters determined by X-ray
diffraction agree well with those of the homologous series of
ordered BimTen bulk crystals published in the literature. The
individual inter-plane distances within and between the
quintuple layers are found to be nearly independent of
composition, whereas the distances in the Bi–Bi doublets and
between the last Te layer in a quintuplet and the first Bi layer
in the following doublet strongly depend on composition and
are thus responsible for the change of the overall lattice
constants. According to our simulations of the diffraction data,
the Bi2Te3 and Bi1Te1 phases are quite well ordered, while the
intermediate phases exhibit a high degree of disorder with a
maximum disorder for  ’ 1 . In these structures, the statistical
distribution of the number of quintuple layers between Bi–Bi
double layers can be approximated by a Poisson distribution.
The composition and disorder strongly affect the electronic
properties of the layers, and low carrier concentrations and
high mobilities can only be achieved for  ’ 0, corresponding
to the Bi2Te3 phase without any Bi–Bi double layers. As shown
previously (Caha et al., 2013; Sanchez-Barriga et al., 2014),
these layers are well suited for investigations of their topological
surface states and their spin polarization using angularresolved
photoemission spectroscopy.
APPENDIX A
Averaging of the diffracted intensity over random
numbers of the quintuple layers
We define the jth structure unit containing nj QLs and one Bi–
Bi DL. From the rules for the construction of the layer
sequence listed in x4, we derive the following formula for the
unit thickness
Dj ¼ ðnj À 1ÞðÁz1 þ 2Áz2 þ 2Áz3Þ þ 2ðÁz4 þ Áz5 þ Áz6Þ þ Áz7;
ð11Þ
where Ázj are the inter-plane distances defined in Fig. 1. The
structure factor of the jth unit is calculated as a sum of the
contributions of individual layers comprising one unit:
FjðqÞ ¼
P5njþ2
t¼1
ftðqÞ expðÀiqz0
tÞ; ð12Þ
where z0
t is the vertical coordinate of the tth layer within the
structure unit, starting from z0
1 ¼ 0. The formula for the
diffracted intensity can be reformulated using the structure
factors of the units as follows,
EðQÞ ¼ A
PP
j¼1
FjðqÞ expðÀiqzjÞ; zj ¼ D1 þ Á Á Á þ DjÀ1; ð13Þ
and for the ensemble-averaged intensity we obtain
IðQÞ ¼jAj2 PP
j¼1

jFjðqÞj2
exp
Â
2ImðqÞzj
Ã
þ 2Re
&
PP
j¼2
PjÀ1
j0¼1
D
FjðqÞFj0 ðqÞÃ
exp
Â
À iðqzj À qÃ
zj0 Þ
ÃE'!
:
ð14Þ
Performing the ensemble averaging h i we assume that the
random numbers nj of of the QLs are statistically independent.
Then, after some algebra we obtain the following final formula
for the averaged intensity,
IðQÞ ¼ jAj2

P
À 1
 À 1
þ 2Re

 À 
P
À 1
 À 1
À
P
À 1
 À 1
 !& '
; ð15Þ
where we used the following notation:
research papers
J. Appl. Cryst. (2014). 47, 1889–1900 Hubert Steiner et al.  Structure and composition of Bi–Te topological insulators 1899
Reprinted page 11 of paper [49] “Structure of Bi2Te3−x films”.
 ¼ expðiqDÞ
 
;  ¼ exp½2ImðqÞDŠ
 
;
 ¼hFi;  ¼ FÃ
expðÀiqDÞ
 
; 
 ¼ jFj2
 
:
ð16Þ
These averages were calculated numerically assuming a 
distribution of the random numbers nj with the averaged value
N and order m. Neglecting the absorption [i.e. putting Im(q) =
0] and assuming a very large number of structure units
(P ! 1), the resulting formula for the averaged intensity is
rather simple:
IðQÞ ! PjAj2

 þ 2Re

1 À 
 !
: ð17Þ
The work was supported by the Czech Science Foundation
(project 14-08124S) and the Austrian Science Fund FWF
(project IRON-SFB025).
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Reprinted page 12 of paper [49] “Structure of Bi2Te3−x films”.
CHAPTER 4. REPRINTED PAPERS 75
4.3 Optical and structural properties of Bi2(SexTe1−x)3 alloy
The Bi2(SexTe1−x)3 alloy layers were prepared using molecular beam epitaxy. The alloy
layers were studied using ellipsometry and reflectivity in the far-infrared to near-UV range
(0.06 eV to 6.5 eV) at low and room temperatures. The band gap of the layers was determined,
considering the Burstein-Moss shift in highly doped semiconductors. The compositional of
the band gap is non-linear with the maximum at about xSe = 30 %. The alloy is a direct
band gap semiconductor for higher selenium concentrations xSe > 30 %. More tellurium-rich
material xSe < 30 % has an indirect band gap with maxima of the valence band slightly off
Γ-point.
PHYSICAL REVIEW B 96, 235202 (2017)
Interband absorption edge in the topological insulators Bi2(Te1−xSex)3
A. Dubroka,1,*
O. Caha,1
M. Hronˇcek,1
P. Friš,1
M. Orlita,2,3
V. Holý,1,4
H. Steiner,5
G. Bauer,5
G. Springholz,5
and J. Humlíˇcek1
1
Department of Condensed Matter Physics and Central European Institute of Technology,
Masaryk University, Kotláˇrská 2, 611 37 Brno, Czech Republic
2
Laboratoire National des Champs Magnetiques Intenses, CNRS-UGA-UPS-INSA-EMFL, 25, avenue des Martyrs, 38042 Grenoble, France
3
Institute of Physics, Charles University in Prague, CZ-121 16 Prague, Czech Republic
4
Department of Condensed Matter Physics, Charles University, Prague, Czech Republic
5
Institut für Halbleiter- und Festkörperphysik, Johannes Kepler Universität, Altenbergerstrasse 69, 4040 Linz, Austria
(Received 25 September 2017; published 12 December 2017)
We have investigated the optical properties of thin films of topological insulators Bi2Te3, Bi2Se3, and their alloys
Bi2(Te1−xSex)3 on BaF2 substrates by a combination of infrared ellipsometry and reflectivity in the energy range
from 0.06 to 6.5 eV. For the onset of interband absorption in Bi2Se3, after the correction for the Burstein-Moss
effect, we find the value of the direct band gap of 215 ± 10 meV at 10 K. Our data support the picture that Bi2Se3
has a direct band gap located at the point in the Brillouin zone and that the valence band reaches up to the
Dirac point and has the shape of a downward-oriented paraboloid, i.e., without a camel-back structure. In Bi2Te3,
the onset of strong direct interband absorption at 10 K is at a similar energy of about 200 meV, with a weaker
additional feature at about 170 meV. Our data support the recent GW band-structure calculations suggesting that
the direct interband transition does not occur at the point but near the Z-F line of the Brillouin zone. In the
Bi2(Te1−xSex)3 alloy, the energy of the onset of direct interband transitions exhibits a maximum near x = 0.3
(i.e., the composition of Bi2Te2Se), suggesting that the crossover of the direct interband transitions between the
two points in the Brillouin zone occurs close to this composition.
DOI: 10.1103/PhysRevB.96.235202
I. INTRODUCTION
Topological insulators belong to a class of materials that
are insulating in the bulk, however on the surface they exhibit
topological spin-polarized conducting states [1–4]. Since the
spin polarization is potentially usable in spintronic devices,
topological insulators have attracted a lot of attention in the
past decade. Bi2(Te1−xSex)3 compounds, originally employed
for thermoelectric devices due to their large Seebeck constant,
belong to this category thanks to the large spin-orbit coupling
due to heavy bismuth atoms. The linearly dispersing surface
states have been observed by angle-resolved photoemission
spectroscopy (ARPES) [3,5–8]. Samples are usually of n-type
with the Fermi level located in the conduction band because
of the antisite doping related to Se vacancies [9].
The infrared and optical responses of Bi2(Te1−xSex)3 compounds
have been studied intensively in order to characterize
their vibrational properties [10], interband absorption [11–
16], and free charge-carrier properties [13,17–19]. Even
the surface states [20–23] and strong Faraday rotation [24]
have been observed by infrared spectroscopy. Despite the
large experimental effort, several questions remain open. For
example, controversial results on the values of the band
gaps determined by optical spectroscopy and ARPES were
reported [14,18], raising questions about the actual position of
the direct interband transition onset in the Brillouin zone. Here
we present an infrared spectroscopy study of Bi2(Te1−xSex)3
thin films that focuses on the absorption edge of interband
transitions. We discuss and account for the Burstein-Moss
(BM) effect in order to obtain band-gap energies. We compare
*
dubroka@physics.muni.cz
our results with ARPES data and band-structure calculations,
and we discuss the location of the onset of direct interband
transitions in the Brillouin zone.
The paper is organized as follows: In Sec. II we describe
the sample growth, x-ray diffraction results, and details of the
analysis of the optical data. The core of the paper is presented
in Sec. III, where we discuss the results concerning the onset of
interband absorption in Bi2Se3 (Sec. III B), Bi2Te3 (Sec. III C),
and finally in Bi2(Te1−xSex)3 alloys (Sec. III D).
II. EXPERIMENTAL TECHNIQUES
A. Sample preparation and x-ray diffraction
Bi2(Te1−xSex)3 epilayers were grown by molecular beam
epitaxy in a Riber 1000 system under ultrahigh-vacuum conditions
at a background pressure smaller than 5 × 10−10
mbar.
The molecular beams were generated using compound bismuth
telluride or bismuth selenide effusion cells (nominal
composition of Bi2Te3 and Bi2Se3, respectively) operated
at around 400–500 ◦
C, and separate tellurium or selenium
cells operated at around 200–300 ◦
C for stoichiometry control.
The ternary alloys were grown combining Bi2Se3 and Te
effusion cells (low Se content) or Bi2Te3 and Se effusion cells
(high Se content), respectively. The particular flux rates of
the compounds were around 1 ˚A/s for compound cells and
2–3 ˚A/s for tellurium or selenium, which were calibrated by
a quartz crystal microbalance. The layers were deposited on
1-mm-thick cleaved BaF2 (111) substrates at a temperature
between 300 and 400 ◦
C as measured with an infrared optical
pyrometer. The surface structure of the films was monitored by
in situ reflection high-energy electron diffraction evidencing
two-dimensional (2D) growth for all samples under the given
2469-9950/2017/96(23)/235202(10) 235202-1 ©2017 American Physical Society
Reprinted page 1 of paper [85] “Optical properties of Bi2(SexTe1−x)3 alloys”.
A. DUBROKA et al. PHYSICAL REVIEW B 96, 235202 (2017)
FIG. 1. Symmetric x-ray diffraction scans of our Bi2(Te1−xSex)3
samples ordered from bottom to top with increasing selenium content
recorded with Cu Kα1 radiation. The spectra are shifted for clarity
with respect to each other. The corresponding diffraction peaks
shift to the higher Qz values with increasing selenium content x
and decreasing lattice constant c. Solid and dashed lines show the
positions of the Bi2Te3 and Bi2Se3 diffraction peaks, respectively.
The symbols denote calculated structure factors of the Bi2(Te1−xSex)3
lattice assuming a random occupation of Te and Se atoms. Thin black
lines represent simulated diffraction profiles corresponding to the
calculated structure factors.
growth conditions. The Bi2Te3 and Bi2Se3 thin films from this
growth series were recently characterized by x-ray and Raman
spectroscopy [25,26].
The crystalline quality and the composition of our thin
films were determined using x-ray diffraction. The symmetric
scans along the (000l) reciprocal space direction are shown in
Fig. 1 with respect to the scattering vector Qz = 4π/λ sin θ,
where λ = 1.540 56 ˚A is the radiation wavelength and θ is
the Bragg angle. The diffraction peaks of the Bi2(Te1−xSex)3
alloy shift toward higher Qz values with increasing selenium
content and decreasing lattice parameter. The peaks are narrow
in the whole composition range, indicating that no phase
separation occurs in the studied samples. Since the structure
factor of the 000.9 and 000.12 diffractions in Bi2Te3 is very
small, the corresponding diffraction peaks are very weak.
The chemical composition x of the Bi2(Te1−xSex)3 alloy was
determined from the c lattice parameter (see Table I) assuming
a linear concentration dependence of the lattice parameter
(Vegard’s law). The intensities of the diffraction peaks in
Fig. 1 correspond well to calculated structure factors of random
Bi2(Te1−xSex)3 alloys, i.e., with the same probability of Se
and Te atoms occupying all of the anionic positions within the
crystalline structure. The solid lines in Fig. 1 show simulations
of the diffraction spectra with the corresponding structure
factors and peak shape given by the Voigt profile with a
constant width of 0.003 ˚A−1
, evidencing excellent agreement
TABLE I. Composition, x, lattice parameter along the c-axis, c,
thickness, d, square of plasma frequency, ω2
pl, and phonon frequency,
ωα and ωβ , of our Bi2(Te1−xSex)3 thin films determined from 300 K
data. The uncertainties of these values are typically 2% for x, 0.05 ˚A
for c, 2% for d, 5% for ω2
pl, and 2 cm−1
for ωα and ωβ .
x c d ω2
pl ωα ωβ
(%) ( ˚A) (nm) (106
cm−2
) (cm−1
) (cm−1
)
0 30.54 267 5.2 52 95
27 30.06 519 3.1 63 115
74 29.23 207 1.1 66
100 28.75 458 3.0 68 129
with the measured data. The width corresponds to the mean
size of 100 nm of the coherently diffracting domains. Sharp
diffraction peaks indicate high crystalline quality of the layers
and homogeneous chemical composition in the layer.
B. The optical spectroscopy and analysis of optical data
The optical properties were probed from the midinfrared to
ultraviolet range using a combination of two commercial ellipsometers,
Woollam IR-VASE (60–700 meV) and Woollam
VASE (0.6–6.5 eV), equipped with variable retarders. In the
ellipsometric experiments, the two ellipsometric angles ,
and the depolarization are recorded [27]. The angles are linked
to the Fresnel reflection coefficients for the p- and s-polarized
waves, rp and rs, respectively, as tan ei
= rp/rs. From the
two angles, using a proper model for the layered structure,
the real and imaginary parts of the dielectric function can
be determined without the Kramers-Kronig relations. The
room-temperature spectra of and with respect to the
photon energy E are shown in Fig. 2 (symbols) together
with those of a model (solid lines) described below. The
ellipsometric data were complemented in the far-infrared
range (4–85 meV, 30–680 cm−1
) with near-normal incidence
reflectance (see Fig. 3) measured with a Bruker Vertex 80v
Fourier transform spectrometer. A gold mirror was used as a
reference. The low-temperature data were acquired in the midinfrared
range with the Woollam IR-VASE ellipsometer using
a closed He-cycle cryostat. The cryostat was equipped with
an ultralow vibration interface in order to decouple vibrations
of the Gifford-McMahon refrigerator from the ellipsometer.
The pressure in the cryostat chamber was 1 × 10−7
mbar
at 300 K.
The data were analyzed with a model of coherent interferences
in a thin film on a substrate. The dielectric function of
BaF2 was obtained from measurements on a bare substrate;
e.g., for far-infrared data, see Fig. 3(a). In the model, we
have taken into account also the incoherent reflections from
the back side of the BaF2 substrate that is cleaved and thus
reflecting. The surface roughness was taken into account using
an effective-medium approximation (Bruggeman model) [27].
The thickness of the surface roughness layer obtained from
the fitting was between 5 and 11 nm, in good agreement with
an rms roughness value between 4 and 9 nm obtained by
atomic force microscopy. The surface roughness correction is
increasingly important with a decreasing wavelength of light
λ, e.g., it significantly influences the dielectric function above
235202-2
Reprinted page 2 of paper [85] “Optical properties of Bi2(SexTe1−x)3 alloys”.
INTERBAND ABSORPTION EDGE IN THE TOPOLOGICAL . . . PHYSICAL REVIEW B 96, 235202 (2017)
10
20
30
40
0.1 1
E [eV]
Ψ[deg]
Ψ data
Ψ model
0
90
180
270
Δ data
Δ model
Δ[deg]
(a) x=0% (Bi2
Te3
)
0.1 1
-90
0
90
180
270
E [eV]
(d)
Δ data
Δ model
Δ[deg]
x=100%
0
10
20
30
40
Ψ[deg]
Ψ data
Ψ model
-90
0
90
180
270
Δ data
Δ model
Δ[deg]
x=74%
0
20
40
60
80
(c)
Ψ data
Ψ model
Ψ[deg]
-90
0
90
180
270
Δ data
Δ model
Δ[deg]
x=27%
0
10
20
30
40
(b)
Ψ data
Ψ model
Ψ[deg]
FIG. 2. Measured ellipsometric angles and at 300 K
(symbols) and model spectra (solid lines) of our Bi2(Te1−xSex)3
samples with x = 0% (a), 27% (b), 74% (c), and 100% (d) as a
function of photon energy E. The angle of incidence was 70◦
.
about 1 eV (λ ≈ 1 μm), however it has a negligible impact
at lower energies. As the first step, we analyzed the response
of the thin films in the whole measured frequency range. We
have modeled the dielectric function of the layer as the sum
ˆε(ω) = 1 −
ω2
pl
ω(ω + iγ )
+
j
ω2
pl,j
ω2 − ω2
j − iγj
+
j
ˆGj (ω),
(1)
where the angular frequency, ω, relates to the photon energy,
E, as E = ¯hω. The model consists of the Drude term for
itinerant electrons (second term on the right-hand side),
Lorentz oscillators for transverse optical phonons (third term
on the right-hand side), and a set of Gaussian oscillators ˆGj (ω)
for interband transitions [27]. The fit of model spectra to the
data was performed using the Woollam WVASE software.
0.0
0.2
0.4
0.6
0.8
1.0
R
(a)
x=0%
(Bi2
Te3
)
BaF2
0 25 50 75
0.0
0.2
0.4
0.6
0.8
1.0
E [meV]
(d)
R
x=100%
(Bi2
Se3
)
0 25 50 75
0.0
0.2
0.4
0.6
0.8
1.0
(c)
R
E [meV]
x=74%
0.0
0.2
0.4
0.6
0.8
1.0
(b)
R
x=27 %
0 200 400 600
wavenumber [cm
-1
]
0 200 400 600
wavenumber [cm
-1
]
FIG. 3. Far-infrared reflectivity of our Bi2(Te1−xSex)3 thin films
on BaF2 substrate at 300 K (symbols) together with model spectra
(solid lines). Shown are results for samples with x = 0% (a), 27%
(b), 74% (c), and 100% (d). In addition, the data (magenta circles)
and the model spectrum (solid line) of the BaF2 substrate are shown
in panel (a).
The obtained best-fit model spectra, which are displayed in
Figs. 2 and 3 as solid lines, are in very good agreement
with the data (symbols). The main features in the raw spectra
in the far-infrared frequency range are as follows (see Fig. 3):
the strong (so-called α) phonon between 52 and 68 cm−1
, the
much weaker (so-called β) phonon between 95 and 130 cm−1
,
and the BaF2 substrate phonon at 186 cm−1
. The frequencies of
the α and β phonons (see Table I) compare well with reported
values [10,14,18]. Between about 0.1 and 0.8 eV (see Fig. 2),
the films are transparent and the raw ellipsometric data exhibit
fringes due to interference in the layer. Above this range, the
thin films are opaque and the features are solely due to the
electronic interband transitions.
First we attempted to obtain the plasma frequency of the
itinerant charge carriers, ωpl, and the thickness of the layer, d.
The results are summarized in Table I. The thickness values
were consequently used in the point-by-point retrieval of the
dielectric function in the frequency range of ellipsometric data.
We have assumed that the response of the layer is isotropic.
This is certainly an approximation for the anisotropic response
of Bi2(Te1−xSex)3 caused by the rhombohedral crystal
structure. In general, in the oblique reflectance geometry of
an ellipsometric measurement, the out-of-plane component
of the dielectric function is probed as well, although the
main contribution to the data usually corresponds to the
in-plane component. However, if the value of the index of
refraction is high, the wave refracts close to the sample normal,
and the anisotropic corrections are quite small unless the
out-of-plane dielectric function has strong resonances in the
loss function [28,29]. These requirements are fulfilled between
0.1 and 0.7 eV, where the index of refraction is high (about
6–7).
235202-3
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A. DUBROKA et al. PHYSICAL REVIEW B 96, 235202 (2017)
0.01 0.1 1
0
5000
10000
300 K
α
σ1
[Ω
-1
cm
-1
]
E [eV]
74%27%
100%
(Bi2
Se3
)
x=0%
(Bi2
Te3
)
0.0 0.2 0.4 0.6
0
10
20
30
40ε2
E [eV]
74%
27%
100%
x=0%
(Bi2
Te3
)
FIG. 4. The real part of the optical conductivity at 300 K of the
Bi2(Te1−xSex)3 samples in the whole measured frequency range. The
inset displays the region of the onset of interband absorption in terms
of ε2.
III. DISCUSSION
A. Overview of the absorption spectra
Figure 4 shows the spectra of our Bi2(Te1−xSex)3 thin films
at room temperature in the whole measured spectral range
in terms of the real part of the optical conductivity σ1(ω) =
ωε0ε2(ω), where ε0 is the permittivity of vacuum and ε2(ω) is
the imaginary part of the dielectric function. The prominent
absorption structures are due to the α phonon between 6 and
9 meV, a weak free charge-carrier response, and the interband
transitions setting in above ≈0.1 eV. In the following, we
focus on the region of interband absorption edge between 0.1
and 0.7 eV, displayed in the inset of Fig. 4 in terms of ε2.
Above the band gap, the maximum values of ε2 range from
about 5 for the least absorbing Bi2Se3 sample up to about 40
for the most absorbing Bi2Te3 sample. These high values are
typical for direct interband transitions. Indirect transitions have
values of ε2 typically several orders of magnitude smaller [30].
Therefore, all the interband transitions discussed in this paper
are direct, and we designate their onset energy as Edirect
g .
The real part of the dielectric function, ε1, shown in Fig. 5,
exhibits large values below the interband transitions (∼0.2 eV)
that range from 30 for Bi2Se3 up to more than 70 for Bi2Te3.
The zero crossing of ε1 above 5 eV indicates the renormalized
plasma resonance of all valence electrons. The electronic
polarizability is essentially due to the interband transitions
below ∼4 eV; the contribution of the interband transitions
above the measured frequency range to the low-energy value
of ε1 is relatively small (about 1). At the lowest measured
energy (∼5 meV; see the inset of Fig. 5), ε1 reaches several
hundred due to the low-lying α-phonon.
B. The absorption edge in Bi2Se3
Figure 6(a) shows the temperature dependence of ε2 of
the Bi2Se3 thin film in the midinfrared range. The onset of
interband transitions with lowering temperature sharpens and
shifts to higher energies similarly to previously published
results [18]. The weak feature near 250 meV, which is most
visible in the 80 K spectrum, is an artefact due to the sharp
0.01 0.1 1
-600
-400
-200
0
200
400
600
800
ε1
E [eV]
74%
27%
100% (Bi2
Se3
)
x=0% (Bi2
Te3
)
0 1 2 3 4 5 6
-20
-10
0
10
20
30
40
50
60
70
80
E [eV]
300 K
ε1
74%
27%
100%
(Bi2
Se3
)
x=0% (Bi2
Te3
)
FIG. 5. The real part of the dielectric function, ε1, at 300 K of
the Bi2(Te1−xSex)3 samples above the phonon energy range. The
inset displays the data on a semilogarithmic scale including the large
polarizability due to the α-phonon.
interference structure at this energy [see Fig. 2(d)]. Below
the onset of interband transitions at low temperature, ε2 is
zero within the uncertainty of the analysis. This is consistent
with the observed transmission values up to 14% measured
on 225-μm-thick single crystal [24], which is possible only if
ε2 0.1.
Due to a significant concentration of free electrons, the
Fermi level, EF, lies in the conduction band. Consequently,
the minimal energy necessary to excite the electrons from the
valence to the conduction band, Emin, is larger than the band
gap Edirect
g because of the Pauli blocking of the states below EF.
The latter effect is known as the Burstein-Moss (BM) effect
or shift [31,32]. In such a case, a step in the absorption is
expected. Indeed, it can be seen in Fig. 6(a) that at 10 K, ε2(E)
has a steplike shape reaching a value of about 5 in a rather
narrow interval 290–340 meV. The representative energy of
such an onset can be estimated as the middle point of the step,
≈310 meV, as shown by the arrow. In a more sophisticated
way, the onset can be determined with the help of the critical
point model fitted to the second derivative of the dielectric
function [33,34]. The contribution of a parabolic critical point
(CP) located at an energy ECP to the jth derivative of the
dielectric function is
dj
ˆε(E)
dEj
= Aeiφ
(E − ECP + i )−n−j
, (2)
where A and φ are the amplitude and the phase factor,
and n has the values −1/2, 0, and 1/2 for a three-, two-,
and one-dimensional CP, respectively. We have modeled the
second derivative (j = 2) of the dielectric function shown
in Fig. 6(b) with a sum of two CP functions of Eq. (2).
The data below 280 meV were omitted because of spurious
structures due to the interference mentioned above. The most
pronounced structure centered at 312 meV was modeled with
a two-dimensional CP (n = 0) that corresponds to the step
in ε2 [27]. Its center energy is very close to the middle
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INTERBAND ABSORPTION EDGE IN THE TOPOLOGICAL . . . PHYSICAL REVIEW B 96, 235202 (2017)
0
1
2
3
4
5
6
7
8
100 200 300 400 500 600 700ε2
300 K
260 K
200 K
120 K
80 K
10 K
(a) Bi2
Se3
100 200 300 400 500 600 700
-4000
-2000
0
2000
d
2
ε1
/dE
2
data
d
2
ε2
/dE
2
data
model
T=10K
d
2
ε1,2
/dE
2
E [meV]
(b)
FIG. 6. (a) Temperature dependence of the imaginary part of the
dielectric function, ε2, of Bi2Se3. The arrows mark the energy of
the lowest critical point at 10 and 80 K, respectively. (b) Second
derivative of the real (red squares) and imaginary part (blue triangles)
of the dielectric function at 10 K together with the spectrum of the
critical point model (solid lines) specified in the text.
point estimated above. The weak structure near 450 meV was
modeled with a three-dimensional CP.
Assuming for simplicity that the conduction and valence
bands are parabolic, Emin and Edirect
g are related as
Emin = Edirect
g +
¯h2
k2
F,a
2
1
ma
e
+
1
ma
h
, (3)
where kF,a is the in-plane Fermi wave vector, and ma
e and ma
h
are the in-plane effective masses of the conduction and valence
band, respectively [12]. With the help of the expression for the
Fermi level with respect to the bottom of the conduction band,
EF = ¯h2
k2
F,a/(2ma
e ), Eq. (3) can be rewritten as
Emin = Edirect
g + EF 1 +
ma
e
ma
h
. (4)
Since Bi2Se3 is anisotropic, the equienergy contour at the
Fermi level has an ellipsoidal shape in k-space. For the case of
biaxial anisotropy, the Fermi level can be calculated from the
concentration of charge carriers n as
EF =
¯h2
2(ma
e mb
emc
e)1/3
3π2
n
2/3
, (5)
where ma
e , mb
e, and mc
e are the three effective masses. In
the case of the uniaxial anisotropy of Bi2Se3, ma
e = mb
e. We
have determined the concentration of charge carriers from
their plasma frequency ωpl (see Table I) as n = ω2
plma
e ε0/e2
,
where e is the elemental charge. For the evaluation of the
BM shift, the following values of effective masses were used:
ma
e = 0.14 m [35] and ma
h = 0.24 m [36], where m is the
free-electron mass. The c-axis effective mass can be calculated
from the effective-mass anisotropy mc
e/ma
e = 1.6 obtained for
a Fermi energy ≈50 meV [37] above the conduction-band
minimum, which is relevant for our sample. With these
values, the BM shift amounts to 98 meV and the resulting
band-gap value is Edirect
g = 215 ± 10 meV at 10 K. The
uncertainty is estimated from that of the effective masses. The
calculation of the BM shift is based on the parabolic profile
of the conduction and valence bands. The latter assumption
is reasonably fulfilled for our relatively weakly doped sample
with n = 4.8 × 1018
cm−3
, which is below the threshold of
≈1019
cm−3
, above which a significant nonparabolicity of the
conduction band has been observed [37]. Similarly, the valence
band was reported [36] to have a parabolic shape for the Fermi
wave vector corresponding to our sample (kF,a ≈ 0.04 ˚A−1
).
In the following, we compare the obtained value of Edirect
g
with literature values for the band gap determined by optical
spectroscopy and corrected for the BM shift. In their early
study, Köhler and Hartman [12] reported on a BM shift in
a series of single crystals with varying levels of doping, and
they found Edirect
g = 160 meV ± 10 % at 77 K. Based on an
extrapolation, these authors estimated that the 0 K value would
be 175 meV ± 10 %. However, it seems that the temperature
shift was underestimated. In our data, the shift of the absorption
edge between 80 and 10 K is about 35 meV. When taking
into account this value, we obtain Edirect
g ≈ 195 meV at 10 K.
In a recent study on thin films [18], Post et al. reported
Edirect
g = 190 meV for a 99 quintuple-layer-thick film. The
onset of absorption was obtained based on the extrapolation
of ε2
2 to zero. If this procedure is used for our data, we obtain
Edirect
g ≈ 200 meV, a value closer to the one obtained by Post
et al. [18]. From a recent transmission experiment on single
crystals, Ohnoutek et al. [24] reported Edirect
g ≈ 200 meV.
Notably, a very recent work [38] combining luminescence,
transmission, and magnetotransport measurements estimated
that the gap value is 220 ± 5 meV, which agrees within the
error bars with our result. The values from all these reports
fall into an interval 190–220 meV at 10 K and represent a
fairly robust estimate for the value of the direct band gap. The
differences between the results are presumably due to different
ways in which the onset of absorption is defined and how the
MB shift is calculated.
Post et al. [18] noted that these values are significantly
smaller than the direct-band-gap value of 300 meV determined
from some early ARPES data [3]. However, in later ARPES
data with an improved signal-to-noise ratio, there is a noticeable
intensity reaching up to the Dirac point located at about
0.2 eV below the bottom of the conduction band [6,39–43].
Explicitly, Chen et al. concluded that the valence band in
Bi2Se3 extends up to the Dirac point from below [6]. In view
of the more recent ARPES data, it becomes clear that the
valence band is a downward-oriented paraboloid located at
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A. DUBROKA et al. PHYSICAL REVIEW B 96, 235202 (2017)
0
10
20
30
40
100 200 300 400 500 600 700
E [meV]ε2
300 K
200 K
100 K
70 K
40 K
10 K
Bi2
Te3
(a)
100 200 300 400 500 600 700
-15000
-10000
-5000
0
5000
10000
d
2
ε1
/dE
2
data
d
2
ε2
/dE
2
data
model
d
2
ε1,2
/dE
2
E [meV]
(b) T=10 K
150 200
5
10
15ε2
FIG. 7. (a) Temperature dependence of the imaginary part of the
dielectric function, ε2, of the Bi2Te3 sample. The inset shows the
spectra on magnified scales. (b) Second derivative of the real (red
squares) and imaginary part (blue triangles) of the dielectric function
at 10 K together with critical point model spectra (solid lines). The
arrows mark the positions of four critical points.
about 0.2 eV below the bottom of the conduction band and
thus in accord with the ≈215 meV direct gap derived above.
The M (or camelback) structure seen in ARPES data might
be due to surface states or to a deeper-lying structure in the
valence bands [40]. The latter scenario is confirmed by recent
Shubnikov–de Haas (SdH) measurements [36] concluding that
the top of the valence band is a downward-oriented paraboloid
with no signatures of an M shape of the top of the valence band.
Note that the M structure of the valence band seen in some
LDA band-structure calculations [44] is absent in the more
realistic results of GW calculations [43,45,46] that exhibit a
paraboloidal shape of the valence band.
C. The absorption edge in Bi2Te3
Figure 7(a) displays the temperature dependence of ε2 of
our Bi2Te3 thin film. The absorption edge blueshifts with lower
temperature similarly to Bi2Se3. To obtain the energy of the
CPs, we have fitted the second derivative of the dielectric
function with a set of three-dimensional CPs of Eq. (2).
Figure7(b) displays thesecondderivativeat T = 10Ktogether
with a model consisting of four CPs centered at 202, 362,
408, and 575 meV as marked by the arrows. At 300 K (not
shown), the obtained energy of the lowest CP is 157 meV.
If the extrapolation of ε2
2(E) toward zero is used to define
Emin, we obtain the values 190 and 152 meV at 10 and 300 K,
respectively. Interestingly, the absorption onset is sharper at
300 K than at 10 K [see the inset of Fig. 7(a)], which is opposite
to what is expected from thermal broadening effects. We have
checked that this effect is not due to a freezing of the residual
atmosphere on the sample at low temperature. Obviously
below the main interband absorption that sets in near 200 meV
at 10 K, an additional weaker interband absorption occurs with
an onset at about 170 meV. Although it is weaker than the main
interband transition, the magnitude of this absorption is still
large (of the order of unity in ε2), therefore it most likely
corresponds to a direct interband transition. The energy of this
onset is the same as that found in an earlier report by Sehr and
Testardi [47].
Chapler et al. [14] reported the onset of interband absorption
in Bi2Te3 thin films between 140 and 150 meV at 300 K,
not too different from our value of 157 meV. Their onset value
did not exhibit a significant blueshift with cooling to 10 K.
A direct gap was observed in Ref. [48] at 220 meV with a
weak onset at 150 meV on relatively highly doped Bi2Te3.
The difference in the reported values is presumably caused by
differences in the doping level and related MB shift and/or by
a difference in the definition of the onset energy. Regardless
of these relatively small differences, as noted by Chapler
et al. [14], the onset of absorption at 10 K (≈200 meV in our
data) is significantly smaller than the 290 meV value of the
direct band gap at the point observed in ARPES [5,49]. Note
that in our data, the value of ε2 at 290 meV is about 25, which
corresponds to a very strong absorption due to direct interband
transitions. Obviously, the onset occurs at a different point
in the Brillouin zone. Band-structure calculations [44,50–52]
indeed suggest that the direct gap should be close to the Z-F
line in the Brillouin zone, where the interband transition energy
is significantly smaller than that at the point. The band-gap
values have been treated theoretically in detail in Ref. [51]
using the GW calculations. Direct interband transitions are
predicted close to the Z-F line with an onset at 168 meV, in
reasonably good agreement with our experimental value. In
the calculations, it appears that their location is not exactly
on the Z-F line but is close to about 1.3Z; see Fig. 3(d) in
Ref. [51]. An indirect fundamental band gap is predicted at a
slightly lower energy of 156 meV.
ARPES results suggest that this interpretation is likely.
The conduction band in Bi2Te3 has a strong hexagonal
warping [5,49]. The ARPES intensity related to the conduction
band is centered at the point, however it has a snowflake-like
shape with protrusions extending into the -M direction. This
direction of the projected surface Brillouin zone measured by
ARPES involves the Z-F line of the bulk Brillouin zone. Since
the valence band has an M shape, its energy increases from the
toward the M point and reaches a maximum at k ≈ 0.13 ˚A−1
,
where the difference between the valence and conduction band
seems to be about 0.2 eV, a value compatible with our optical
spectroscopy data.
According to the GW calculations [51,52], the structure
of the calculated valence and conduction band along the Z-F
line is rather complicated; it seems to have several extrema.
It is possible that with changing temperature, the position of
the lowest direct band gap changes, and at low temperature
an interband transition with a smaller joint density of states
235202-6
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INTERBAND ABSORPTION EDGE IN THE TOPOLOGICAL . . . PHYSICAL REVIEW B 96, 235202 (2017)
compared to the main one sets in and gives rise to the observed
onset at 170 meV.
We estimate that the BM shift in Bi2Te3 is much smaller
than in Bi2Se3. The main reason is that, as seen in the ARPES
data [5,49], the electrons populate first the conduction-band
states located at the point or along the -Z line [52] that
lie at a smaller energy than those along the Z-F line. As a
consequence, the minimum excitation energy is not increased
for weakly doped samples. The BM shift likely occurs only
for strongly doped samples where the Fermi level enters the
conduction bands at the Z-F line. Secondly, the very steep
increase of ε2 above the band-gap edge is caused by a quite
large joint density of states due to fairly flat bands where only
a relatively small BM shift can be expected.
As a summary for Bi2Te3, at 10 K we observed a strong
direct interband transition at about 200 meV accompanied
with an onset of a weaker direct interband transition at about
170 meV. As suggested by band-structure calculations, the
direct transition occurs near the Z-F line in the Brillouin zone.
Since along the -Z line the energy of the conduction band
lies at a lower energy than along the Z-F line, as suggested
by the band-structure calculations and ARPES [51,52], there
should be an indirect band gap with an energy even lower than
170 meV, i.e., Bi2Te3 is an indirect semiconductor. However,
these indirect transitions are masked in our data by the much
stronger response of free charge carriers that yields a value of
about 5 for ε2 below Edirect
g . Since typically an indirect gap
will not contribute to ε2 with a value larger than about 0.1,
consequently for our thin-film samples we cannot observe its
contribution to the absorption.
D. The absorption edge in Bi2(Te1−xSex)3
Figure 8(a) shows ε2 spectra at 10 K of our alloy x =
27% and 74% samples. For comparison, the spectra of Bi2Se3
and Bi2Te3 are shown as well. The spectrum of the x = 27%
sample is qualitatively similar to that of Bi2Te3, i.e., it exhibits
a very steep increase above the onset at 390 meV, reaching high
values of ε2 of about 25. On the contrary, the spectrum of the
x = 74% sample is qualitatively similar to that of Bi2Se3, i.e.,
it displays a relatively gradual increase of absorption above
the edge up to the values of ε2 ≈ 10. This suggests that the
absorption edge occurs at the same point in the Brillouin zone,
i.e., the point for the x = 74% sample, whereas for the
x = 27% sample it is rather at a point close to the Z-F line of
the Brillouin zone, as for Bi2Te3.
We have analyzed the spectra in a similar way to that
described above by fitting the second derivative of ˆε(E) with
the CP model of Eq. (2). The second derivative of ˆε(E) for
the x = 74% sample is shown in Fig. 8(b) together with the
model consisting of two CP contributions marked by arrows.
Similarly to Bi2Se3, the strong CP centered at 300 meV is
modeled with a two-dimensional CP, and the weak one at
525 meV is modeled with a three-dimensional CP. Using the
same formulas as for the Bi2Se3 sample, the BM shift amounts
to 33 meV, and the band-gap value is 270 ± 10 meV.
The second derivative of ˆε(E) of the x = 27% sample is
shown in Fig. 8(c). Unfortunately, here the spectra, similarly
to our Bi2Se3 sample, exhibit near 180 and 330 meV artefacts
that correspond to interference fringes [see Fig. 2(b)]. These
0
10
20
30
40
50
100 200 300 400 500 600 700
100 % (Bi2
Se3
)
74%
27%
photon energy [meV]
ε2
x=0%
(Bi2
Te3
)
Bi2
(Te1-x
Sex
)3
, T=10 K
EM
(a)
-4000
-3000
-2000
-1000
0
1000
2000
3000
d
2
ε1
/dE
2
data
d
2
ε2
/dE
2
data
model
model
x=27%, T=10 K
x=74% , T=10 K
d
2
ε1,2
/dE
2
(b)
100 200 300 400 500 600 700
-40000
-20000
0
20000
d
2
ε1
/dE
2
data
d
2
ε2
/dE
2
data
d
2
ε1,2
/dE
2
photon energy [meV]
(c)
FIG. 8. (a) The imaginary part of the dielectric function of our
Bi2(Te1−xSex)3 samples at 10 K. The arrows mark the energy EM of
the maximum of ε2. (b) The second derivative of the real (black thin
line) and imaginary part (red thin line) of the dielectric function at
10 K of the x = 74% sample together with the critical point model
spectra (thick lines). The arrows mark the position of two critical
points. (c) The second derivative of the real (black line) and imaginary
part (red line) of the dielectric function at 10 K of the x = 27%
sample. The arrow marks the position of the main critical point.
The structures near 180 and 330 meV are interference artefacts, as
discussed in the text.
artefacts prevent us from fitting the data with the CP model;
nevertheless, it is clear that the strongest feature centered
at about 400 meV (marked by the arrow) corresponds to
the strongest CP related to the onset of the direct interband
transitions. Similarly to Bi2Te3, below this CP a weaker
absorption occurs with the onset at about 340 meV; see
Fig. 8(a). The plasma frequency of this sample is even smaller
than that of the Bi2Te3 sample (see Table I), and thus, similarly
to Bi2Te3, we estimate that the BM shift is either absent or
negligibly small. Both the CP energy of 400 meV and the
onset at 340 meV are significantly larger than the band-gap
value of 290 meV reported [21] for a sample with similar Se
content x = 33%. However, the energy of the maximum of
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A. DUBROKA et al. PHYSICAL REVIEW B 96, 235202 (2017)
(a)
(b)
(c) (d)
FIG. 9. (a) The energy EM of the maximum of ε2 of
Bi2(Te1−xSex)3 marked by the arrows in Fig. 8. The dashed line
is a guide to the eye. (b) Extracted values of the onset of direct
interband transitions, Edirect
g , at 10 K defined as the center position of
the main lowest critical point (squares). The values for x = 76% and
100% were corrected for the Burstein-Moss shift as described in the
text. The triangles represent the onset of a weaker direct interband
absorption below the main critical point. The circles are previously
reported [11] absorption edge energies at 300 K corrected for the
Burstein-Moss effect. Parts (c) and (d) schematically represent the
position of the direct interband transitions (red arrows) in the band
structure for Se content x < xc (c) and x > xc (d), respectively, where
xc ≈ 30%. The green arrow in (c) depicts the indirect fundamental
gap (see Refs. [51,52]).
ε2 denoted here as EM [see the arrows in Fig. 8(a)] occurs
at different energy, namely at 520 meV at 10 K in the case
of Ref. [21], whereas it is at 475 meV in our data. Since the
energy of this maximum strongly increases with increasing
x [see Fig. 9(a)], it is likely that the composition of the two
samples is different, the one of Ref. [21] having a significantly
larger value of x than our sample. We attribute the maximum
EM to a CP related to the Z-F line whose energy increases
monotonically with Se content.
Figure 9(b) displays the extracted values of the onset of
direct interband transitions, Edirect
g , at 10 K of all our samples.
The squares correspond to the main CP energies. For the
x = 74% and 100% samples, these were corrected for the
BM shifts, while for the other two samples we expect that
the BM shift is absent or small. The triangles correspond to a
weaker absorption observed in the spectra of the x = 0% and
27% samples that is likely due to a weaker direct interband
transition, as discussed above. In general, the dependence
of the band-gap value on selenium content has a rooflike
shape with a maximum for the x = 27% sample. This shape
is very similar to the one reported for band-gap values at
300 K corrected for the Burstein-Moss effect in the early
work of Greenaway and Harbecke [11], which are added
for comparison to Fig. 9(b) as circles. The latter dependence
exhibits a pronounced maximum of the direct gap near x =
30% content; our values are of course larger since they were
obtained at 10 K. Similarly to their conclusion, we suggest that
the direct interband transitions on the left and right side of the
maximum corresponds to different points in the Brillouin zone.
The position of the onset of direct interband transitions in the
band structure for the two cases is schematically represented
in Figs. 9(c) and 9(d) by red arrows. Figure 9(d) depicts a
direct band gap in the center of the Brillouin zone between
parabolic-like bands that occurs on the Bi2Se3 side of the
Bi2(Te1−xSex)3 alloy. On the Bi2Te3 side shown in Fig. 9(c),
the direct band gap occurs off the Brillouin-zone center near the
Z-F line, between the wing of the M-shaped valence band and
a conduction band [51,52]. The green arrow depicts the indirect
fundamental gap, which, however, has orders of magnitude
lower absorption and therefore is masked in our data by the
much stronger free charge-carrier response.
IV. CONCLUSION
We have examined the optical response of Bi2(Te1−xSex)3
thin films, which reveal direct interband transitions. In Bi2Se3,
after the correction for the Burstein-Moss effect, we find a
band-gap value of 215 ± 10 meV at 10 K, in good agreement
with the values from 190 to 220 meV reported in the
literature [12,18,24,38]. Our result supports the conclusion
of ARPES [6], GW calculations [45,46], and SdH measurements
[36] that the direct band gap of Bi2Se3 is located at the
point in the Brillouin zone, and the valence band reaches
up to the Dirac point and has a shape of a downward-oriented
paraboloid.
In Bi2Te3, we observe a strong interband absorption that
sets in at ≈200 meV at 10 K and a weaker albeit still direct
interband transition with an onset at about 170 meV. These
values support GW band-structure calculations that proposed
that the direct interband transition occurs near the Z-F line.
In the ternary Bi2(Te1−xSex)3 alloys, the energy of the onset
of the direct interband transition goes through a maximum for
a Se content of about 30%. This behavior indicates that there
is a crossover of the position of the direct interband transitions
between the two different points in the Brillouin zone at this
Se content.
ACKNOWLEDGMENTS
We acknowledge helpful discussions with I. Aguilera.
This work was financially supported by the European
Regional Development Fund Project CEITEC Nano+
(No. CZ.021.01/0.0/0.0/16_013/0001728), CEITEC Nano Research
Infrastructure (ID LM2015041, MEYS CR, 2016–
2019), CEITEC Brno University of Technology, and by EC
via the TWINFUSYON project (No. 692034).
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INTERBAND ABSORPTION EDGE IN THE TOPOLOGICAL . . . PHYSICAL REVIEW B 96, 235202 (2017)
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CHAPTER 4. REPRINTED PAPERS 86
4.4 Manganese doping of Bi2Se3 topological insulator
The (Bi,Mn)2Se3 layers on BaF2 were prepared and analyzed. The ARPES analysis has
shown a band gap in Dirac point to be large ≈ 100 meV, and temperature independent. The
ferromagnetic Curie temperature of about 10 K was determined by SQUID magnetometry
and XMCD. The magnetic easy axis direction is in-plane. The band gap surviving up to
room temperature is of non-magnetic origin.
ARTICLE
Received 13 Jun 2015 | Accepted 26 Dec 2015 | Published 19 Feb 2016
Nonmagnetic band gap at the Dirac point of the
magnetic topological insulator (Bi1 À xMnx)2Se3
J. Sa´nchez-Barriga1, A. Varykhalov1, G. Springholz2, H. Steiner2, R. Kirchschlager2, G. Bauer2, O. Caha3,
E. Schierle1, E. Weschke1, A.A. U¨nal1, S. Valencia1, M. Dunst4, J. Braun4, H. Ebert4, J. Mina´r4,5, E. Golias1,
L.V. Yashina6, A. Ney2, V. Holy´7 & O. Rader1
Magnetic doping is expected to open a band gap at the Dirac point of topological insulators
by breaking time-reversal symmetry and to enable novel topological phases. Epitaxial
(Bi1 À xMnx)2Se3 is a prototypical magnetic topological insulator with a pronounced surface
band gap of B100 meV. We show that this gap is neither due to ferromagnetic order in the
bulk or at the surface nor to the local magnetic moment of the Mn, making the system
unsuitable for realizing the novel phases. We further show that Mn doping does not affect the
inverted bulk band gap and the system remains topologically nontrivial. We suggest that
strong resonant scattering processes cause the gap at the Dirac point and support this by the
observation of in-gap states using resonant photoemission. Our findings establish a
mechanism for gap opening in topological surface states which challenges the currently
known conditions for topological protection.
DOI: 10.1038/ncomms10559 OPEN
1 Helmholtz-Zentrum Berlin fu¨r Materialien und Energie, Elektronenspeicherring BESSY II, Albert-Einstein-Strae 15, 12489 Berlin, Germany. 2 Institut fu¨r
Halbleiter und Festko¨rperphysik, Johannes Kepler Universita¨t, Altenbergerstr. 69, 4040 Linz, Austria. 3 Department of Condensed Matter Physics, CEITEC,
Masaryk University, Kotlarska 2, 61137 Brno, Czech Republic. 4 Department Chemie, Ludwig-Maximilians-Universita¨t Mu¨nchen, Butenandtstr. 5-13,
81377 Mu¨nchen, Germany. 5 New Technologies Research Centre, University of West Bohemia, Univerzitni 8, 306 14 Pilsen, Czech Republic. 6 Department of
Chemistry, Moscow State University, Leninskie Gory 1/3, 119991 Moscow, Russia. 7 Department of Condensed Matter Physics, Charles University, Ke Karlovu 5,
12116 Prague, Czech Republic. Correspondence and requests for materials should be addressed to J.S.-B. (email: jaime.sanchez-barriga@helmholtz-berlin.de) or
to O.R. (email: rader@helmholtz-berlin.de).
NATURE COMMUNICATIONS | 7:10559 | DOI: 10.1038/ncomms10559 | www.nature.com/naturecommunications 1
Reprinted page 1 of paper [86] “Temperature independent gap in (Bi,Mn)2Se3 layers”.
T
he topological surface state (TSS) of the three-dimensional
topological insulator (3D TI) Bi2Se3 forms a Dirac cone in
the band dispersion E(k||) of electron energy E versus wave
vector component k|| parallel to the surface1. Differently from
graphene, the electron spin is nondegenerate and locked to k||,
and the Dirac crossing point is protected by time-reversal
symmetry (TRS) against distortions of the system1,2. This stability
has been theoretically investigated demonstrating that
nonmagnetic impurities at the surface and in the bulk can form
a resonance in the surface-state density of states (DOS) without
opening a band gap3–5. A magnetic field breaks TRS lifting the
Kramers degeneracy E(k||, m) ¼ E( À k||, k) between up (m) and
down (k) spins, and can open a band gap at the Dirac point1. For
the two-dimensional quantum-spin-Hall system HgTe, the effect
of a perpendicular magnetic field on the topologically protected
edge state has been demonstrated successfully6, and similar
effects are expected from magnetic impurities in this system7.
In subsequent studies on HgTe, the effect of the magnetic
field was much smaller, and recently in an inverted electronhole
bilayer from InAs/GaSb, helical edge states proved
robust in perpendicular magnetic fields of 8 T (ref. 8). At the
surface of a 3D TI, calculations show that magnetic impurities
can open a gap at the Dirac point and exhibit ferromagnetic
order with perpendicular anisotropy mediated by the TSS
through Ruderman–Kittel–Kasuya–Yosida (RKKY) exchange
coupling4,9,10.
3D TIs with magnetic impurities have been studied by angleresolved
photoelectron spectroscopy (ARPES). The magnetic
impurities have been incorporated into the bulk11 and at the
surface of Bi2Se3 (ref. 10). For Fe impurities, the opening of large
surface band gaps of B100 meV was reported in both cases10,11.
In a previous work, however, we found that Fe deposited on
Bi2Se3 does not open a gap for a wide range of preparation
conditions, revealing a surprising robustness of the TSS towards
magnetic moments12. This conclusion also extends to Gd/ Bi2Se3
(ref. 13) and Fe/Bi2Te3 (ref. 14).
The absence of a surface band gap is consistent with the recent
finding that Fe on Bi2Se3 does not favour a magnetic anisotropy
perpendicular to the surface, at least in the dilute limit15. In this
respect, bulk impurities in TIs have an advantage over surface
impurities in that ferromagnetic order and perpendicular
magnetic anisotropies have been achieved in the bulk
systems11,16–21. Fe incorporated in bulk Bi2Te3 is known to
order ferromagnetically with a Curie temperature (TC) of B12 K
for concentrations of x ¼ 0.04 showing an easy axis perpendicular
to the base plane16,17. On the other hand, (Bi1 À xFex)2Se3 has not
been found to be ferromagnetic at temperatures above 2 K
(ref. 17). For x ¼ 0.16 and 0.25, ferromagnetic order was found at
2 K (ref. 11). By ARPES22, surface-state band gaps in
(Bi1 À xFex)2Se3 were reported and assigned to a magnetic origin
for Fe concentrations from x ¼ 0.05 to 0.25 including nonferromagnetic
concentrations such as x ¼ 0.12 with a band gap of
45 meV (ref. 11). These band gaps have been attributed to shortrange
magnetic order. Concerning Mn incorporation, bulk
(Bi1 À xMnx)2Se3 with x ¼ 0.02 has been shown to exhibit a
surface band gap with an occupied width of 7 meV (ref. 11),
which was suggested as an indication of ferromagnetic order
induced by the TSS11. However, much larger surface band gaps
were observed for n-doped (Bi1 À xMnx)2Se3 films20, where ferromagnetic
order of Mn at the surface was found to be strongly
enhanced with TC up to B45 K. The ferromagnetic order resulted
in an unusual spin texture of the TSS. The TC at the surface was
much higher than in the bulk20, which was partially attributed to
Mn surface accumulation. A strong enhancement of the surface
TC was also predicted by mean-field theory for this system
(for example, from 73 K (bulk) to 103 K (surface))23. Magnetically
doped TIs with ferromagnetic order are important as realizations
of novel topological phases. When spin degeneracy is lifted by the
exchange splitting, bulk band inversion can occur selectively for
one spin. If also the Fermi level is in the band gap, as predicted
for Cr and Fe in Bi2Se3 (ref. 24), this gives rise to an integer
quantized Hall conductance sxy in thin films termed the
quantized anomalous Hall effect7,24. This has recently been
reported for Cr in (Bi,Sb)2Te3 (ref. 25). When a perpendicular
magnetization breaks TRS at the surface of a bulk TI, the resulting
mass and surface band gap give rise to quantized edge states. In
this case sxy is half-integer quantized yielding a half quantum
Hall effect26 which can be probed at ferromagnetic domain
boundaries at the surface27 and leads to exotic topological
magnetoelectric effects such as the point-charge-induced image
magnetic monopole28,29. Another topological phase predicted for
magnetically doped Bi2Se3 is the realization of a 3D Weyl fermion
system in which the Dirac-like dispersions become a property of
the bulk30.
Here we present a detailed investigation on the correlation
between the TSS and magnetic properties in the Bi-Mn-Se system,
where the magnetic impurity Mn is introduced in the bulk of
B0.4 mm thick (Bi1 À xMnx)2Se3 epilayers with concentrations up
to x ¼ 0.08. By ARPES we find remarkably large band gaps of
B200 meV persisting up to temperatures of 300 K far above TC,
which is found to be B10 K at the surface showing only a limited
enhancement by r4 K over the bulk TC. We find that the
magnitude of the band gaps by far exceeds that expected from
TRS breaking due to magnetic order. By ARPES from quantumwell
states we exclude that Mn changes the inverted bulk band
gap. Using resonant photoemission and ab initio calculations we
conclude that, instead, impurity-induced resonance states destroy
the Dirac point of the TSS. We further support our conclusion by
showing that extremely low-bulk concentrations of nonmagnetic
In do also open a surface band gap in Bi2Se3. Our findings have
profound implications for the understanding of the conditions for
topological protection.
Results
Concentration and temperature dependence of surface band gap.
Figure 1 shows Mn-concentration-dependent high-resolution
ARPES dispersions of the TSS and bulk valence-band (BVB)
states of (Bi1 À xMnx)2Se3 with x up to 0.08 measured at 12 K and
50 eV photon energy. At this energy, contributions from the
bulk-conduction band (BCB) do not appear due to the dependence
of the photoemission transitions on the component of the
electron wave vector perpendicular to the surface k> (ref. 22), but
the BCB is partially occupied as data at 21 eV photon energy
reveal (Supplementary Fig. 1). The pure Bi2Se3 film (Fig. 1a) is
n-doped and exhibits a well-resolved Dirac point with high
photoemission intensity at a binding energy of ED B0.4 eV that is
seen as an intense peak in the energy-distribution curve at zero
momentum superimposed as red curve on the right-hand side of
the panel. The intact and bright Dirac point marked by a
horizontal dashed line in Fig. 1a demonstrates that the TSS is
gapless in Bi2Se3. At larger binding energies, the lower half of the
Dirac cone overlaps with the BVB, which is observed
for all (Bi1 À xMnx)2Se3 samples (Figs 1b–d). Increasing Mn
concentration, we find a gradual upward shift of the band edges
in energy, revealing a progressive p-type doping (hole doping).
Most notably, a surface band gap opens at the Dirac point with
increasing Mn content. In each energy-distribution curve, the
opening of the gap is also evident from the development of an
intensity dip at the binding energy of the original Dirac point.
Thus, the energy separation between the upper Dirac band
minimum and the energy position of the intensity dip is about
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half of the gap size. Note that the horizontal dashed
lines in Figs 1b–d highlight the minimum limit of the gap size
after taking into account the contribution from the linewidth
broadening to the ARPES spectra (see Supplementary Note 1 and
Supplementary Fig. 2). The surface band gap rapidly increases
with Mn content and exceeds 200 meV for x ¼ 0.08. For x ¼ 0.02,
the suppression of the Dirac point intensity as compared with the
undoped Bi2Se3 film indicates the existence of a small gap. This is
consistent with the fact that the TSS dispersion becomes slightly
parabolic and is characterized by an increased effective mass of
m* E 0.09me for x ¼ 0.02. This value increases further to
E0.15me for x ¼ 0.08, where me is the free-electron mass.
The observed surface band gaps are similar to those previously
reported20, which have been attributed to long-range
ferromagnetism and TRS breaking of the topologically
protected surface state20. Figures 2a–d show high-resolution
ARPES dispersions of the TSS, as well as the normal-emission
spectra through the Dirac point at temperatures of 12 and 300 K
for x ¼ 0.08 (see also Supplementary Fig. 3). Strikingly, there is no
significant change as temperature is raised, and very clearly the
band gap in the TSS persists up to room temperature. Moreover,
we find a similar behaviour for the whole sample series
independently of the Mn content, which challenges the
dominant role of ferromagnetic order in inducing the band gap
in the TSS, unless the surface TC is above room temperature.
Bulk and surface magnetism. We begin in Fig. 3 with characterizing
the bulk magnetic properties using superconducting
quantum-interference device (SQUID) magnetometry. The
comparison of measurements with in-plane and out-of-plane
applied magnetic field in Fig. 3a shows that at a temperature of
2 K the bulk easy axis lies in the surface plane. This holds
irrespective of the Mn concentration. Since the opening of a gap
at the Dirac point requires a magnetization perpendicular to the
surface9, we concentrate in the following on the out-of-plane
component of the magnetization. In the hysteresis loops
displayed in Fig. 3b measured with an out-of-plane applied
magnetic field at different temperatures, we observe a narrow
magnetic hysteresis at 4.2 K, whereas paramagnetic behaviour
emerges at 7 K once the ferromagnetic transition has been crossed
(inset in Fig. 3b). For a better determination of TC we present in
Fig. 3c modified Arrott plots according to a 3D Heisenberg
ferromagnet, normalized to the mass of the sample, with
exponents b ¼ 0.348 and g ¼ 1.41, from which we deduce
TC ¼ 5.5 K in the bulk (see also Supplementary Fig. 4). This is
well below the temperature of our ARPES measurements shown
in Figs 1 and 2.
The only remaining possibility that long-range ferromagnetism
opens the gap at the Dirac point is an enhanced surface
magnetism with magnetization perpendicular to the surface9,20,23.
This cannot be verified directly by the bulk-sensitive SQUID
magnetometry. Therefore, we perform X-ray magnetic circular
dichroism (XMCD) measurements at the Mn L2,3-edges to probe
the near-surface ferromagnetic order. The detection by total
electron yield leads to a probing depth in the nanometre range.
Figure 4a shows for x ¼ 0.04 the normalized intensity of the Mn
L2,3 absorption edges obtained upon reversal of the photon
helicity at a temperature of 5 K with an out-of-plane applied
magnetic field of 3 T. The XMCD difference spectrum is shown in
Fig. 4b, with the normalized XMCD difference signal following
one part of the out-of-plane hysteresis as a function of the
applied magnetic field as inset. The temperature dependence
of the XMCD signal measured in remanence (0 T applied
magnetic field) is presented in Fig. 4c for Mn concentrations of
x ¼ 0.04 and 0.08. This signal is obtained after switching off an
0.8
0.6
0.4
0.2
0.0
0.20.10.0–0.1–0.2
Electronbindingenergy(eV)
Wave vector k|| (Å–1
) Wave vector k|| (Å–1
) Wave vector k|| (Å–1
) Wave vector k|| (Å–1
)
0.20.10.0–0.1–0.2 0.20.10.0–0.1–0.2 0.20.10.0–0.1–0.2
a cb d
Figure 1 | Effect of Mn doping on the electronic band dispersions of (Bi1 À xMnx)2Se3. (a–d) Mn-concentration-dependent high-resolution ARPES
dispersions measured at 50 eV photon energy and a temperature of 12 K for x values of (a) 0, (b) 0.02, (c) 0.04 and (d) 0.08. The red lines represent EDCs
obtained in normal emission (k|| ¼ 0). A surface band gap opens at the Dirac point of the TSS which increases in size with increasing Mn content. The
horizontal white-dashed lines highlight the minimum limit of the gap size after taking into account the contribution from the linewidth broadening. The
opening of the gap leads to an intensity dip in the EDCs around the energy region of the original Dirac point. For x ¼ 0.02, the suppression of intensity at the
Dirac point and the more parabolic surface-state dispersion are signatures of a small gap. Besides the increased linewidth broadening due to the Mn
impurities, these effects become more pronounced with increasing Mn content.
0.6
0.4
0.2
0.0 T =12 K T =300 K
a
Electronbindingenergy(eV)
0.10.0–0.1
Wave vector k|| (Å–1
) Wave vector k|| (Å–1
)
b
0.10.0–0.1
0.6
0.4
0.2
0.0
Figure 2 | Temperature dependence of the large energy scale surface
band gap. (a,b) Energy-momentum ARPES dispersions obtained for
Mn-doped Bi2Se3 epilayers with 8% Mn concentration. The red lines are the
energy-distribution curves obtained in normal emission (k|| ¼ 0). The
horizontal white-dashed lines highlight the surface gap. Measurements are
taken at 50 eV photon energy and a temperature of (a) 12 K and (b) 300 K.
The surface band gap does not show a remarkable temperature
dependence.
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms10559 ARTICLE
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–80 –60 –40 –20 0 20 40 60 80
–20
–10
0
10
20
M(kAm–1
)
μ0H (mT)
4% Mn
8% Mn
a
T=2 K
ip oop
ip oop
M1/γ
(emu–1
g)1/γ
800600400200
c
8% Mn
B [111]
b
8% Mn
–1,000
–500
0
500
1,000
M(emumol–1
)
H (kOe)
–10 –5 0 5 10
0
2
4
8
6
10
12
14
16
0 1,000
T=4.25 K
T=7.0 K
T=4.25 K
T=6.75 K
T=9 K
T=11 K
T=13 K
Tc =5.5 K
δT=0.25 K
B [111]
H/M1/β
(Oe emu–1
g)1/β
–75 0
0
75
H (Oe)
–25
25
M(emumol–1
)
n
Figure 3 | Characterization of the bulk magnetic properties of Mn-doped Bi2Se3 films. (a) In-plane (ip) and out-of-plane (oop) magnetization curves for
Mn concentrations of x ¼ 0.04 and x ¼ 0.08, measured at a temperature of 2 K using SQUID magnetometry. The magnetic anisotropy lies in the surface
plane irrespective of the Mn concentration. (b) Corresponding hysteresis loops for x ¼ 0.08 measured at a temperature of 4.25 K (squares) and 7 K
(triangles), respectively. The applied magnetic field is perpendicular to the (111) sample surface (see sketch). Inset: a zoom-in around zero magnetic field
showing hysteresis at 4.25 K and a paramagnetic state at 7 K. (c) Arrott plots at various temperatures from which a Curie temperature TC of 5.5 K is
deduced. Between 4.25 K and 6.75 K, data are shown for temperature increments of dT ¼ 0.25 K.
Intensity(a.u.)
n
B
hν
a
4% Mn
XMCD(%)
–20
0
660655650645640635
20
15
10
5
0
3210
XMCD(%)
B (T)
–10
Photon energy (eV)
b
4% Mn
T = 5 K
B = 3 T
XMCD(%)
Circ. Pos.
Circ. Neg.
660655650645640635
Photon energy (eV)
c
643642641640639
5 K
7 K
10 K
Photon energy (eV)
–4
0
–2
–6
4% Mn
–4
–2
2520151050
T (K)
4% Mn
8% Mn
0
B = 0 T
XMCD(%)
Magnetization(10–5
emu)
ip
8% Mn
oop
ip oop
4% Mn
2 4 6 8 10 12 14
0
2
4
6
8
10
12
14
Temperature (K)
d
16
e
–4
–2
0
2
4
XMCD(%)
Figure 4 | XMCD in total electron yield at the Mn L2,3-edges. (a) X-ray absorption spectra measured for opposite helicities of the circularly polarized
incident light at 5 K with an out-of-plane applied magnetic field of 3 T. A sketch of the experimental geometry is also shown. (b) Corresponding XMCD
difference spectrum. The inset shows XMCD measurements for different applied magnetic fields. (c) Temperature dependence of the remanent XMCD for
a Mn concentration of x ¼ 0.04. Inset: detailed temperature dependence for x ¼ 0.04 and 0.08. (d) To re-examine the bulk magnetic properties,
field-cooling measurements are obtained under an in-plane (ip) and out-of-plane (oop) applied magnetic field of 10 mT using SQUID magnetometry. The
temperature dependence for x ¼ 0.04 and 0.08 compares well with the surface-sensitive measurements shown in the inset of (c). (e) XMCD-PEEM image
obtained using photoelectron microscopy for x ¼ 0.08 at room temperature, revealing the absence of magnetic domains with partial or full out-of-plane
magnetic order. Scale bar, 500 mm (horizontal white-solid line).
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applied magnetic field of 5 T perpendicular to the surface, and
represents the remanent XMCD, which is proportional to the
remanent magnetization of the film surface. We clearly observe a
ferromagnetic Mn component in the remanent XMCD appearing
around 640 eV which becomes increasingly more pronounced at
lower temperatures. The lineshape of the XMCD spectrum is
similar to that of Mn in GaAs31, indicating a predominant
d5 configuration. More specifically, the lineshape compares rather
well with Mn in Bi2Te3 for which the comparison with an
Anderson impurity model recently gave a superposition of 16%
d4, 58% d5 and 26% d6 character32. The ferromagnetic Mn
component shows surface ferromagnetic order in the remanent
XMCD only below 10 K for Mn concentrations of x ¼ 0.04 and
0.08 (inset in Fig. 4c). On one hand, this result is not inconsistent
with the predicted strong-surface enhancement of TC since the
enhancement effect vanishes already when chemical potential and
Dirac point differ by 0.2 eV (ref. 23). On the other hand, our
XMCD result means that the magnetically induced gap would
have to close above 10 K.
Having established that the bulk and surface magnetic
properties of our samples are very similar, as a next step, we
performed field-cooling experiments to re-examine the bulk
magnetic properties. Figure 4d shows field-cooled SQUID data
for an applied magnetic field of 10 mT parallel and perpendicular
to the surface plane. Above TC, there is no preferential orientation
of the anisotropy axis perpendicular to the surface. Additional
zero-field-cooled SQUID data compare rather well with these
results (Supplementary Fig. 5). Further XMCD measurements
under an in-plane and out-of-plane applied magnetic field are
consistent with the SQUID data and are shown in Supplementary
Fig. 6. These XMCD and SQUID results strongly suggest that
above TC also short-range static magnetic order does not play a
role at the surface or in the bulk, respectively (see Supplementary
Note 2), and that domains with partial or full out-of-plane
magnetic order are absent. We further support this conclusion by
additional XMCD measurements carried out by the means of
X-ray photoelectron emission microscopy (XMCD-PEEM) at
room temperature, with a lateral resolution of B20 nm. Figure 4e
shows the XMCD image which due to the light incidence
(16° grazing) is sensitve to both in- and out-of-plane components
of the magnetization, with additional data given in Supplementary
Figs 7,8. The XMCD image displays no magnetic
domains at room temperature thus also excluding short-range
static inhomogeneous magnetic order with magnetization
partially or fully in or out of the surface plane, at least within
our lateral resolution (see Supplementary Note 3 for details).
A similar conclusion can be drawn regarding out-of-plane
magnetic short-range fluctuations (see discussion in Supplementary
Note 4 and Supplementary Fig. 9). All our observations
taken together lead us to the important conclusion that the
surface band gap is not due to magnetism and, thus, the novel
topological phases cannot be realized with (Bi1 À xMnx)2Se3.
Absence of topological phase transition with concentration.
There exists an alternative nonmagnetic explanation for the
surface band gap. It is in principle possible that the incorporation
of Mn changes the bulk band structure and even reverts the
bulk band inversion, rendering Mn-doped Bi2Se3 topologically
trivial. This topological phase transition with concentration is,
for example, the basis for the HgTe quantum spin-Hall insulator6.
Interestingly, it has been argued that a gap in the TSS can
be a precursor of a reversed bulk band inversion, as discussed
for TlBi(S1 À xSex)2 (ref. 33). Indium substitution in Bi2Se3
behaves similarly, and leads to a topological-to-trivial quantumphase
transition with an inversion point between 3 and 7% In in
thin films34. Figure 5 shows that the bulk band gap stays
constant within 4% of its value for 8% Mn incorporation. This
statement is possible because at low photon energies changes in
the bulk band gap are traced most precisely from quantum-well
states in normal emission (k|| ¼ 0). The simultaneous
quantization of BCB and BVB is created by surface band
bending after adsorption of small amounts of residual gas35.
This means that the scenario of reversed bulk band inversion
does not hold here.
Another remarkable feature is the measured size of the surface
band gap. A perpendicular magnetic anisotropy has recently been
predicted by density-functional theory (DFT) for Co in Bi2Se3
(ref. 36) as well as for 0.25 monolayer Co adsorbed on the surface
in substitutional sites, leading to a surface band gap of B9 meV
(ref. 36), which, however, is one order of magnitude smaller than
the gaps observed here. For (Bi1 À xMnx)2Te3, a surface band gap
of 16 meV has been calculated under the condition of
perpendicular magnetic anisotropy37. For Mn in Bi2Se3 at
the energetically favoured Bi-substitutional sites, an in-plane
magnetic anisotropy is predicted38. The size of the gap at the
Dirac point is only 4 meV (ref. 38). Perpendicular anisotropy and
ferromagnetic order are absent in our samples at the temperature
of the ARPES measurements.
Role of the local magnetic moment and intercalation scenarios.
If the large local magnetic moment of the Mn is responsible for
the measured band gaps via TRS breaking, the effect should be
equal or larger when Mn is deposited directly on the surface. Here
we argue in the following way: If TRS is broken only due to the
Mn magnetic moment, we do not require hybridization to open a
gap. By depositing Mn we create a completely different environment
for the Mn at the surface, allowing us to understand
whether the Mn magnetic moment is solely responsible for the
opening of large surface band gaps via TRS breaking and, ideally,
without hybridization playing a role. Mn is very well suited for
such comparison, as due to the high stability of its half-filled d5
configuration, its high magnetic moment is to a large extent
independent of the atomic environment and the resulting
hybridization. DFT obtains 4.0 mB for most substitutional sites
(except for the hypothetical Se-substitutional site with still 3.0 mB)
and only for interstitial Mn the moment peaks with 5.0 mB
(ref. 38). Mn deposition was performed at B30 K in order to keep
the Mn atoms isolated from each other and on the surface. As the
XMCD showed a predominant d5 configuration for Mn bulk
impurities, which is most stable, we can assume the same
magnetic moment for Mn impurities deposited on the surface.
Figure 6 shows that a similar p-doping occurs as with the Mn in
the bulk. In another respect, the magnetic moments do not act in
a similar way as in the bulk. Even 30% of a Mn monolayer on
Bi2Se3 does not open a band gap at the Dirac point. This result is
similar to what we have observed for Fe on Bi2Se3 (ref. 12) and
Bi2Te3 (ref. 14).
Most recently, the appearance of surface band gaps in ARPES
at the Dirac point of the TSS has been discussed based on
different mechanisms. One is momentum fluctuations of the
surface Dirac fermions in real space as observed by scanning
tunnelling microscopy measurements of Mn-doped Bi2Te3 and
Bi2Se3 bulk single crystals39. However, these fluctuations amount
to 16 meV (ref. 39), much less than the present band gaps.
Another mechanism is top-layer relaxation, that is, breaking of
the van-der-Waals bond between quintuple layers during cleavage
of bulk crystals as proposed in Xu et al.20 This would open a gap
due to hybridization of TSS’s through the layer40 but such an
effect does not occur for epitaxial layers where no sample cleavage
is used for surface preparation.
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If such a separation of quintuple layers occurs, it is more
likely caused by the Mn. Principally, intercalated Mn in the
van-der-Waals gaps could separate quintuple layers electronically,
although such effect has not been seen in experiments yet. At
these new interfaces TSS’s could form and if they would behave
like in ultra-thin Bi2Se3 films, they would hybridize and open a
band gap40. However, band gaps of the order of B100 meV
would correspond to an unrealistic Mn intercalation pattern
grouping three quintuple layers when compared with the films of
Zhang et al.40 In order to estimate the amount of Mn
intercalation, we have analysed the change of the bulk lattice
constant in our samples by X-ray diffraction (see Supplementary
Note 5, Supplementary Figs 10–13 and Supplementary
Tables 1,2). We find that the c-lattice constant increases by
B0.15% for 4% Mn and by B0.45% for 8% Mn. If we would
assume that this is completely due to an expansion of the
van-der-Waals gaps, the interlayer distance would increase by
only B1.8% for 4% Mn and by less than B5% for 8% Mn.
According to DFT, intercalation of transition metals into the first
van-der-Waals gap of Bi2Se3 leads to an expansion between 10
and 20% (ref. 41). New surface-state features can appear inside
the bulk band gap but in order to be split remarkably off the BVB
and BCB edges, expansions between 20 and 50% are required41.
In addition, we point out that, despite our observation of a large
surface band gap at room temperature, we observe a nearly zero
spin polarization perpendicular to the surface (Supplementary
Fig. 14). The absence of a hedgehog spin texture pinpoints a
non-TRS breaking mechanism underlying the origin of the gap, a
fact which is consistent with our conclusions derived from the
magnetic properties. Moreover, it is understood that we cannot
verify a small magnetic band gap opening of few meV as
calculated in Schmidt et al.36 and Henk et al.37 because much
larger gaps are present in the whole temperature range.
Topological protection beyond the continuum model. As we
find that neither ferromagnetic order in the bulk or at the surface,
nor the local magnetic moment of the Mn are causing the large
band gaps that we observe, as we can exclude the nonmagnetic
explanation of a reversal of the bulk band inversion and as we do
not find sufficient indications for the nonmagnetic explanation of
surface-state hybridization by van-der-Waals-gap expansion, we
point out a different mechanism based on impurity-induced
resonance states that locally destroy the Dirac point.
In fact, recently the treatment of the topological protection in
the continuum model3–5 has been extended for finite bulk band
gaps42,43. As a result, surface42 and bulk impurities43 can mediate
scattering processes via bulk states and the localized impurityinduced
resonance states emerging at and around the Dirac point
lead to a local destruction of the topological protection of the
Dirac point. The resulting band gap opening depends on the
resonance energy, impurity strength U as well as spatial location
of the impurities42,43. A typical gap size is of the order of 100 meV
0.8
0.6
0.4
0.2
0.0
BCB
QWS
BVB
QWS
500 meV500 meV500 meV
h = 18 eV
Electronbindingenergy(eV)
BCB
QWS
BVB
QWS
Wave vector k||(Å–1
) Wave vector k||(Å–1
) Wave vector k||(Å–1
)
0.10.0–0.1
a b c
d e f
0.8
0.6
0.4
0.2
0.0
0.10.0–0.10.10.0–0.1
500 meV500 meV500meV
h = 16 eV
Figure 5 | Tracing changes in the bulk band gap of Mn-doped Bi2Se3 films. Changes in the bulk band gap are traced most precisely from quantum-well
states (QWS) in normal emission (red curves on the right-hand side of each panel).(a–c) Energy-momentum dispersions acquired at a photon energy of
hn ¼ 18 eV for (a) Bi2Se3, (b) 2% and (c) 8% Mn doping. The simultaneous quantization of bulk-conduction band (BCB) and valence-band (BVB) is created
by surface band bending after adsorption of small amounts of residual gas35. It is found that Mn doping does not change the bulk band gap of Bi2Se3.
(d–f) Similar results as in a–c, respectively, but at a photon energy of hn ¼ 16 eV, where large apparent surface band gaps are observed. This unexpected
photon-energy dependence of a surface state is interpreted as coupling to bulk states mediated by the Mn impurities.
a
0.4
0.2
0.0
0.5
0.4
0.3
0.2
0.1
0.0
Intensity (a.u.)
Wave vector kII (Å–1
)
b
Electronbindingenergy(eV)
0.10.0–0.1
Figure 6 | Effect of Mn deposition on the surface of Bi2Se3 films.
(a) Energy-momentum ARPES dispersion showing a gapless Dirac cone in
pure Bi2Se3 films after deposition of 0.3 monolayer Mn at 30 K on the
surface. Measurements are performed at the same temperature using
50 eV photon energy. (b) EDCs extracted from the measurements shown in
a. The red curves in a and b emphasize the EDC in normal emission
(k|| ¼ 0).
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(ref. 42). Moreover, the gap does not rely on a particular magnetic
property of the impurity and, therefore, the mechanism should
apply for magnetic impurities as well. The model can also explain
the absence of the gap when Mn impurities are placed on the
surface, since bulk-like resonance states do not form when Mn is
placed only on the surface. A definite assignment, however,
requires realistic electronic structure calculations since a simple
atomic Mn d5 configuration does not lead to states at the Dirac
point.
To identify impurity resonances, we calculated for 8% Mn in
Bi2Se3 at the Bi-substitutional sites the corresponding DOS by ab
initio theory. The model structure used in the calculations is
shown in Fig. 7a, where Bi atoms (yellow) acquire Mn character
(blue wedges). The results of the calculation are shown in Fig. 7b,
where it is seen that Mn impurity states (blue) strongly contribute
to the total DOS (red) near the BVB maximum. The Mn impurity
states in the gap are clearly identified by assuming ferromagnetic
order and subtracting the minority from majority spin DOS. In
experiment, impurity-band states are difficult to observe as the
example of Ga1 À xMnxAs shows44, where—similarly to the
present case—impurity states emerge near the BVB maximum.
There are, in fact, indications for the impurity resonances in our
data. If we look at the photon-energy dependence from 16 to
21 eV in the ARPES results shown in Supplementary Fig. 15, we
see that the surface band gap is only well defined with respect to
the minimum of the upper Dirac cone and consistent for
16–21 eV as well as 50 eV (for 50 eV see Figs 1,2, where the BCB
does not appear). The lower Dirac cone exhibits despite its
a b
Total DOS
Mn DOS
0.0
–0.2
–0.4
–0.6
0.2
0.4
BVB
BCB
E-EF (eV)
NormalizedDOS(a.u.)
0.4
0.3
0.2
0.1
0.5
0.40
0.35
0.30
0.25
0.20
0.15
0.0
–0.1 0.0 0.1
Intensity(a.u.)
Low
High
Intensity(a.u.)
Low
High
c d
fe
Mn 3p
Mn 3d
Evac
EF
e–
h
Initial state Final state
Electronbinding
energy(eV)
Wave vector k|| (Å–1
) Wave vector k|| (Å–1
)
0.40
0.35
0.30
0.25
0.20
0.15
Electronbinding
energy(eV)
–0.1 0.0 0.1
Electronbinding
energy(eV)
–0.1 0.0 0.1
Wave vector k|| (Å–1
)
Figure 7 | Resonant photoemission and ab initio calculations. (a) The structure of Bi2Se3 doped with 8% Mn at the Bi-substitutional sites used in the
calculations. Within the coherent-potential approximation, the Bi atoms (yellow) acquire Mn character (blue wedges). Se atoms are shown in grey colour.
(b) Calculated density of states (DOS). The total DOS (red) contains contributions from impurity resonances (vertical blue arrows) of strong d-character, a
seen in the partial Mn DOS (blue). For the purpose of the calculation, ferromagnetic order at T ¼ 0 K was assumed. (c,d) Resonant photoemission at the
Mn M-edge, focusing on the region of the surface gap (8% Mn). (c) Off-resonant (48 eV photon energy) and (d) on-resonant data (50 eV). (e) Schematics
of the resonant process. At the resonance energy, the excitation occurs via 3p–3d transitions. The exciting photon energy (hn) corresponds to a transition
from an occupied core level to a valence-band empty state between the Fermi (EF) and vacuum (Evac) levels. The relaxation of excited electrons leads to
enhanced photoemission from d-like Mn states. (f) Intensity difference obtained after subtracting off-resonant from on-resonant data. The resonances
are seen in blue contrast and are marked with arrows, similar to the calculations shown in b.
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two-dimensional nature a photon-energy (wave vector perpendicular
to the surface, k>) dependence when Mn is incorporated.
The reason for this difference is that the lower Dirac cone
strongly overlaps with the BVB while the upper Dirac cone does
not overlap with the BCB. This can also be seen in Fig. 5, where
an apparent band gap of B200 meV occurs for 2% Mn at
hn ¼ 16 eV. At this small concentration, such an apparent gap
seems to be nearly closed at 18 eV, where the suppression of the
Dirac point intensity and the more parabolic TSS dispersion as
compared with the undoped Bi2Se3 film indicates the existence of
a small gap, in agreement with the results of Fig. 1. Note that the
minimum band gap in the photon-energy dependence defines the
gap size (see Supplementary Fig. 16). The minimum gap size
observed at low photon energies agrees well with the one obtained
at 50 eV. At 8% Mn, the surface band gap opens at all photon
energies and reaches a minimum of B200 meV, that is, it is
determined rather unambiguously, but some intensity appears in
the surface band gap. Such intensity also appears in Xu et al.20
The role of the impurity resonance is exactly to couple the TSS to
bulk states. This 3D coupling is naturally different for the upper
and lower Dirac cone due to the different bulk overlap and thus
seen as the photon-energy dependence of the lower half of the
Dirac cone.
We applied resonant photoemission which fortunately is
comparatively strong for Mn due to its half-filled d-shell.
Figures 7c and d show for 8% Mn off-resonant (hn ¼ 48 eV) and
on-resonant photoemission (50 eV) measurements via the Mn 3p
core level, focusing on the region of the surface gap, respectively.
The spectra were normalized to the photon flux after taking into
account the photon-energy dependence of the photoionization
cross sections of Bi 6p and Se 4p, respectively. Subtracting
off-resonant from on-resonant data allows us to visualize directly
the contribution from impurity resonances in the ARPES
spectrum, as there is enhanced photoemission from d-like Mn
states through decay of electrons that are excited via 3p–3d
transitions (Fig. 7e). The difference spectrum shown in Fig. 7f
reveals the existence of impurity resonances inside the surface
band gap and near the valence-band maximum. The resonances
are seen in blue contrast and are marked with arrows, similar to
the calculations shown in Fig. 7b. The unexpectedly strong dispersion
of the resonant states with wave vector k|| is in qualitative
agreement with our one-step model photoemission calculations
(see Supplementary Fig. 17 and Supplementary Note 6), and
additionally supports the physical picture of Mn-induced
coupling to the bulk states. We should emphasize that the Mn
d5 configuration confirmed by our XMCD measurements offers
much fewer states in the energy range of the Dirac cone than the
other magnetic transition metals. The fact that already Mn breaks
the Dirac cone indicates that the present result is of general
importance for TIs doped with magnetic transition metals.
As nonmagnetic control experiment we have chosen thick
In-doped Bi2Se3 bulk samples which give rise to a trivial phase
close to B5% In concentration. Supplementary Fig. 18 shows that
a large band gap of the order of B100 meV appears at the Dirac
point already for a much smaller In concentration, namely 2%, far
away from the inversion point of the topological quantum-phase
transition (see Supplementary Note 7 and Supplementary Fig. 19
for more details). In addition, spin-resolved ARPES measurements
around k|| ¼ 0 for In-doped samples (Supplementary
Fig. 14) reveal that the out-of-plane spin polarization is zero,
similarly to the result for the gapped Dirac cone in Mn-doped
samples. Interestingly, the size of the band gap for 2% In is of the
same order as the one for 8% Mn whereas no gap appears for 4%
Sn (Supplementary Fig. 18). This indicates that the concentration
range at which the large surface gap develops varies from dopant
to dopant. On the basis of ideas proposed recently42,43, this might
be associated with the impurity-dependent strength U, regardless
whether the dopant is magnetic or not. Our control experiments
demonstrate the existence of a mechanism for surface band
gap opening which is not directly connected to long-range or
local magnetic properties. Although it is not possible to directly
search for In impurity resonances in the photoemission
experiment as there is no resonant photoemission condition
available, for completeness we point out that our conclusion on
the nonmagnetic origin of the surface band gap in Mn-doped
Bi2Se3 films would not have been possible unless several findings
in our experiment differed from previous experiments20. This
refers to the in-plane magnetic anisotropy, the absence of a
temperature dependence of the gap, a much lower TC, no out-ofplane
spin polarization at the gapped Dirac point, no enhanced
surface magnetism, a photon-energy dependence of the band gap,
and an available resonant condition via the Mn 3p core level
allowing us to directly observe the contribution from in-gap
states.
To summarize, we revealed the opening of large surface band
gaps in the TSS of Mn-doped Bi2Se3 epilayers that strongly
increase with increasing Mn content. We find ferromagnetic
hysteresis at low temperatures, with the magnetization oriented
parallel to the film surface. Magnetic surface enhancement is
absent. Even above the ferromagnetic transition, we observe
surface band gaps which are one order of magnitude larger than
the magnetic gaps theoretically predicted and, moreover, they do
not show notable temperature dependence. No indication for a
Mn-induced reversal of the bulk band inversion and no
significant enhancement of the surface magnetic ordering
transition with respect to the bulk are found. Control experiments
with nonmagnetic bulk impurities, conducted in the topological
phase, reveal that surface band gaps of the order of B100 meV
can be created without magnetic moments. In line with recent
theoretical predictions, we conclude that the band gap opening up
to room temperature in Mn-doped films is not induced by
ferromagnetic order and that even the presence of magnetic
moments is not required. Our results are important in the context
of topological protection and provide strong circumstantial
evidence that Mn-doped Bi2Se3 is not suited for observing
the quantized anomalous Hall effect or the half quantum
Hall effect.
Methods
Sample growth and structural characterization. The samples were grown by
molecular beam epitaxy on (111)-oriented BaF2 substrates at a substrate
temperature of 360 °C using Bi2Se3, Mn and Se effusion cells. The Mn concentration
was varied between 0 and 8%, and a two-dimensional growth was
observed by in situ reflection high-energy electron diffraction in all cases
(see Supplementary Fig. 20 and Supplementary Note 8). All samples were single
phase as indicated by X-ray diffraction. After growth and cooling to room
temperature, the B0.4-mm-thick epilayers were in situ capped by an amorphous
50-nm thick Se layer, which was desorbed inside the ARPES and XMCD chambers
by carefully annealing at B230 °C for B1 h. The Mn concentrations determined
by core-level photoemission were in good agreement with those obtained from
energy dispersive microanalysis, indicating no significant Mn accumulation at the
surface of the samples (see Supplementary Fig. 21 and Supplementary Note 9).
High-resolution and spin-resolved ARPES. Temperature-dependent ARPES
measurements were performed at the UE112-PGM2a beamline of BESSY II at
pressures better than 1 Â 10À 10 mbar using p-polarized undulator radiation.
Photoelectrons were detected with a Scienta R8000 electron energy analyser and
the spin-resolved spectra were obtained with a Mott-type spin polarimeter coupled
to the hemispherical analyser. For the spin-resolved measurements of Mn-doped
Bi2Se3 samples, a magnetic field of þ 0.3 T was applied perpendicular to the surface
plane at 20 K right before the acquisition of the spectra. Overall resolutions of
ARPES measurements were 5 meV (energy) and 0.3° (angular). Resolutions for
spin-resolved ARPES were 80 meV (energy) and 0.75° (angular).
Magnetic characterization. The characterization of the bulk magnetic properties
was done by SQUID magnetometry. The bulk magnetization was recorded as a
ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms10559
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Reprinted page 8 of paper [86] “Temperature independent gap in (Bi,Mn)2Se3 layers”.
function of temperature and applied magnetic field applied either perpendicular
(out-of-plane) or parallel (in-plane) to the surface of the films. The diamagnetic
contribution of the BaF2 substrate was derived from the field-dependent
magnetization curves at room temperature and subtracted from all data. The
characterization of the surface magnetic properties was done by XMCD and
XMCD-PEEM measurements at the UE46-PGM1 and UE49-PGM1a beamlines of
BESSY II, respectively. The experiments were performed using circularly polarized
undulator radiation and under the same pressure conditions as the ARPES
measurements. The XMCD spectra were taken using a high-field diffractometer as
a function of temperature and applied magnetic field, and the XMCD-PEEM
measurements were performed at room temperature and under grazing incidence
(16°) with a lateral resolution of B20 nm.
Theoretical calculations. The one-step model photoemission calculations were
performed using the results of ab initio theory as an input, and taking into account
wave vector and energy-dependent transition matrix elements. The ab initio
calculations were performed within the coherent-potential approximation using
the Munich SPR-KKR program package45,46, with spin-orbit coupling included by
solving the four-component Dirac equation.
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Acknowledgements
Financial support from the priority program SPP 1666 of the Deutsche
Forschungsgemeinschaft (Grant No. EB154/26-1 and RA1041/7-1) and the Impuls-und
Vernetzungsfonds der Helmholtz-Gemeinschaft (Grant No. HRJRG-408) is gratefully
acknowledged. J.M. is supported by the CENTEM (CZ.1.05/2.1.00/03.0088) and
CENTEM PLUS (LO1402) projects, co-funded by the ERDF as part of the Ministry of
Education, Youth and Sports OP RDI programme. V.H. acknowledges the support of the
Czech Science Foundation (project 14-08124S). G.S., H.S., R.K. and G.B. acknowledge
support of the Austrian Science Funds (project SFB 025, IRON).
Author contributions
J.S.-B. and A.V. performed the photoemission experiments; G.S., G.B. and L.V.Y.
provided samples and performed the growth and characterization; H.S., R.K. and A.N.
performed the SQUID measurements; O.C. and V.H. performed X-ray diffraction
measurements; J.S.-B., E.S. and E.W. performed the XMCD measurements; J.S.-B.,
A.A.U¨ . and S.V. performed the XMCD-PEEM measurements; J.M., M.D., J.B. and H.E.
carried out the calculations; J.S.-B. and E.G. performed the numerical simulations; J.S.-B.
performed data analysis and figure planning; J.S.-B. and O.R. performed draft planning
and wrote the manuscript with input from all the authors; J.S.-B. and O.R. were
responsible for the conception and the overall direction of the study.
Additional information
Supplementary Information accompanies this paper at http://www.nature.com/
naturecommunications
Competing financial interests: The authors declare no competing financial interests.
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How to cite this article: Sa´nchez-Barriga, J. et al. Nonmagnetic band gap at the Dirac
point of the magnetic topological insulator (Bi1-xMnx)2Se3. Nat. Commun. 7:10559
doi: 10.1038/ncomms10559 (2016).
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Reprinted page 10 of paper [86] “Temperature independent gap in (Bi,Mn)2Se3 layers”.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Supplementary Figure 1: Probing the bulk‐conduction band at low photon energy. In contrast 
to Fig. 1 of the main text, the bulk‐conduction band (BCB) is probed at 21 eV. (a, b) Energy‐
momentum ARPES dispersions of (a) undoped Bi2Se3 and (b) 8% Mn‐doped Bi2Se3. The upward 
shift of the BCB in (b) is due to the p‐type doping and not to a change in the bulk band gap or 
even a reversal of the bulk band inversion (see also Supplementary Fig. 15). The topological 
surface state (TSS) appears with weaker photoemission intensity which makes it difficult to 
observe when it approaches the BCB for 8% Mn in (b). The signal from the bulk‐valence band 
(BVB) is also observed at higher binding energies. The TSS is better visible at 50 eV in Fig. 1 of 
the main text and in Supplementary Fig. 3. The horizontal white‐dashed lines in (b) highlight 
the opening of the surface gap. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Reprinted supplement page 1 of paper [86] “Temperature independent gap in (Bi,Mn)2Se3 layers”.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Supplementary  Figure  2:  Surface  band  gap  for  different  Mn  concentrations.  (a‐c)  The 
experimental energy‐distribution curves (EDCs) at zero momentum (kII=0, red circles), obtained 
from the ARPES spectra acquired at 50 eV photon energy and 12 K temperature, are fitted 
(solid black lines) considering a Shirley‐like background [1]. The fitting procedure is explained 
in detail in Supplementary Note 1. The fit results for (a) 2%, (b) 4% and (c) 8% Mn‐doped Bi2Se3 
films are shown.  (d) Size of the surface band gap obtained from the fits in (a‐c). The surface 
band  gap  is  determined  from  the  energy  separation  between  the  fitted  Lorentzian  peaks 
shown  in  blue  (green)  color,  which  are  located  at  the  energy  minimum  (maximum)  of  the 
upper  (lower)  half  of  the  Dirac  cone.  The  Lorentzian  peaks  shown  in  gray  color  are 
contributions from the bulk‐valence bands. Error bars in (d) correspond to the uncertainty of 
determining the energy position of the band dispersions. The error bars are estimated from 
the standard deviations of the peak positions over several fitting cycles. 
 
 
 
 
 
 
 
 
 
 
 
 
 
Reprinted supplement page 2 of paper [86] “Temperature independent gap in (Bi,Mn)2Se3 layers”.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Supplementary Figure 3: Temperature dependence of the surface band gap. (a, b) Data as in 
Fig.  2  of  the  main  text  for  8%  Mn‐doped  Bi2Se3  and  (c,  d)  in  a  different  representation  as 
energy‐distribution curves (EDCs), showing the absence of a temperature dependence of the 
surface band gap. Measurements were obtained at a temperature of (a, c) 12 K and (b, d) and 
300 K. The red solid lines in (a‐d) emphasize the EDCs in normal emission (kII=0). The horizontal 
white‐dashed lines in (a, b) highlight the surface band gap. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Reprinted supplement page 3 of paper [86] “Temperature independent gap in (Bi,Mn)2Se3 layers”.
 
 
 
 
                              
Supplementary  Figure  4:  Conventional  mass‐normalized  Arrott  plot.  In  Fig.  3c  of  the  main 
text,  we  showed  a  modified  Arrot  plot  according  to  a  3D  Heisenberg  ferromagnet  [2,  3] 
normalized to the mass of the sample with the exponents = 0.348 and  = 1.41, from which 
we deduce a TC of 5.5 K. Here we show for the same data a conventional mass‐normalized 
Arrott  plot.  A  similar  presentation  was  used  previously  [4]  for  the  determination  of  the 
ferromagnetic Curie temperature in (Bi1‐xMnx)2Te3. From the present plot, we deduce a by 2 K 
higher TC. 
Reprinted supplement page 4 of paper [86] “Temperature independent gap in (Bi,Mn)2Se3 layers”.
 
 
Supplementary Figure 5: Temperature‐dependence of the bulk magnetization. Comparison between 
field‐cooling  (FC) and zero‐field‐cooling (ZFC)  measurements obtained using  SQUID  magnetometry 
for (a) 4% and (b) 8% Mn doping. The temperature dependence of both the in‐plane (ip) and out‐of‐
plane (oop) components of the magnetization is shown.  The FC measurements are performed under 
an applied magnetic field of 10 mT parallel and perpendicular to the surface. The ZFC and FC results 
are  very  similar  for  each  composition,  and  compare  well  to  the  surface‐sensitive  XMCD 
measurements shown in the main text (see Supplementary Note 2 for details).  
Reprinted supplement page 5 of paper [86] “Temperature independent gap in (Bi,Mn)2Se3 layers”.
 
 
Supplementary  Figure  6:    Surface‐sensitive  XMCD  measurements  for  8%  Mn‐doped  Bi2Se3.  The 
spectra were obtained at the Mn L3‐edge and a temperature of 20 K under an applied magnetic field 
of  ‐2T  parallel  (red  circles)  and  perpendicular  to  the  surface  (black  solid  line).  The  x‐ray  beam 
impinged the sample in normal incidence (black solid line) and at a gracing incidence angle of 30° 
with respect to the surface plane (red circles); see Supplementary Notes 2 and 4 for details.                     
Reprinted supplement page 6 of paper [86] “Temperature independent gap in (Bi,Mn)2Se3 layers”.
 
 
Supplementary Figure 7: Absorption spectrum measured for the (Bi1‐xMnx)2Se3 sample doped 
with 8% Mn using X‐PEEM. The spectrum is obtained across the Mn L2,3‐edges from the same 
region of the sample shown in the XMCD images of Supplementary Fig. 8 below and plotted as 
the result of the sum of two absorption spectra recorded with opposite light helicity; see also 
Supplementary Note 3.  
 Intensity (arb.units)
654652650648646644642640638
Photon energy (eV)
L3
L2
Reprinted supplement page 7 of paper [86] “Temperature independent gap in (Bi,Mn)2Se3 layers”.
 
 
Supplementary  Figure  8:  A  sequence  of  XMCD‐PEEM  measurements.  (a‐l)  XMCD‐PEEM 
measurements for the (Bi1‐xMnx)2Se3 sample doped with 8% Mn. (a, b, c, g, h) XMCD images 
obtained at the Mn L3 ‐edge after pre‐edge subtraction. Each XMCD consisted of 160 images (3 
seconds  integration  time  each).  Panels  (d,  e,  f,  j,  k)  show  the  corresponding  XMCD  profiles 
across the same line [blue dotted line on panel (a)]. Panels (i) and (l) show the average XMCD 
and XMCD profile, respectively. The scale bar (horizontal white‐solid line) shown in (a) is 500 
m and applies to all panels. Note the absence of correlation between the different individual 
measurements  as  well  as  the  contrast  decrease  after  averaging,  indicating  absence  of 
ferromagnetic domains at room temperature; see Supplementary Note 3 for more details. 
 
Reprinted supplement page 8 of paper [86] “Temperature independent gap in (Bi,Mn)2Se3 layers”.
 
 
Supplementary Figure 9: Simulations of spectral weight at the Dirac point. (a) Schematic of a 
topological insulator hosting bulk magnetic impurities (green spheres) with random magnetic 
moments  represented  by  green  arrows.  (b)  A  random  magnetic  moment  in  our  simplified 
model is illustrated as a green arrow in the three‐dimensional space. The in‐ and out‐of‐plane 
projection  of  the  magnetic  moment  varies  only  with  the  polar  angle  θ  and  a  randomized 
collection of magnetic impurities covers the whole polar and azimuthal (φ) range. The dashed 
line indicates the in‐plane projection of the magnetic moment while the dashed circle encloses 
the full solid angle covered by a specific polar value. (c) Evaluation of the spectral weight using 
our model for different constraints in the magnetic moment orientation, plotted as a function 
of the energy away from the Dirac point (E‐ED). The constraints are chosen in accordance with 
the results of our magnetic characterization, which reveals either preferentially‐oriented in‐
plane  magnetic  moments  below  Tc  or  random  orientations  of  the  Mn  magnetic  moments 
above  Tc.  The  black  curve  corresponds  to  a  fully  randomized  population  after  integration 
across  all  possible  values  of  θ  and  φ.  Blue,  green,  red  and  pink  curves  correspond  to 
randomized magnetic moments constrained by symmetric polar angles with respect to the x‐y 
plane which add up to the total solid angle indicated in the legend. 
 
 
      
 
 
 
Reprinted supplement page 9 of paper [86] “Temperature independent gap in (Bi,Mn)2Se3 layers”.
 
        
 
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Reprinted supplement page 10 of paper [86] “Temperature independent gap in (Bi,Mn)2Se3 layers”.
CHAPTER 4. REPRINTED PAPERS 107
4.5 Manganese doping of Bi2Te3 topological insulator
The magnetic alloy layers of (Bi,Mn)2Te3 were grown on BaF2. The manganese positions were
analyzed using x-ray absorption spectroscopy. The manganese positions were identified as an
octahedral interstitial in the van der Waals gap. The crystalline structure is increasingly
disordered with increasing manganese content. The ARPES measurements lack sufficient
resolution and low enough temperature to observe magnetic band gap opening. However, we
were unaware that Mn atoms occupy the septuple layers MnBi2Te4 at the time of publication.
The structural analysis interpretation is not entirely correct.
New J. Phys. 17 (2015) 013028 doi:10.1088/1367-2630/17/1/013028
PAPER
Structural and electronic properties of manganese-doped Bi2Te3
epitaxial layers
J Růžička1,2
, O Caha1,2
, V Holý3
, H Steiner5
, V Volobuiev5
, A Ney5
, G Bauer5
, T Duchoň4
, K Veltruská4
,
I Khalakhan4
, V Matolín4
, E F Schwier6
, H Iwasawa6
, K Shimada6
and G Springholz5
1
CEITEC, Masaryk University, Kotlářská 2, 61137 Brno, Czech Republic
2
Department of Condensed Matter Physics, Faculty of Science, Masaryk University, Kotlářská 2, 61137 Brno, Czech Republic
3
Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University in Prague, Ke Karlovu 5, 12116 Praha,
Czech Republic
4
Department of Surface and Plasma Science, Faculty of Mathematics and Physics, Charles University in Prague, V Holešovičkách 2, 18000
Praha, Czech Republic
5
Institut für Halbleiter- und Festkörperphysik, Johannes Kepler Universität, Altenbergerstr. 69, 4040 Linz, Austria
6
Hiroshima Synchrotron Radiation Center, Hiroshima University Kagamiyama 2-313, Higashi-Hiroshima, Hiroshima 739-0046, Japan
E-mail: holy@mag.mff.cuni.cz
Keywords: topological insulators, thin layers, EXAFS, ARPES
Abstract
We show that in manganese-doped topological insulator bismuth telluride layers, Mn atoms are
incorporated predominantly as interstitials in the van der Waals gaps between the quintuple layers and
not substitutionally on Bi sites within the quintuple layers. The structural properties of epitaxial layers
with Mn concentration of up to 13% are studied by high-resolution x-ray diffraction, evidencing a
shrinking of both the in-plane and out-of plane lattice parameters with increasing Mn content. Ferromagnetism
sets in for Mn contents around 3% and the Curie temperatures rises up to 15 K for a Mn
concentration of 9%. The easy magnetization axis is along the c-axis perpendicular to the (0001) epilayer
plane. Angle-resolved photoemission spectroscopy reveals that the Fermi level is situated in the
conduction band and no evidence for a gap opening at the topological surface state with the Dirac cone
dispersion is found within the experimental resolution at temperatures close to the Curie temperature.
From the detailed analysis of the extended x-ray absorption fine-structure experiments (EXAFS)
performed at the MnK-edge, we demonstrate that the Mn atoms occupy interstitial positions within
the van der Waals gap and are surrounded octahedrally by Te atoms of the adjacent quintuple layers.
1. Introduction
Bismuth telluride (Bi2Te3) is a prototypical example for a three-dimensional (3D) topological insulator with a
gapped bulk band structure and a topological two-dimensional (2D) surface state with Dirac-like energy–
momentum dispersion and spin–momentum locking [1–3]. The surface states are protected by time-reversal
symmetry and are immune to surface impurities and backscattering. When 3D transition metals such as Mn, Fe,
Cr or V are incorporated as magnetic dopants [4], however, their local exchange fields can break time reversal
symmetry and thus may lift the degeneracy of the Dirac points with a concomitant gap opening of the
topological surface state [1–3, 5–8]. In addition, novel phenomena arising from the interaction between
topologically protected states and ferromagnetic order have been theoretically predicted [1–3], including the
topological magneto-electric effect, the quantum anomalous Hall effect, half-integer charges at magnetic
domain boundaries [3]; some of these were already observed experimentally [9].
The solubility of magnetic ions in topological insulators is typically limited to a few percent and Mn-doped
Bi2Te3 crystals and thin films with concentrations of up to 10% were found to be ferromagnetic with Curie
temperatures around 10 K [10–16]. In some of these works, Mn-doped Bi2Te3 showed p-type conduction
[10, 11] or at least a weak acceptor-like behavior of Mn [17] as evidenced by a downward shift of the Fermi level
[10, 11, 17]. From this it was concluded that Mn ions preferentially occupy substitutional Bi lattice sites, forming
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Reprinted page 1 of paper [87] “Properties of Manganese doped Bi2Te3”.
(Bi −x1 Mnx)2Te3 [11]. However, the downward shift of the Fermi level observed by angle-resolved photoelectron
spectroscopy (ARPES) was rather small, i.e., much less than expected for purely substitutional Mn
incorporation. In most other works, Mn-doped Bi2Te3 even retained its n-type character [14, 17], indicating a
non-substitutional Mn incorporation. Indeed, recent compositional analysis of bulk crystals has revealed that
Mn may also be incorporated interstitially as in MnxBi2Te3 [14], but no precise information on the actual
incorporation sites was reported. It has also been suggested that Mn may incorporate in excess Bi–Bi double
layers [12, 15] easily formed in bismuth telluride when grown under tellurium deficient conditions [12, 18, 19].
Thus, the mechanism of Mn incorporation has been rather unclear. Nevertheless, in all cases, Mn doping has
resulted in ferromagnetic behavior, but without any remarkable dependence of the Curie temperatures on the
carrier concentration [11, 14, 15, 20].
Due to the complex crystal structure of Bi2Te3 with its large hexagonal unit cell consisting of three Te–Bi–
Te–Bi–Te quintuple layers (QLs) bonded together across a van der Waals (vdW) gap, several different possible
lattice sites exist for the incorporation of magnetic dopants. These include substitutional incorporation for Bi
atoms within the QLs as well as interstitial incorporation within the quintuple layers or within the van der Waals
gap between the QLs in different local coordinations. Evidently, different lattice sites for Mn incorporation are
expected to result in quite different electronic and magnetic properties of the material [16] and, thus, to a
different influence on the topological surface states. Therefore, the determination of the actual position of Mn in
the lattice of Bi2Te3 is of utmost importance for further studies on its striking topological properties and their
interplay with ferromagnetism.
To resolve this issue, in this paper we report a detailed study on the lattice sites of Mn incorporation in
Bi2Te3. For this purpose, we performed a systematic investigation on a series of Mn-doped epitaxial Bi2Te3 layers
using high-resolution x-ray diffraction (XRD) and extended x-ray absorption fine-structure (EXAFS)
measurements. These were complemented by magnetic characterization using a superconducting quantum
interference magnetometer (SQUID), which revealed that the layers are ferromagnetic with Curie temperatures
of up to 15 K. Angle-resolved photoelectron spectroscopy (ARPES) shows no opening of a gap of the topological
surface state at temperatures down to 12 K. By detailed theoretical analysis of the XRD and EXAFS spectra, we
show that Mn is incorporated predominantly as interstitial in octahedral positions within the vdW gaps of
Bi2Te3, i.e., between two Te layers of adjacent QLs.
2. Growth
Mn-doped Bi2Te3 layers were grown by MBE on(111)-orientated BaF2 substrates using a compound bismuth
telluride effusion cell, a Mn cell, and an additional tellurium cell for stoichiometry control. The in-plane latticeconstant
of BaF2 (111) is almost exactly lattice-matched to the lattice constant a of the hexagonal basal planes of
Bi2Te3 (lattice-mismatch less than 0.04 %) and, thus, growth proceeds with the c-axis orientation perpendicular
to the surface [18]. A whole series of samples was grown where the Mn concentration was varied between 0 and
13%. For all samples, the substrate temperature was 330 °C and a background pressure of⩽ × −
5 10 10
mbar was
maintained during growth. The flux rates from the sources were measured using a cooled quartz crystal
microbalance moved into the substrate deposition. The mass deposition rates were converted into the flux rate
of atoms arriving at the surface using the density and molar mass of each component. The total growth rate of
(Bi,Mn)2Te3 was∼0.15 QL−1
or∼1.5 Å s−1
and a high excess tellurium flux above 2.5 Å/s was provided during
growth, corresponding to an overall Te-to-Bi(Mn) flux ratio of∼5:1. Under these conditions, stoichiometric
Bi2Te3 epilayers are obtained with no indication of formation of Bi–Bi double layers, as shown in detail by our
previous work [18, 19]. The Mn concentration in the samples varied from =x 0Mn to 13% and was determined
by the measured Mn-to-Bi flux ratios, where we defined xMn as the ratio of Mn atoms relative to the number of
the sum of Bi and Mn atoms. Thus, the overall layer composition can be represented by MnxBi −x1 Tey, where
⩽y 1.5 depends on the type of Mn incorporation. For purely substitutional Mn, y = 1.5, whereas for purely
interstitial Mn, = −y x1.5(1 ), provided that the 2:3 ratio between Bi and Te is retained. Nice streaked
reflection high-energy electron diffraction (RHEED) patterns were observed during growth for all samples
irrespective of the Mn content, indicating 2D growth in all cases. All layers exhibit n-type conduction with an
electron density of∼1019
cm−3
that does not change significantly with Mn content.
3. Structural characterization by x-ray diffraction
The rhombohedral crystal structure of Bi2Te3 with R3¯ m symmetry and the different possible incorporation
sites of Mn are illustrated in figure 1. The unit cell with the hexagonal lattice parameters a = 0.4385 nm and
c = 3.051 nm [18] consists of fifteen (0001) hexagonal lattice planes grouped in three Te(1)
–Bi-Te(2)
–Bi-Te(1)
QLs stacked in ABCABC…sequence [see figure 1(a)]. The QLs are weakly bonded together by a double layer of
2
New J. Phys. 17 (2015) 013028 J Růžička et al
Reprinted page 2 of paper [87] “Properties of Manganese doped Bi2Te3”.
Te atoms forming the vdW gaps of the structure. Because of the large inter-planar distance of the vdW gap,
interstitial positions within the vdW gaps are expected to be favorable for Mn incorporation. Two possible
interstitial positions in the vdW gaps exist, either tetrahedral or octahedral sites with 4, respectively, 6 nearest
neighboring Te atoms, as illustrated in figures 1(b) and (c). Substitutional Mn is expected to reside on Bi atom
positions within the QLs. The corresponding expected nominal nearest neighbor (NN) distances for these three
different incorporation sites are listed in table 1, together with the NN distances of Mn in Bi–Bi DL in Te-deficit
Bi2Te δ−3 , as proposed by [12, 15]. Also listed are the NN Mn–Te distances in several other manganese telluride
compounds such as zinc blende (zb) MnTe ( =a 6.3380 Å) [21], wurzite (wz) MnTe (a = 6.49 Å, c = 6.701 Å)
[22], hexagonal, i.e., NiAs-type MnTe (a = 4.148 Å, c = 6.710 Å) [22] and cubic (pyrite) MnTe2 (a = 6.943 Å)
[23, 24]. In zb- and wz-MnTe, the Mn ions are tetrahedrally coordinated, whereas in the other two compounds
Mn has an octahedral coordination. As illustrated by figures 1(d) and (e), in MnTe2 the Mn ions are similarly
coordinated as in the octahedral lattice sites in Bi2Te3.
In order to study the crystal structure of Mn-doped Bi2Te3, high resolution x-ray diffraction experiments
were performed using CuKα radiation and a diffractometer equipped with multilayer parabolic optics, a
4 × (220) Ge Bartels monochromator and a 2 × (220) Ge analyzer crystal. Symmetrical L(000 )scans of the
Figure 1. (a) Hexagonal unit cell of Bi2Te3 consisting of three Te(1)–Bi–Te(2)-Bi–Te(1) quintuple layers (QL) stacked in an ABCABC…
sequence. The dotted lines denote the vdW gaps between two adjacent Te layers. Tetrahedral and octahedral interstitial positions in a
vdW gap are illustrated in panels (b) and (c), respectively. (d) Unit cell of the cubic pyrite MnTe2 phase [23, 24], in which the Mn
atoms are also octahedrally coordinated. In (e) the atom positions around an octahedral coordinated Mn in the vdW gap in Bi2Te3 is
compared to the Te positions in the first coordination shell of MnTe2. The green lines denote the connections of the central Mn atom
to the Te atoms in the first coordination shell.
Table 1. Nominal nearest-neighbor (NN) distances of Mn in the Bi2Te3 lattice for various possible positions of the Mn ions (see figure 1). For
comparison, the NN Mn–Te distances in various other manganese telluride compounds [zinc blende (zb), wurzite (wz) and hexagonal
MnTe (NiAs type) as well as cubic MnTe2 (pyrite type)] are listed.
Mn position NN distance (nm)
Substitutional Mn on Bi site in Bi2Te3 0.3032
Tetrahedral Mn as interstitial in vdW gap 0.2542
Octahedral Mn as interstitial in vdW gap 0.2885
Substitutional Mn in Bi-Bi DL in Bi2Te δ−3 0.3268
Tetrahedral Mn in zb MnTe 0.2774
Tetrahedral Mn in wz MnTe 0.2513
Octahedral Mn in hexagonal MnTe
(NiAs type)
0.2924
Octahedral Mn in MnTe2 (pyrite type) 0.2904
3
New J. Phys. 17 (2015) 013028 J Růžička et al
Reprinted page 3 of paper [87] “Properties of Manganese doped Bi2Te3”.
samples with different Mn content are presented in figure 2(a), where the scattered intensities are plotted as
functions of the length Q of the scattering vector. The pure Bi2Te3 layer exclusively shows the diffraction maxima
with = …L 9, 15, 18, 21, characteristic for the perfect Bi2Te3 phase (see [18, 19] for details), evidencing the
absence of additional Bi–Bi double layers in the structure [19]. With increasing Mn content xMn, the diffraction
maxima are shifted, and additional satellite maxima appear as indicated by the blue arrows in figure 2.
To analyze the diffraction data, we start with the diffraction data of the non-doped Bi2Te3 sample ( =x 0Mn ).
The unit cell of Bi2Te3 is non-primitive and consists of three identical QLs mutually shifted in a lateral direction
[see figure 1(a)]. Therefore, in symmetric L(000 )diffraction [figure 2(a)], the structure factors of the
quintuplets are identical and the effective structure unit of the crystal is one-third of the hexagonal unit cell c
with a height =d c 3QL . Thus, only diffraction maxima = …L 3, 6, 9, are allowed and the positions of these
maxima are indicated by red dotted lines in figure 2. Ignoring the small differences in the inter-planar distances
within the QLs and between them [19], Bi2Te3 can be considered as a periodic sequence of 2D hexagonal basal
planes of atoms with ABC... stacking similar to a face-centered cubic lattice. In this layer sequence, the (Bi,Te)
occupation of the lattice positions varies periodically along the [0001] growth direction. Replacing the true
atoms in the lattice by a virtual ‘mixture’ of Bi and Te, the diffraction maxima of such a crystal will appear at
π= 〈 〉Q n d2 , where n is an integer and〈 〉d is the mean distance of the (0001)-planes of the virtual crystal, i.e.,
the average distance between the basal planes in the actual lattice. Since〈 〉 = =d d c5 15QL , the diffraction
maxima of this virtual lattice appears at = …L 15, 30, 45, (red arrows in figure 2). As a result, these are the
major diffraction maxima, whereas all other (000 L) maxima with = … …L , 9, 12, 18, 21, 24, 27, 33, ) can be
considered as modulation maxima caused by the periodic modulation of the occupation of the lattice planes
either by Te or Bi atoms. Taking into account the modulation of the periodic sequence of QLs, we thus obtain the
diffraction pattern of the Bi2Te3 phase, and the corresponding additional peaks are denoted by green arrows in
figure 2. From this analysis, it follows that only the maxima L = 15, 30 (red arrows) can be used for determination
of the average spacing〈 〉d of the lattice planes, i.e., for derivation of the average lattice constant along the c-
direction.
As shown in figure 2, with increasing Mn concentration, additional (satellite) maxima appear in the
diffraction spectra (blue arrows). These satellites are caused by an additional modulation of the structure along
the growth direction with a period π Δ=L Q2mod that is given by the distance ΔQ between these satellite
maxima. This is similar to the case of the tellurium deficit in the Bi2Te δ−3 structures, where additional Bi–Bi
double layers are randomly inserted between the quintuple layers [19]. In Mn-doped Bi2Te3, we assume that this
Figure 2. (a) Symmetric x-ray L(000 )-diffraction scans of Mn doped Bi2Te3 epilayers with Mn content xMn increasing from 0 to 13%
from bottom to top. The BaF2 substrate peaks are labeled by ‘S’. (b) Simulated L(000 )diffraction curves for various average
contractions Δ〈 〉d of the mean inter-planar lattice distance due to interstitial Mn incorporation (see text for details). In both panels,
the vertical dotted lines and the red numbers denote the positions and L indexes of the diffraction maxima of the ideal Bi2Te3 lattice.
The red and green arrows denote the diffraction maxima of the hypothetic virtual crystal and of the pure Bi2Te3 phase; the blue arrows
denote the additional satellite maxima arising from the additional modulation of the spacing of the Mn gaps with different values of
Δ〈 〉d as described in the text.
4
New J. Phys. 17 (2015) 013028 J Růžička et al
Reprinted page 4 of paper [87] “Properties of Manganese doped Bi2Te3”.
modulation comes from Mn incorporated in the vdW gaps between the QL layers, which changes the distance
between the facing Te–Te layers in the gap in a modulated manner. To support this idea, a series of diffraction
curves was simulated assuming that after every mth quintuple layer the distance of the Te–Te vdW gap and the
distance between the first Te layer and the subsequent Bi layer is changed by Δ −dTe Te and Δ −dTe Bi, respectively.
We averaged the diffracted intensity over random values of m with an average value of〈 〉m and a root-mean
square (rms) deviationσm with respect to this value. The such-created modulation period is related to m by
= 〈 〉L d m2 2QLmod . The corresponding simulation results for different Δd andσ = 0.8m are presented in
figure 2(b), where Δ〈 〉d denotes the deviation of the mean inter-planar distance from the value in the pure
Bi2Te3 phase. From the structure of Bi2Te3, it follows that Δ Δ Δ〈 〉 = + 〈 〉− −d d d m( 2 ) (5 )Te Te Te Bi . The
simulations reveal that the diffraction curves sensitively depend on Δ〈 〉d ; the dependence on the individual
deviations Δ − −dTe Te,Te Bi turned out to be negligible for Δ ⩽− −d| | 0.005Te Te,Te Bi nm.
As illustrated by figure 2(b), with this model, key features of the diffraction curves can be explained, such as
the appearance of the additional modulation peaks (blue arrows in figure 2) with increasing Mn concentration,
as well as the shifts of the diffraction peaks. Still, the model is too simple to exactly reproduce the shapes of the
diffraction curves. From the simulations, it follows that with increasing negative values of Δ〈 〉d , the lattice
constants c decreases, and, consequently, the ‘true’ diffraction peaks (red and green arrows) move to larger Q.
With increasing Δ〈 〉d , the envelope curve of the diffraction maxima changes due to the change of the form factor
within the structure period, similar to what is seen in the experiments. This is why, for instance, the maximum at
L = 30 in the Δ〈 〉 = −d 0.006 nm curve is smaller than its first satellite, whereas this maximum is completely
suppressed for Δ〈 〉 = −d 0.01nm. This effect must be taken into account in the determination of Δ〈 〉d from the
measured diffraction data.
For further evaluation of the experimental data, for each sample we have determined the mean inter-planar
distances〈 〉d , the mean modulation period〈 〉m , as well as its rms deviationσm from the positions of the ‘true’,
respectively, additional satellite peaks. In addition, the in-plane lattice parameter a of the layers was determined
from the peak positions of the asymmetric (101¯4) diffraction peaks measured by reciprocal space mapping [18].
The results are listed in table 2 and plotted in figure 3 as a function of the Mn concentration xMn. Clearly, the
vertical average inter-planar distance〈 〉d and thus, the lattice parameter c, as well as the in-plane lattice
parameter a continuously decrease with increasing Mn content. This indicates that Mn is indeed incorporated in
the bismuth telluride host lattice, and that Mn does not induce the formation of additional Bi–Bi double layers
between the quintuplets as proposed by Lee et al [15]. As in the latter case, the in-plane lattice constant a should
Table 2. Lattice parameters a and c and additional structure modulation〈 〉m and its rms fluctuationσ 〈 〉mm for Mn-doped bismuth telluride
epilayers with different Mn concentrations xMn as determined by x-ray diffraction. Also listed are the Curie temperatures derived from
SQUID data.
xMn (%) a (nm) c (nm) 〈 〉m σ 〈 〉mm TC (K)
0 0.4380 ± 0.0001 3.0508 ± 0.0015 — — 0
1 0.4380 ± 0.0003 3.0399 ± 0.0045 13.8 ± 1.0 0.16 ± 0.02 0
3 0.4374 ± 0.0003 3.0101 ± 0.0075 2.6 ± 1.0 0.18 ± 0.02 7.5
6 0.4368 ± 0.0006 3.0098 ± 0.0105 2.2 ± 1.0 0.16 ± 0.02 10
9 0.4365 ± 0.0006 2.9850 ± 0.0150 2.0 ± 1.0 0.16 ± 0.02 15
13 0.4340 ± 0.0010 — 1.4 ± 2.0 0.25 ± 0.04 12
Figure 3. (a) Mean inter-planar distance〈 〉d (blue) and the in-plane lattice parameter a of Mn-doped bismuth telluride plotted as a
function of Mn concentration obtained by x-ray diffraction. The horizontal dotted lines represent the nominal values of pure Bi2Te3.
(b) Mean modulation periods〈 〉m (blue) and their rms deviationσm from the average value determined from the positions and widths
of the satellite peaks in figure 2.
5
New J. Phys. 17 (2015) 013028 J Růžička et al
Reprinted page 5 of paper [87] “Properties of Manganese doped Bi2Te3”.
increase [19] rather than decrease with increasing alloy concentration. No additional modulation periodicity is
found for =x 0Mn . For =x 1Mn %, the modulation period〈 〉m is about 14, i.e., very large, but it rapidly decreases
for higher xMn to〈 〉 ≈m 2.5 without significant further changes. For =x 13Mn %, the value of〈 〉d cannot be
determined, since its diffraction curve does not exhibit the ‘true’ red- and green-arrow peaks and the diffraction
maxima become very broad, so that the uncertainty in determining〈 〉m is rather large. As in this case, the Mn
concentration is close or even above the solubility limit, so it is likely that for this structure already some phase
separation has occurred, with the formation of small amounts of secondary Mn–Te phases, leading to a
structural degradation. However, the amount of secondary phases must still be small, as no extra diffraction
peaks for secondary phases are observed in the diffraction data.
4. Magnetic and electronic properties
The magnetic properties of the Mn-doped Bi2Te3 epilayers were characterized by SQUID magnetization
measurements, where the magnetization M(H) and M(T) were recorded as a function of temperature from 2 K
to 300 K, and magnetic field H applied either perpendicular (out-of-plane) or parallel (in-plane) to the surface of
the films. The diamagnetic contribution of the BaF2(111) substrate was derived from M(H) curves at 300 K and
was subtracted from all data. Note, that identical sample pieces were used for in-plane and out-of-plane
measurements, as described in [25]. Figure 4 shows the in-plane and out-of-plane magnetization curves for the
4% and 9% Mn-doped Bi2Te3 samples at 2 K, representative for the entire sample series. For both samples, a
clear hysteresis is observed, evidencing ferromagnetic properties, and in both cases, the c axis, i.e., the out-ofplane
orientation, is clearly the easy axis of magnetization, similar to the findings of bulk samples [11, 14] and
films grown on InP(111) [15]. The inset of figure 4(a) shows the dependence of the Curie temperatureTC on xMn
estimated from the M(T) measurements.TC increases from 8.5 K for =x 3Mn % up to 15 K for =x 10Mn %,
consistent with previous findings [14, 15]. At high xMn, a slight decrease inTC is observed, accompanied by a
finite positive slope in the 2 K M(H) curves at a high magnetic field above 1 T (not shown). We tentatively ascribe
this observation to the onset of the formation of a secondary antiferromagnetic Mn-containing phase such as
hexagonal MnTe or cubic MnTe2, which reduces the effective concentration of ferromagnetic Mn incorporated
in the bismuth telluride host. A detailed analysis of this secondary phase will be reported elsewhere.
To characterize the topological surface state and electronic band structure of the epitaxial layers, ARPES
investigations were performed at the beamline BL-1 of the Hiroshima Synchrotron Radiation Center (HiSOR)
at Hiroshima University, with a set-up described in detail elsewhere [26]. In order to avoid surface deterioration
during air exposure of the samples during transportation, the samples were capped in situ in the MBE chamber
by a Te/Se double layer after cooling to room temperature. This provides effective protection against surface
oxidation. Prior to ARPES measurements, the samples were decapped in UHV by annealing at 130 °C and
°250 C for 15 minutes to completely desorb the Se and Te capping layers and regain a clean epilayer surface. This
was checked and confirmed by low-energy electron diffraction. Low-temperature ARPES data recorded at 12 K
for the series of samples with various xMn from 0 up to 13% are shown in figure 5.
For all Mn-doped bismuth telluride layers, the ARPES data shows a well-pronounced Dirac cone of their
topological surface states up to highest xMn of 13%, i.e., no apparent gap opening at the Dirac point is observed
within the experimental resolution of 30 meV. This is in contrast to previous results for Bi −x2 MnxSe3 reported
Figure 4. In-plane (blue) and out-of plane (red) magnetization curves M(H) measured at 2 K for two Mn-doped bismuth telluride
epitaxial layers with =x 4Mn % (a) and 9% (b). The inset shows the dependence of the Curie temperatureTC on the Mn concentration.
6
New J. Phys. 17 (2015) 013028 J Růžička et al
Reprinted page 6 of paper [87] “Properties of Manganese doped Bi2Te3”.
by Xu et al [27], who have found a gap opening even above the bulk ferromagnetic Curie temperature, which was
attributed to an enhanced ferromagnetic order at the surfaces. This is not found for our Mn-doped Bi2Se3
epilayers at T = 12 K. However, since the theoretically predicted gap opening is below 20 meV in the
ferromagnetic phase for substitutional Mn incorporation [8], our observations do not completely rule out such
an effect. It is noted that the absence of a gap opening as revealed by our experiments is in agreement with
observations for bulk Bi −x2 MnxTe3 [10, 11] and moreover, it has been theoretically predicted that under certain
conditions, the topological surface states may survive upon moderate Mn doping [8]. For all our samples, the
Fermi energy is within the conduction band (dashed horizontal lines in figure 5) irrespective of the Mn
concentration. Thus, we do not observe a notable p-doping of bismuth telluride by Mn incorporation, i.e., Mn
does not show an acceptor-like behavior. This is a first indication that Mn is not substitutionally incorporated on
Bi lattice sites.
5. X-ray absorption spectroscopy
To gain further insights on the Mn incorporation, we have performed EXAFS experiments at the BM32
beamline of the European Synchrotron Radiation Facility in Grenoble. EXAFS measurements were performed at
the MnK-edge (6.55 keV) at the incidence angle of 2.5° with respect to the sample surface. The
MnKα fluorescence signal was detected using an energy dispersive detector placed nearly horizontally to the
sample in order to suppress the elastic scattering signal of the horizontally polarized synchrotron x-ray beam.
Several spectra were averaged, and the normalized EXAFS part χ E( )was extracted using the Athena software
[28] as χ μ μ Δμ= −E E E( ) ( ( ) ( ))0 0, where μ E( )denotes the measured absorption spectrum, μ E( )0 is its
smooth background corresponding to a absorption of an isolated (‘bare’) Mn atom and Δμ0 is the height of the
absorption edge. The photon energy is transformed into wave vector k of the excited electron as
= + E E k m(2 )edge
2 2
e , where Eedge is the energy of the absorption edge andme is the electron mass.
Normalized EXAFS spectra for the samples with different Mn concentration are presented in figure 6. Evidently,
the spectra collected from various samples do not show significant differences, indicating that the Mn
incorporation does not depend much on the Mn content of our samples. The signal from the sample with Mn
content of xMn = 1% was too low compared to the background noise, so we did not include this sample in the
data evaluation.
For the determination of the preferentially occupied Mn lattice sites, extensive ab initio simulations of the
EXAFS spectra using the FEFF9 software [29] were carried out. In the simulations, octahedral and tetrahedral
interstitial Mn positions within the vdW gaps, as well as substitutional Mn on Bi lattice sites, as well as
Figure 5. ARPES spectra at 12 K for Mn-doped Bi2Te3 layers with =x 0Mn % (a), 4% (b), 6% (c), 9% (d), and 13% (e). The data was
measured along the K-Γ-K cut of momentum space at ν =h 50 eV. (f) Energy distribution curves (EDC) of the sample with
=x 13%Mn with an obvious maximum in the Dirac point. The horizontal dotted lines denote the Fermi energy.
7
New J. Phys. 17 (2015) 013028 J Růžička et al
Reprinted page 7 of paper [87] “Properties of Manganese doped Bi2Te3”.
substitutional Mn in extra Bi–Bi double layers between QL layers as suggested by [12, 15] were considered. For
further comparison, simulations were also performed for various other manganese telluride phases, including
zb, wz and hexagonal MnTe (NiAs-type) lattices, as well as cubic pyrite MnTe2 (see figure 1) with the NNdistances
listed in table 1. For all possible Mn sites, series of simulations were performed using variable cluster
sizes up to 1.2 nm. The simulations showed that increasing the cluster radius beyond 0.9 nm did not cause any
changes of the calculated results. Therefore, a cluster size of 0.9 nm was used for all simulations, which included
85 to 140 atoms, depending on the lattice structure assumed. This cluster size is typical for these types of
simulations.
In figure 7, the experimental EXAFS spectrum for the sample with =x 9Mn % is compared with the results of
the FEFF9 simulations for the different Mn incorporation sites. It turns out that only for the octahedral
interstitial Mn positions within the vdW gap (top curve in figure 7) the measured data is reproduced very well by
the simulation, while for Mn incorporation at the other positions, the simulations strongly differ from the
experimental spectra. The same result was also found for all other samples with different Mn concentrations.
Thus, we conclude that Mn in Bi2Te3 is predominantly incorporated in the middle of the van der Waals gap
between the QLs in octahedral coordination—at least under the given growth conditions. In the further data
evaluation we therefore consider only the octahedral Mn interstitial position.
Figure 6. Normalized MnK-edge EXAFS spectra for the Mn-doped bismuth telluride epilayers with different Mn concentrations. The
spectra are shifted vertically for clarity.
Figure 7. Measured EXAFS spectrum of the bismuth telluride sample with =x 9Mn % (black lines) compared with spectra derived
from ab initio atomistic simulations (red lines) assuming different Mn positions in the Bi2Te3 lattice from Mn in the vdW gap to
substitutional Mn in the QLs, or Bi–Bi DLs as suggested by [12, 15]. Also plotted for comparison, are the simulated spectra (blue lines)
for various MnTe (zb, wz, hexagonal) and MnTe2 (pyrite) lattices described in the text. The spectra are shifted vertically for clarity.
8
New J. Phys. 17 (2015) 013028 J Růžička et al
Reprinted page 8 of paper [87] “Properties of Manganese doped Bi2Te3”.
For the refinement of the lattice structure around the Mn ion in the octahedral interstitial site, we have fitted
the measured χ k( )EXAFS spectra, using the Artemis (IFEFFIT) software package [28]. In the fit we have
included six Te atoms in the first coordination shell and two Bi atoms in the second coordination shell. The
measured and fitted χ k( )and χ R( )curves of samples with =x 4, 6, 9, 13Mn % are displayed in figures 8(a) and
(b). From these fits, the NN and next-nearest neighbor (NNN) distances −dMn Te and −dMn Bi are obtained and
the results are listed in table 3. We obtained ≈−d 0.291Mn Te nm and ≈−d 0.303Mn Bi nm for all samples, with an
insignificant variation in dependence of the Mn content. This value is very close to the nominal value expected
for undistorted pure Bi2Te3, whereas for the other possible incorporation sites, much different values would be
expected (see table 1). The low Mn concentration for the =x 4Mn % sample and the resulting comparatively
high noise level in the data, did not allow us to fit the positions of the Bi atoms in the second coordination shell,
i.e., only the Te positions in the first shell were refined for this sample.
We note that for the samples with low Mn contents of =x 4Mn and 6%, the theoretical χ R( )curves differ
significantly in the range <R 0.15 nm. This region corresponds to long-range oscillations in energy dependence
of the absorption spectrum μ E( ), which is very sensitive to method used for the background subtraction. Since
the measured fluorescence signal is proportional to the Mn content, the background and signal-to-noise is how
itʼs usually stated ratio is higher for the samples with lower Mn content compared to those obtained for high
x .Mn The error limits in table 3 were determined as the reproducibility of the fitted distances with respect to
various normalization methods of χ R( )obtained by the several data normalization methods available by the
Athena software. The fitted −dMn Te values correspond within the error limits to the expected theoretical value of
the ideal Bi2Te3 lattice listed in table 1. On the other hand, from the XRD data, we found that increasing the Mn
concentration induces a contraction of the averaged lattice, both in lateral and vertical directions, which should
affect the −dMn Te distances determined by EXAFS. However, the error limits of the EXAFS data are much larger
than error limits of the XRD data, i.e., they are as large as the XRD observed-lattice contraction. Therefore, the
sensitivity of EXAFS data does not allow us to see the effect of the small average lattice contraction to the first
coordination around interstitial Mn atoms that was deduced by x-ray diffraction.
In [15], it has been suggested that Mn induces the creation of excess Bi–Bi double layers into which Mn
atoms are substitutionally incorporated. According to this work, when increasing the Mn content, the structure
Figure 8. Comparison of the measured (points) and fitted (line) EXAFS spectra χ k( )(a) and χ R( ) (b) of bismuth telluride samples
with different Mn concentrations. The curves are shifted vertically for clarity.
Table 3. Distances of the six nearest tellurium atoms and two nearest bismuth atoms to the central Mn atom in octahedral configuration in
Mn-doped bismuth telluride with different Mn concentrations xMn = 0 to 13% as determined from the fit of the χ R( )EXAFS data using the
model of Mn incorporated interstitially in octahedral positions in the vdW Te–Te gap.
x (%)Mn −dMn Te (nm) −dMn Bi (nm)
4 0.290 ± 0.009 —
6 0.292 ± 0.004 0.304 ± 0.010
9 0.292 ± 0.004 0.303 ± 0.010
13 0.291 ± 0.006 0.306 ± 0.014
9
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Reprinted page 9 of paper [87] “Properties of Manganese doped Bi2Te3”.
should change from pure Bi2Te3 phase towards the Bi2Te2 phase, in which a Bi–Bi DL occurs periodically after
each pair of Te–Bi–Te–Bi–Te QLs. In our previous work [19], the structure of various Bi2Te δ−3 phases was
studied in detail, revealing that with increasing δ, i.e., when moving from Bi2Te3 towards Bi2Te2, the in-plane
lattice parameter a increases, whereas the vertical lattice parameter c decreases. This is in contradiction to our
results observed for Mn-doped Bi2Te2, where both lattice parameters a and c decrease with increasing xMn (see
figure 3 and table 2). This fact supports our conclusion that the Mn atoms occupy interstitial places and do not
evoke the creation of Bi–Bi DLs.
Finally, we compare the positions of the Te atoms in the first coordination shell around octahedral Mn
interstitials in the vdW gaps with those of the Te atoms surrounding Mn in cubic MnTe2 [24] [figures 1(d) and
(e)]. We find that the structure of both first coordination shells, as well as the NN distances, is very similar
indeed. Thus, the local lattice configuration around an occupied octahedral Mn interstitial can be considered as
slightly deformed MnTe2. This similarity is also obvious from the comparison of the measured and simulated
EXAFS spectra in figure 7, where the spectrum simulated for the pyrite MnTe2 is quite close to the experimental
data for larger energies, i.e., for larger lengths of the photoelectron wave vector k. This coincidence implies the
similarity of the first coordination shell around Mn in the investigated samples and in MnTe2.
As the origin for the additional modulation of the lattice along the growth direction [0001] with the period of
≈L D2 ,mod we propose that the Mn-occupation of the adjacent vdW gaps is not statistically independent, and a
self-organized Mn modulation wave is created. This hypothesis needs further investigation. We note that if the
Mn ions exclusively occupy octahedral positions and these sites occur on average only in every mth vdW Te–Te
gap, the full occupation of these places corresponds to the phase Mn m1 Bi2Te3. From this, it follows that in
samples with =x 13Mn % and m = 2, every fourth of the possible octahedral sites within the vdW gaps is
occupied.
6. Summary
Structural investigations of epitaxial ferromagnetic layers of the Mn-doped topological insulator Bi2Te3 reveal
that the Mn dopant ions are incorporated mostly in octahedral interstitial positions in the middle of the van der
Waals gaps between the adjacent Te layers of the quintuple layers. The local environment of the Mn ions
corresponds to a distorted cubic MnTe2 lattice with a nearest neighbor Mn–Te distance of 0.2901 Å. From the
EXAFS data, we can rule out that Mn resides in sizable amounts on substitutional Bi sites or on tetrahedrally
coordinated interstitial sites. This explains the rather small effect of Mn on the carrier type and concentration of
the samples. These findings provide an important input for the ongoing experimental and theoretical
investigations on the mechanisms that mediate ferromagnetism in n-type transition-metal-doped topological
insulators in which charge carriers do not seem to play any dominant role, unlike in conventional Mn-doped
ferromagnetic III–V semiconductors. Moreover, our findings are important for theoretical modeling of the
effect of Mn incorporation on the topological surface state of bismuth telluride.
Acknowledgments
The assistance of Cornelius Strohm of BM23 beamline at ESRF is acknowledged. The work was supported by the
Czech Science Foundation (projects P204/12/0595 and 14-08124S), by the Austrian Science Fund (project SFB-
025 IRON), and by the Hiroshima Synchrotron Radiation Center (proposal 12-B-17).
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[16] Li Y, Zou X, Li J and Zhou G 2014 J. Chem. Phys. 140 124704
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[17] Vobornik I et al 2014 J. Phys. Chem. 118 12333–9
[18] Caha O et al 2013 Cryst. Growth Des. 13 3365–73
[19] Steiner H, Volobuev V, Caha O, Bauer G, Springholz G and Holy V 2014 J. Appl. Cryst. 47 1889–900
[20] Chapler B C, Post K W, Richardella A R, Lee J S, Tao J, Samarth N and Basov D N 2014 Phys. Rev B 89 235308
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Thin Solid Films 267 74–78
[22] Wyckoff R W G 1963 Cryst. Struct. 1 85–237
[23] Elliott N 1937 J. Am. Chem. Soc. 59 1958–62
[24] Johnston W D, Miller R C and Damon D H 1965 J. Less Common Met. 8 272–87
[25] Ney A 2011 Semicond. Sci. Technol. 26 064010
[26] Shimada K et al 2000 Nucl. Instrum. Meth. 467 504–7
[27] Xu S Y et al 2012 Nat. Phys. 8 616–22
[28] Ravel B and Newville M 2005 J. Synchrotron Radiat. 12 537
[29] Rehr J J, Kas J J, Vila F D, Prange M P and Jorissen K 2010 Phys. Chem. Chem. Phys. 12 5503
11
New J. Phys. 17 (2015) 013028 J Růžička et al
Reprinted page 11 of paper [87] “Properties of Manganese doped Bi2Te3”.
CHAPTER 4. REPRINTED PAPERS 119
4.6 Band gap in manganese doped topological insulators Bi2Te3
and Bi2Se3
The Mn-doped samples were grown and analyzed using magnetic measurements, XRD, XAFS,
HRTEM, and other methods. The structure was composed of random stacking of Bi2Te3
quintuple layers and MnBi2Te4 septuple layers. The concentration of septuple layers increases
with manganese doping. The Curie temperature was found to be approximately 20 K, and
the magnetization easy-axis is out-of-plane. The low-temperature ARPES and spin-resolved
ARPES experiments have shown a band gap opening in the Dirac point with a size of 90 meV.
The temperature dependence of the band gap size correlates with remanence magnetization.
The paper presented the first direct observation of a magnetic band gap in the topological
surface state. Bismuth selenide, on the contrary, does not show a magnetic band gap since
its magnetization easy-axis is in-plane.
Nature | Vol 576 | 19/26 December 2019 | 423
Article
LargemagneticgapattheDiracpointin
Bi2Te3/MnBi2Te4 heterostructures
E. D. L. Rienks1,2,3,14
, S. Wimmer4,14
, J. Sánchez-Barriga1,14
, O. Caha5,14
, P. S. Mandal1,7
,
J. Růžička5
, A. Ney4
, H. Steiner4
, V. V. Volobuev4,8,13
, H. Groiss9
, M. Albu10
, G. Kothleitner10
,
J. Michalička6
, S. A. Khan11
, J. Minár11
, H. Ebert12
, G. Bauer4
, F. Freyse1,7
, A. Varykhalov1
,
O. Rader1
* & G. Springholz4
*
MagneticallydopedtopologicalinsulatorsenablethequantumanomalousHalleffect
(QAHE),whichprovidesquantizededgestatesforlosslesscharge-transport
applications1–8
.TheedgestatesarehostedbyamagneticenergygapattheDirac
point2
,buthithertoallattemptstoobservethisgapdirectlyhavebeenunsuccessful.
Observingthegapisconsideredtobeessentialtoovercomingthelimitationsofthe
QAHE,whichsofaroccursonlyattemperaturesthatareonetotwoordersof
magnitudebelowtheferromagneticCurietemperature,TC (ref.8
).Hereweuselow-
temperaturephotoelectronspectroscopytounambiguouslyrevealthemagneticgap
ofMn-dopedBi2Te3,whichdisplaysferromagneticout-of-planespintextureand
opensuponlybelowTC.Surprisingly,ouranalysisrevealslargegapsizesat1 kelvinof
upto90 millielectronvolts,whichisfivetimeslargerthantheoreticallypredicted9
.
Usingmultiscaleanalysisweshowthatthisenhancementisduetoaremarkable
structuremodificationinducedbyMndoping:insteadofadisorderedimpurity
system,aself-organizedalternatingsequenceofMnBi2Te4 septupleandBi2Te3
quintuplelayersisformed.Thisenhancesthewavefunctionoverlapandsizeofthe
magneticgap10
.Mn-dopedBi2Se3 (ref.11
)andMn-dopedSb2Te3 formsimilar
heterostructures,butforBi2Se3 onlyanonmagneticgapisformedandthe
magnetizationisinthesurfaceplane.Thisisexplainedbythesmallerspin–orbit
interactionbycomparisonwithMn-dopedBi2Te3.Ourfindingsprovideinsightsthat
willbecrucialinpushinglosslesstransportintopologicalinsulatorstowardsroom-
temperatureapplications.
The QAHE was first demonstrated in chromium-doped tetradymite
topologicalinsulators2–5
.Subsequently,replacingchromiumwithvana-
diumwasasuccessfulstrategyforachievingprecisequantizationwith
vanishing longitudinal resistance6,7
. The effect occurs because of a
modificationofthebandinversionintheferromagneticstate.Exchange
splitting and spin–orbit coupling lead to a release of the inversion of
one of the spin sub-bands2
. This should manifest itself as a magnetic
gap that opens up at the Dirac point when the system is cooled below
theCurietemperature.Sofar,however,directobservationofthisgap
has remained elusive and no clear correlation with ferromagnetism
has been established.
Angle-resolvedphotoemissionspectroscopy(ARPES)isthemethod
of choice for the direct observation of the magnetic gap. Nevertheless,
the situation has been confusing: large gaps of 0.05–0.2 eV were
first reported for Mn-doped Bi2Se3 (refs. 12,13
), but were later shown
not to be of magnetic origin14
. Such gaps, however, did not appear
when magnetic impurities were deposited on the surface of Bi2Se3
(refs.14–16
).Atlowtemperatures,amobilitygapof32 meVwasinferredfrom
scanning tunnelling Landau level spectroscopy of V-doped Sb2Te3
(ref.17
),butscanningtunnellingspectroscopy(STS)didnotshowagap
in this system17
. STS did reveal gaps of 20–100 meV in Cr-doped (Bi,
Sb)2Te3 (ref.18
),butthetemperaturedependencewasnotinvestigated.
In fact, a similar gap of around 75 meV was found for Cr-doped Bi2Se3
even at room temperature19
. This suggests a nonmagnetic origin for
these effects, because the ferromagnetic TC is well below 50 K in all of
these systems.
Interestingly,theconfigurationofthemagneticdopantsisalsocontradictory.
For isovalent magnetic doping, it has been predicted that
https://doi.org/10.1038/s41586-019-1826-7
Received: 10 May 2018
Accepted: 18 October 2019
Published online: 18 December 2019
1
Helmholtz-Zentrum Berlin für Materialien und Energie, Elektronenspeicherring BESSY II, Berlin, Germany. 2
Institut für Festkörperphysik, Technische Universität Dresden, Dresden, Germany.
3
Leibniz-Institut für Festkörper- und Werkstoffforschung Dresden, Dresden, Germany. 4
Institut für Halbleiter- und Festkörperphysik, Johannes Kepler Universität, Linz, Austria. 5
Department of
Condensed Matter Physics, Masaryk University, Brno, Czech Republic. 6
Central European Institute of Technology, Brno University of Technology, Brno, Czech Republic. 7
Institut für Physik und
Astronomie, Universität Potsdam, Potsdam, Germany. 8
National Technical University ‘Kharkiv Polytechnic Institute’, Kharkiv, Ukraine. 9
Christian Doppler Laboratory for Nanoscale Phase
Transformations, Zentrum für Oberflächen- und Nanoanalytik, Johannes Kepler Universität, Linz, Austria. 10
Graz Center for Electron Microscopy, Institute of Electron Microscopy and
Nanoanalysis, Graz University of Technology, Graz, Austria. 11
New Technologies Research Centre, University of West Bohemia, Pilsen, Czech Republic. 12
Department Chemie, LudwigMaximilians-Universität,
München, Germany. 13
Present address: International Research Centre MagTop and Institute of Physics, Polish Academy of Sciences, Warsaw, Poland. 14
These authors
contributed equally: E. D. L. Rienks, S. Wimmer, J. Sánchez-Barriga, O. Caha. *e-mail: rader@helmholtz-berlin.de; gunther.springholz@jku.at
Reprinted page 1 of paper [69] “Magnetic band gap in MnBi2Te4-Bi2Te3 heterostructures”.
424 | Nature | Vol 576 | 19/26 December 2019
Article
Bi2Se3, Bi2Te3 and Sb2Te3 will form a QAHE state, which should thus
occur when Bi or Sb are substituted by Cr or Fe, but not when the sub-
stituentsareTiorV,owingtotheirmetallicity2
.Moreover,nonisovalent
magnetic dopants turn out to have surprisingly little effect on carrier
concentration: that is, Mn-doped Bi2Se3 and Bi2Te3 always remain
n-type14,20
, even though divalent Mn replacing trivalent Bi should act
as a strong acceptor.
To resolve these issues, we present a comprehensive study of
Mn-dopedBi2Te3 andBi2Se3 thatunequivocallyrevealsalargemagnetic
exchange splitting at the Dirac point of Bi2Te3. This splitting vanishes
above the Curie temperature, which is clear-cut evidence for its mag-
neticorigin.NoincreaseinthegapsizeisobservedforMn-dopedBi2Se3
attemperaturesdownto1 K.Throughamultiscalestructuralanalysis,
werevealthattheactuallatticestructureisverydifferenttotheanticipated
random impurity system, as Mn doping induces the formation
of self-organized heterostructures. This turns out to be crucial for
obtaining large magnetic gaps10
.
Bandgap,spintextureandmagnetism
Figure 1a–g shows the ARPES dispersions of Mn-doped Bi2Te3 and
Bi2Se3 measuredaboveandbelowtheferromagneticphasetransition
(TC = 10 Kand6 K,respectively).ForMn-dopedBi2Te3,thephotoemission
spectrum recorded at hν = 50 eV at the centre of the surface Brillouin
zone shows an intensity maximum at a binding energy of 0.3 eV from
thebulkvalence band,whiletheDiracpointofthetopologicalsurface
state (TSS) contributes a smaller peak at around 0.2 eV. On cooling
from 20 K through TC down to 1 K, the low energy flank of the peak
develops a pronounced shoulder, forming a plateau at around 0.2 eV
(Fig. 1a–c). Assuming that the single component for the topological
surfacestateat20 Kbecomessplitintotwoequallyintensecomponents
at 1 K (Fig. 1d), we arrive at a gap, Δ, of 90 ± 10 meV at low temperature
(see Methods section ‘ARPES’ and Extended Data Fig. 1). Because TC is
10 K in this sample, this proves the magnetic origin of this gap. This is
the central result of our study.
To confirm the magnetic origin, we carried out spin-resolved
ARPES. For the spectra shown in Fig. 1h–j, we chose a photon energy
of hν = 30 eV at which bulk transitions are strong from the bulk conduction
band (BCB) but overlap much less with the Dirac point of the
TSS.At6.5 K,thespectrumattheDiracpoint—measuredinremanence
afterfieldcooling(M−
)—isclearlyspin-polarized,withspinorientation
perpendicular to the surface and spin split by Δ = 56 ± 4 meV (Fig. 1h
andExtendedDataFig. 2).BecausethetemperatureisclosertoTC,this
value is smaller than that derived at 1 K. Subsequent measurement at
room temperature (Fig. 1i) shows that the spin polarization has completely
disappeared, whereas subsequent cooling in an oppositely
Mn-doped Bi2Se3
Δ
Δ
Δ
Binding energy (eV)
0.4 0.2 0.00.6
1 K
Bindingenergy(eV)
0.0
0.4
0.8
0.20.0–0.2
h = 50 eV
Binding energy (eV)
0.20.50.8
0 40
T (K)
20
0.2
0
Δ
Δ
(eV)
Binding energy (eV)Binding energy (eV)
Intensity(a.u.)Intensity(a.u.)
Intensity(a.u.)
Intensity(a.u.)
Intensity(a.u.)
Intensity(a.u.)
0.00.5
20 K
0.00.5
1 K
a
b
50 eV
Binding energy (eV)
Simulation
0.10.20.30.4
20 K
1 K 1 K
S2
Δ
S1
Bulk VB
Δ
Δ
Bulk VB
E
0.0
0.2
0.4
0.4 0.3 0.2 0.1 0.0
S1
0.28 0.22
21 meV
S2
0.18 0.14
12 meV
c d
h i j k
g
f
e
20 K
1 K
k|| (Å–1)
k|| k|| k||
k|| (Å–1)
1 K
0.0–0.2 0.2
Mn-doped Bi2Te3
Mn-doped Bi2Te3
M||
(T)
M(a.u.)
1
0
k|| = 0
k|| = 0
k|| = 0
k|| = 0
k||
Out-of-plane spin (h = 30 eV) In-plane spin
300 K
TSS
BCB
6.5 K
TSS
Spin-resolvedintensity(a.u.)
Spin-resolvedintensity(a.u.)
Spin-resolvedintensity(a.u.)
–20
0
20
0.00.5
Spinpolarization
(%)
Spinpolarization
(%)
Spinpolarization
(%)
–20
0
20
0.00.5
–60
0
60
0.00.5
Binding energy (eV) Binding energy (eV) Binding energy (eV)
k|| = 0.09 Å–1
+k||
–k||
0.0
0.4
0 0.2–0.2
0.0
0.4
0 0.2–0.2
0.0
0.4
0 0.2–0.2
M+
M–
TSS
BCB
EB
EB
EB
TSS
300 K
Spin up
Spin down
100
80
60
40
20
0
3020100
16
14
12
10
8
6
4
2
0
300250
(meV)
T > TcT < Tc
Temperature (K)
Magnetization(×10–6emu)
M⊥(T)
Δ
Fig.1|MagneticgapofMn-dopedBi2Te3. a–d, ARPESfor Bi2Te3 with6%Mn,
aboveandbelowtheCurie temperature (TC) ofaround 10 K. Thespectrain
c, dandthosemarkedbythick linesin a, b correspond to thecentreofthe
surfaceBrillouin zoneat k∥ = 0.Line fits in theregionsS1and S2in cyielda
splittingofmore than33 meVbetween 20 K and 1 K; accordingto the
simulations shown ind,thissplitting corresponds to a magneticgap,Δ,of
90 ± 10 meV.The inset incshowsthe energy, E, versusk∥ momentummapat1 K.
a.u.,arbitraryunits. VB, valenceband. e–g, Same analysisforBi2Se3 with6%Mn
andaTC of6 K,revealing onlya temperature-independent nonmagneticgap,
Δ,thatdoesnot correlatewith magnetization (see inset).h, i, Spin-resolved
ARPESofBi2Te3 with6%Mnat6.5 K(h)and300 K(i),showingthatbelowTC the
gapattheDiracpointisferromagneticallyspin-splitwithout-of-planespin
orientation.At6.5 K,themagneticgapisΔ = 56 ± 4 meV.j,AwayfromtheDirac
point,theconventionalhelicalin-planespintextureismeasured.Theout-of-
planecomponentofthespinpolarizationreverseswiththereversalin
magnetization(M)(asshowninthelowerpartofh),andthein-planespin
componentreverseswiththein-planewavevectork∥ (lowerpartofj).k,The
sametemperaturedependenceismeasuredforΔ(T) andthemagnetization
M(T).Theinsetshowsasketchofthemeasuredspintexturesbelowand
aboveTC.
Reprinted page 2 of paper [69] “Magnetic band gap in MnBi2Te4-Bi2Te3 heterostructures”.
Nature | Vol 576 | 19/26 December 2019 | 425
orientedfield(M+
)leadstotheoppositespinpolarization(Fig. 1h,lower
panel).Thisunambiguouslyprovesthattheout-of-planespinpolarizationbelowTC
isduetoferromagneticorderingofthesystem.Figure 1j
showsthat,awayfromtheDiracpoint,thecharacteristichelicalin-plane
spintextureoftheparentBi2Te3 ispreserved,suchthatanoverallspin
texture as displayed in Fig. 1k is formed.
Ourmeasurementofthegapprobestheexchangesplittingofp elec-
tronsofthehostmaterial,whichferromagneticallycoupletothelocal-
izedmagneticmomentsoftheMnions9
.Themagnitudeofthegapthus
dependsontheexchangecoupling,J,andthemagnetization,M,along
the surface normal direction21
. Indeed, the gap size nicely follows the
temperature dependence of the perpendicular magnetization, M⊥
(Fig. 1k, blue crosses). This clearly demonstrates the direct correlation
between the gap and ferromagnetism in the system. In Fig. 1e–g
weshowthatsuchtemperaturedependenceisnotobservedforBi2Se3
with a similar Mn concentration of 6%, where instead a large gap of
roughly 200 meV exists at all temperatures from 1 K to 300 K (ref. 14
).
Inparticular,thegapsizedoesnotincreasewhencoolingdownto1 K,
well below the TC of about 6 K (Fig. 1g, inset). This rules out a substantial
contribution of magnetism to the Dirac gap for Mn-doped Bi2Se3,
in contrast to Bi2Te3, and serves as a cross-check for the magnetic gap
opening.
Figure 2 shows the magnetization of Bi2Te3 and Bi2Se3 for comparable
Mn concentrations. The Mn-doped Bi2Te3 film shows an easy-axis
magnetization normal to the surface: that is, M⊥ is greater than M∥.
This perpendicular anisotropy is robust because it does not depend
on the Mn concentration (Extended Data Fig. 3) and also occurs for
bulksinglecrystals22
.Bycontrast,forMn-dopedBi2Se3 theeasyaxisis
paralleltothesurfaceplane(M⊥ islessthanM∥)forallinvestigatedMn
concentrations.ThecoercivefieldissubstantiallylargerforMn-doped
Bi2Te3 thanforMn-dopedBi2Se3,andtheanisotropyfieldatwhichthe
in- and out-of-plane magnetizations are equal is two times higher for
Mn-doped Bi2Te3 (Extended Data Fig. 3). Finally, the ferromagnetic TC
ofMn-dopedBi2Te3 isconsiderablyhigher(7–15 K)thanforMn-doped
Bi2Se3 (5–7 K) (Fig. 2a, b, insets, and Supplementary Information on
SQUID measurements). Altogether this shows that Mn-doped Bi2Te3
isthemorerobustandanisotropicferromagnet.Theoppositeanisotropy
is also revealed by the magnetotransport measurements shown
in Fig. 2c, d, where, with magnetic fields applied perpendicular to the
films, only Mn-doped Bi2Te3 displays a pronounced anomalous Hall
effect below TC, whereas it is negligible in Mn-doped Bi2Se3 (Fig. 2d).
ThisperpendicularanisotropyinMn-dopedBi2Te3 ispreciselythepre-
conditionforthemagneticbandgapopeningandtheQAHE,whereasan
in-planemagnetizationasobservedforMn-dopedBi2Se3 merelyshifts
the Dirac cone in momentum parallel to the surface9,23
.
Multiscalestructureanalysis
To clarify how Mn is actually incorporated into Bi2Te3 and Bi2Se3, we
carriedoutamultiscalestructureanalysisforbothsystems.Figure 3a
showsMn-dopedBi2Te3 inhigh-resolutionscanningtransmissionelec-
tronmicroscopy(HRSTEM).Strikingly,weobservetheemergenceofa
new structure composed of septuple and quintuple layers, instead of
the expected periodic sequence of Te–Bi–Te–Bi–Te quintuple layers.
The septuple layers consist of the sequence Te–Bi–Te–Mn–Te–Bi–Te,
where the Mn atoms predominantly occupy the centre of the septu-
ple24
. This self-organized heterostructure formation does not exist
for stoichiometric Bi2Te3 and Bi2Se3 (Extended Data Fig. 4a) and obviously
disagrees with the commonly held notion of substitutional Mn
incorporation9,12,14,22,25
. Figure 3b and Extended Data Fig. 4b show that
thesameMn-inducedseptuple/quintupleheterostructureformation
alsooccursinBi2Se3,inagreementwithrecentobservations11,26
.Thus,
it is a universal mechanism in both material systems. Moreover, we
identify this structure as the explanation for the surprisingly small
effect14,20,27
ofMndopingonthecarrierconcentrationandFermilevelof
thesystem:MninMnBi2Te4 iselectricallyneutralbecauseeachseptuple
– –800 400 0 400 800
–20 –10
–5–10
0
10
20
–100 –50 0 50 100
0
5
10
0 2 4 6 8 10 12 14
0
3
6
9
–400 –200 0 200 400
0.0
0.5
1.0
–1.0
–0.5
0 2 4 6 8 10 12 14
0
5
10
15
20
Mn (3%)
dc
Curie temperature Curie temperature
Mn:Bi2Te3
M⊥
M⊥
a
T = 2 K T = 2 K
Magnetization,M(kAm–1)
Magnetization,M(kAm–1)
Magnetic field, 0H (mT)
Magnetic field, 0H (mT)
–400 –200 0 200 400
Magnetic field, 0H (mT)
Magnetic field, 0H (mT)
Magnetization
Out-of-plane
In-plane
Magnetization
Out-of-plane
In-plane
Mn (4%)
b
Mn:Bi2Se3
AHE(×10–1Ω)
0.0
0.5
1.0
–1.0
–0.5
AHE(×10–1Ω)
4 K
5 K
10 K
20 K
M⊥
Mn (8%)
Anomalous Hall effect Anomalous Hall effect
Mn (6%)
2 K
3 K
5 K
10 K
20 K
I
B
VH
TC(K)
TC(K)
Mn content (%) Mn content (%)
Mn-doped Bi2Te3
Mn-doped Bi2Te3
Mn-doped Bi2Se3
Mn-doped Bi2Se3
M||
M||
M⊥ M||
M||
Fig.2|Magneticproperties.a, b, In-planeand out-of-plane magnetization
M(H)ofMn-dopedBi2Te3 (a) and Bi2Se3 (b) filmswith Mn concentrationsof
3%and4%at2 K, measured with the magnetic field parallel, respectively,
perpendicular tothe surface, showing a perpendicular anisotropy(easyaxis)
forBi2Te3 andanin-planeeasyaxis for Bi2Se3.The insetsshow theCurie
temperatureasafunctionofMnconcentration.c, d,AnomalousHalleffect
(AHE)ofMn-dopedBi2Te3 (c) andBi2Se3 (d)measuredbetween2 Kand20 K.The
contributionoftheordinaryHalleffectextracted fromthehighfielddatawas
subtracted(see Methods).Owingto theperpendicularmagneticanisotropy,
onlyMn-doped Bi2Te3 displaysapronouncedanomalousHalleffectbelowTC.
Reprinted page 3 of paper [69] “Magnetic band gap in MnBi2Te4-Bi2Te3 heterostructures”.
426 | Nature | Vol 576 | 19/26 December 2019
Article
is formed by insertion of a charge-compensated MnTe double layer
into a quintuple layer.
To obtain element-specific information on the Mn-incorporation
sites,wecarriedoutX-rayabsorptionnear-edgespectroscopy(XANES)
and extended fine structure spectroscopy (EXAFS) at the Mn K-edge
(Fig. 3c–f). We analysed the absorption spectra through simulations
ofallpossibleMn-incorporationsites(see Methodssectionon‘XANES
andEXAFSmeasurementsandsimulations’andExtendedDataFigs. 6,
7),showingthatMninBi2Te3 indeedpreferstobeincorporatedintothe
newlyformedseptuplelayers,andthatonlyaminorityisincorporated
in the quintuple layers. Although the EXAFS data do not completely
rule out the incorporation of Mn into octahedral sites in the van der
Waals gap, the fact that septuples are never seen in undoped Bi2Te3
clearly suggests that the Mn sites are closely linked to the septuple
layers. This is supported by high-resolution energy-dispersive X-ray
(EDX) elemental maps of the Bi, Te and Mn atoms, in which Mn does
notappearinthevan derWaalsgapsbutmostlyintheseptuplelayers
(Extended Data Fig. 4c).
Turning to Mn-doped Bi2Se3 we do not observe as intense EXAFS
oscillations as for Bi2Te3, indicating that Mn is distributed over different
lattice sites, with a larger amount of substitutional Mn and a
lesser fraction within the septuple layers. This is highlighted by the
XANESspectra,whichexhibitacharacteristicdouble-peakstructure,
with the higher energy peak being attributed to Mn at the centre of
the septuple and the lower energy peak to substitutional Mn. Again
forBi2Se3 thesignalfromMnintheseptuplesisweakercomparedwith
thatinBi2Te3.FortetrahedrallycoordinatedinterstitialMnandMnon
Te (Se) antisites, the simulations do not agree with the experiments,
indicatingthatthesearenotfavourableforMnincorporation.Overall,
we conclude that for Bi2Te3 the vast majority of Mn is incorporated
within the septuple layers and that substitutional Mn is more readily
formed in Bi2Se3, especially at lower Mn concentrations.
10 nm2 nm 10 nm2 nm
QL
QL
QL
QL
QL
QL
QL
QL
SL
SL
SL
SL
Mn-doped Bi2Te3 Mn-doped Bi2Se3a b
c d
e f
[1120]
_
[0001]
SL
QL
SL
QL
QL
QL
QL
QL
QL
QL
QL
QL
SL
SL
SL
SL
[1010]
_
[0001]
QL
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
6.5 6.55 6.6 6.65 6.7 6.75 6.8
Centre of septuple
Substitutional in QL
Octahedral in vdW
Tetrahedral in vdW
Mn on Te(1) site
Mn on Te(2) site
Centre of septuple
Substitutional in QL
Octahedral in vdW
Tetrahedral in vdW
Mn on Te(1) site
Mn on Te(2) site
χ(a.u.)
χ(a.u.)
Measurement
Calculation
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
6.5 6.55 6.6 6.65 6.7 6.75 6.8
Measurement
Calculation
6.54 6.55 6.56 6.57
0.0
0.5
1.0
1.5
6% Mn-doped Bi2Se3
4% Mn
8% Mn
6% Mn-doped Bi2Te3EXAFS EXAFS
6.54 6.55 6.56 6.57
0.0
0.5
1.0
1.5
XANES(normalized)
XANES(normalized)
Photon energy (keV) Photon energy (keV)
Photon energy (keV) Photon energy (keV)
Experiment
3% Mn
10% Mn
Simulation
Substitutional Mn in QL
Mn in septuple layer
Experiment
Simulation
Substitutional Mn in QL
Mn in septuple layer
XANES XANES
Mn K-edge Mn K-edge
Mn-doped Bi2Te3
Mn-doped Bi2Se3
Fig.3|StructureanalysisbySTEMandX-rayabsorptionspectroscopy.
a, b,STEMcross-sectionsof Mn-dopedBi2Te3 (a) andBi2Se3 (b),revealingthe
formationoflayeredheterostructuresconsisting ofMnBi2Te4 (MnBi2Se4)
septuplelayers (SLs) inserted between Bi2Te3 (Bi2Se3) quintuplelayers(QLs).
Theimageswere recordedalong the[1100](a) and[1210]zoneaxes(b).Owing
totheatomic-number contrast, the heavyatoms(Bi) appear brighterinthe
high-angleannular dark field (HAADF) images. Asa result, theseptuplelayers
appeardarker in the overview images because of incorporationofthelighter
Mnatoms.TheMnconcentrationwas10%ina,andlocally9%andonaverage 6%
inb,accordingtoX-raydiffractionmeasurements(Fig. 4).c–f,Spectroscopic
determinationoftheMn-incorporationsitesinMn-dopedBi2Te3 (c, e)and
Bi2Se3 (d,f) byX-rayabsorptionspectroscopy(XANESin c,d andEXAFSin e,f)
attheMnK-edge.Experimentaldata(symbols) arecompared with simulations
(solidlines)performedfordifferentMn-incorporationsitesintheseptupleand
quintuplelayers,inthevan derWaals(vdW)gaporonTe(Se)antisites(see
ExtendedDataFig. 6).
Reprinted page 4 of paper [69] “Magnetic band gap in MnBi2Te4-Bi2Te3 heterostructures”.
Nature | Vol 576 | 19/26 December 2019 | 427
Tosystematicallymapoutthestructureevolutiononalargerlength
scale, we carried out X-ray diffraction investigations as summarized
in Fig. 4a–d. For both systems we find a pronounced change with
increasingMnconcentration,shownbytheappearanceofadditional
diffractionpeaksthatsignifytheemergenceofseptuplelayersinthe
structure.Theseptuplesare,however,notincorporatedperiodically
at fixed distances, but rather stochastically after a varying number,
NQL,ofquintuplelayers.ThisisseenintheSTEMcross-sections,where
NQL varies between one to seven. To evaluate the diffraction data,
we have thus developed an one-dimensional paracrystal model, in
whichtheoverallstructureisdescribedasastatisticallyvaryingsequence
of quintuple segments alternating with single septuple layers
(see  Methods section ‘X-ray diffraction and simulation with
random stacking model’ and Extended Data Fig. 8). Each sequence is
characterized by the average number, N⟨ ⟩QL , of quintuples between
subsequentseptuplesandtherandomnessofthestatisticalNQL distribution—that
is, their root mean square (r.m.s.) deviation from the
average value.
The model fits (black lines in Fig. 4a, b) show a remarkably good
agreementwiththediffractionspectra.Thiscorroboratestheformation
of self-organized quintuple/septuple heterostructures in both
systems.Fromthefits,weobtaintheaverage N⟨ ⟩QL betweentheseptu-
plelayersaswellasther.m.s.deviationasafunctionofMnconcentration.
As shown in Fig. 4c, N⟨ ⟩QL  rapidly decreases and thus the density
ofseptuplesincreaseswithincreasingMnconcentration,underlining
that the septuple formation is indeed driven by the Mn doping. This
alsoexplainswhyTC variessolittlewiththeMnconcentrationinFig. 2:
the magnetic properties of the samples are largely those of the individualseptuplelayers.Apparently,inBi2Te3
theformationofseptuple
layersstartsatalowerMnconcentrationthaninBi2Se3 andtheaverage
separation N⟨ ⟩QL between the septuples is smaller. This difference is
highlighted in Fig. 4d, where the number of available Mn sites in the
septuplesisplottedversustheactualMnconcentration,revealingthat
in Bi2Te3 all Mn atoms can be incorporated in the septuple layers,
whereasinBi2Se3 thedensityofseptuplesatlowMnconcentrationsis
toosmalltoaccommodateallMnatoms,whichmustthusbeincorpo-
ratedatothersitesaswell.Weemphasizethatourmodelofself-organ-
izedseptuple/quintupleheterostructuresappliesnotonlytoMn,but
also to other nonisovalent dopants such as Ge, Sn and Pb. As a result,
very similar diffraction spectra that are well described by the same
paracrystal model are obtained, as shown in Fig. 4e, f and Extended
DataFig. 9.Thishighlightsthatthisnewtypeofincorporationmechanism
is completely generic in the tetradymite chalcogenide material
systems.
Discussion
The electronic structure of transition-metal impurities in Bi2Te3 and
Bi2Se3 hasbeenstudiedextensivelythroughdensityfunctionaltheory
(DFT)calculations9,25
.ForMninBi2Se3,anonmagneticbandgapofthe
measured size (200 meV) does not appear in any DFT calculation.
Although in principle, depending on orbital symmetry, small gaps of
around 4 meV might open even for an in-plane magnetization25
, this
isobviouslymuchlessthanwhatweobserveexperimentally.Theonly
predictionofanonmagneticgapofthemagnitudeseeninourexperi-
mentsisfromcalculationsthatassumeanon-siteCoulombinteraction,
U,attheimpuritysite28
.Ontheonehand,Mnformsmoresubstitutional
sites in Bi2Se3 than in Bi2Te3. They will lead to a larger Coulomb U than
forMninthecentreoftheseptuplelayer,whereMn3dlevelscandelocalize
in the plane. The size of U, also termed the impurity strength28
,
indeed affects the nonmagnetic gap: comparing Mn with In doping
for Bi2Se3, we find that to reach the same gap size as for 8% Mn, only
2% In is required29
. On the other hand, the effect of impurities on the
nonmagnetic gap decreases with higher spin–orbit interaction in the
hostmaterial29
,sothatBi2Te3 islesssusceptibletoanonmagneticgap
opening than Bi2Se3.
ToexplainthemarkeddifferenceinthemagneticanisotropyofMndopedBi2Te3
andBi2Se3,wecalculatedthemagnetocrystallineanisotropy
for the Bi2Y3/MnBi2Y4 (Y = Te, Se) heterostructures (see Methods
section ‘DFT calculation of magnetic anisotropy’). In agreement with
recent model calculations10
, we find that the strong magnetocrystal-
lineanisotropyfavoursout-of-planemagnetizationinthetelluride.In
the selenide, however, because of the reduced spin–orbit interaction
themagnetocrystallineanisotropyis3.5timessmallerandpractically
cancelled by the shape anisotropy. Thus, the higher spin–orbit interaction
in the telluride heterostructures turns the magnetization out
of the plane and enables the magnetic gap to form at the Dirac point.
Mn-doped Bi2Te3
1020
1015
1010
105
100
100
105
1010
1015
1020
1025
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
a
Mn
Intensity(a.u.)
1020
1015
1010
105
100
Intensity(a.u.)
Qz along [0001] (Å−1)
Intensity(a.u.)
Qz along [0001] (Å−1)
Qz along [0001] (Å−1)
S S
11%
9%
6%
4%
1%
0%
b
Mn
S S
10%
8%
6%
4%
2%
0%
10
−1
10
0
10
1
102
0 2 4 6 8 10 12
c
NQL
Mn content (%)
Bi2Te3:Mn
Bi2Se3:Mn
Bi2Te3:Mn
Bi2Se3:Mn
Number of QL between SL
Relative r.m.s. deviation of NQL
Average <NQL>
0
5
10
15
20
0 2 4 6 8 10 12
dSitesinmiddleofSLperntotal(%)
Mn content (%)
Available Mn sites in septuple layers
0 1 2 3 4 5
e f
Natural heterostructures Structure model
Bi2Te3
Bi2Te3
Bi2Te3/XBi2Te4
XBi2Te4SL
NQL
X = Mn, Ge, Sn, Pb...
Bi
Te/Se
X
Undoped
Mn-doped
Nonmagn.
doped
S S
Bi2Te3:Ge
Bi2Te3:Sn
Bi2Te3:Pb
Sb2Te3:Mn
Bi2Te3:Mn
Bi2Te3
QL
SL
Bi
Bi
Bi
Bi
Mn
vdW gap
Mn-doped Bi2Se3
Fig.4|X-raydiffractionanalysisofself-organizedheterostructuresin
Mn-dopedBi2Te3 andBi2Se3 asafunctionofMnconcentration. TheMn
concentration variedfrom0% to 11%. a, b, Measured diffraction spectra(red
andbluelines) recordedalong the vertical Qz direction for Mn-dopedBi2Te3 (a)
andBi2Se3 (b) at different Mn concentrations. The diffractionpeaksofthe
substrateare indicatedby‘S’. Thespectra were fitted using a paracrystalmodel
of statisticallyvaryingalternationsofBi2Y3 quintuple (Y =Te, Se) andMnBi2Y4
septuplelayers (see Methods).An excellent fit (black lines) is obtainedforboth
systems.c,The derivedaverage number ofquintuples N⟨ ⟩QL betweenthe
septuples(open symbols)andthe r.m.s. width ofthe random distribution
(filledsymbols) areplotted against Mn concentration.A smalleraverage
distance N⟨ ⟩QL —that is,ahigher concentrationofseptuples—isfoundforBi2Te3
thanforBi2Se3.d, Thenumber of availableMn sites in the centreofthe
septuplesrelativetothe total number, ntot, ofincorporated Mnatomsisplotted
againstthenominalMn concentration. Thenumber expectedforunity
occupancyisindicatedbythe dashedline.Experimental pointsbelowthisline
indicateasubstantialfraction ofMnatomsresiding in other latticesites.This
appliestoBi2Se3 but nottoBi2Te3.e, Structure analysisfor Bi2Te3 dopedwithGe,
Snor Pbandfor Sb2Te3 doped withMn.The good fit ofthe diffractiondatawith
theparacrystal model(black lines) revealsthat thesametypeofself-organized
heterostructures (f) isformed in all cases.
Reprinted page 5 of paper [69] “Magnetic band gap in MnBi2Te4-Bi2Te3 heterostructures”.
428 | Nature | Vol 576 | 19/26 December 2019
Article
Finally,ourmagneticgapsizeof90 meVforMn-dopedBi2Te3 isfive
times larger than that predicted theoretically for substitutional Mn9
.
Thishugeenhancementarisesfromthenaturallyformedheterostructure
and the enhanced wavefunction overlap of the TSS with the Mn
atoms in the MnBi2Te4 septuple layer, which supports large magnetic
gapsof38–87 meV,aspredicted10
.Mn-dopedSb2Te3 displaysthesame
heterostructure formation and out-of-plane magnetic anisotropy as
Bi2Te3 (ExtendedDataFig. 10),andbecauseitisp-type,theFermilevel
can be tuned into the magnetic gap by alloying of these systems. This
demonstratesthegreatpotentialofsuchstructuresforstabilizingedge
transport in QAHE devices. Theory also suggests that the nontrivial
topologyisretainedintheheterostructures10
,inaccordancewiththe
persistenceoftheDiracconesurfacestateandout-of-planespintexture
seeninourARPESexperiments.Therefore,Mn-basedtopologicalinsulator
heterostructures might not only boost edge transport in QAHE
devices, but also facilitate the realization of new topological phases
suchastheaxioninsulatorstate30,31
andthechiralMajoranafermion32
.
Onlinecontent
Anymethods,additionalreferences,NatureResearchreportingsummaries,
source data, extended data, supplementary information,
acknowledgements, peer review information; details of author contributions
and competing interests; and statements of data and code
availabilityareavailableathttps://doi.org/10.1038/s41586-019-1826-7.
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© The Author(s), under exclusive licence to Springer Nature Limited 2019
Reprinted page 6 of paper [69] “Magnetic band gap in MnBi2Te4-Bi2Te3 heterostructures”.
Methods
Samplegrowth
Mn-doped Bi2Te3, Bi2Se3, and Sb2Te3 layers were grown by molecular
beam epitaxy (MBE) on BaF2(111) substrates using a Riber 1000 and
a Varian GEN II MBE system. Compound Bi2Te3, Bi2Se3, and Sb2Te3 as
well as elemental sources for Mn, Te and Se were used for control of
stoichiometry andcomposition.For Pb-, Sn-andGe-doped Bi2Te3, we
used additional PbTe, SnTe and GeTe sources. Deposition was carried
outatagrowthtemperatureof330 °CforBi2Te3 andSb2Te3 and360 °C
for Bi2Se3 to obtain perfect two-dimensional growth independently
of dopant concentrations. This was verified by in situ reflection highenergy
electron diffraction (RHEED; Extended Data Fig. 9). Details of
growth procedures have been reported previously14,20
. Our notation
ofx%MninBi2Te3 referstoanominalcompositionof(Bi1−xMnx)2Te3+3x.
All layers exhibited n-type conduction with electron concentrations
oftheorderofafewtimes1019
 cm−3
(seeExtendedDataFig. 5c), except
forMn-dopedSb2Te3 whichisp-typewithaholeconcentrationof afew
times 1020
 cm−3 
. Immediately after growth, samples used for ARPES
werecappedin situwithamorphousSeandTecappinglayersatroom
temperature to protect the surface against oxidation. This cap was
removed justbefore theARPESexperiments byin situsputteringand
annealing.
ARPES
Photoemission experiments were performed with the ARPES-13
end
station at the UE112-PGM2b undulator beam line of the BESSY II synchrotron
radiation source. The lowest reachable temperature is 1 K.
The experimental geometry has the following characteristics: with
the central axis of the analyser lens and the polar rotation axis of the
sampledefinedasthexandz axesofasphericalcoordinatesystem,the
photons impinge the sample under an azimuthal angle φ of 45° and a
polarangleof84°.Thelightpolarizationishorizontal(alongthex axis).
Theentranceslitofthehemisphericalanalyserisplacedparalleltothe
z axis.Themeasurementsathν = 50 eVwereperformedwithanenergy
resolutionof10 meV.Thetemperature-dependentleading-edgeshifts
inFig. 1candExtendedDataFig. 1aareobtainedbyapproximatingthe
photoemissionintensityintheindicatedrangeswithaline.Theslopeof
thislineisconstrainedtobeidenticalforthelow-andhigh-temperature
spectra within the same section. Our notation Δ refers to the full gap.
The measurement of the magnetic exchange splitting at the Dirac
point through the temperature dependence in ARPES is in a certain
sense analogous to the case of gadolinium metal. In both cases the
magneticcouplingoflocalizedmagneticmoments(3dinMn,4finGd)is
mediatedbyitinerantelectrons(5pinTe,5dinGd)whichcanbeprobed
byARPES.AttheDiracpoint,electronicstatesoftheTe5pcharacterare
probed.InGd,the5dbandprobedbyARPESsplitsby0.85 eVwhenthe
temperatureisloweredfrom1.02 TC to0.27 TC (TC = 293 KforbulkGd)33
.
Spin-resolvedARPES
Spin-resolved ARPES was measured at the RGBL2 end station at the
U125/2 undulator beamline of BESSY II. It comprises a Scienta R4000
hemispherical analyser with two Mott-type spin polarimeters oper-
atedat26 kV(ref.34
).Thelowesttemperatureis6.5 K.Lightisincident
under an azimuthal angle of 45° and a polar angle of 90° (Extended
DataFig. 2a).Thelightpolarizationishorizontal(alongthex axis).The
spinpolarimeterdetectstheout-of-planeandonein-planecomponent
of the spin polarization. The measured in-plane projection is tangential
to the Dirac cone and perpendicular to the analyser entrance slit
andelectronmomentum.Theout-of-planecomponentlieswithinthe
electronemissionplaneandisparalleltothesamplenormalalongthe
z-direction.Theangularresolutionwas0.75°andtheenergyresolution
of the measurement at a photon energy of 30 eV was set to 45 meV.
We note that the measurement of the spin splitting is not limited by
the energy resolution because the spin-up and spin-down channels
countindependentlyofeachother.Anexampleofthisistheexchange
splitting of a Ni(111) surface state, measured by spin-resolved inverse
photoemissionas18 ± 3 meVatanenergyresolutionof300–400 meV
(ref. 35
).
Transportmeasurements
Temperature-dependenttransportmeasurementswereperformed in
van der Pauw geometry with out-of-plane magnetic fields ranging
from 0 T to 2 T and temperatures down to 1 K using a Cryogenic mini
cryogen-free system. Extended Data Fig. 5 shows the complete data
set (Hall resistance plotted against magnetic field, as well as carrier
concentration,n,andcarriermobility,μ,plottedagainsttemperature)
for the Mn-doped Bi2Te3 and Bi2Se3 films with respectively 6% and 8%
Mn.BelowtheferromagnetictransitionTC (10 Kand6 K,respectively),
theHallresistancecomprisesthecontributionfromtheordinaryHall
effect (proportional to 1/ne) and the anomalous Hall effect (proportional
to the magnetization, M). Because the latter is proportional to
theperpendicularmagnetization,theanomalousHallcontributionis
minute for Mn-doped Bi2Se3 films, for which the magnetization vector
is nearly parallel to the film plane. Above TC the anomalous Hall
contribution is absent.
Magneticcharacterization
The magnetic properties were determined by measuring magnetiza-
tion,M,asafunctionoftheappliedexternalfield,H,andasafunction
of temperature, T (ranging from 2 K to 300 K), using a superconducting
quantum interference device (SQUID) magnetometer (Quantum
Design MPMS-XL5). We determined the Curie temperature from the
M(T)curvesasexemplifiedinExtendedDataFig. 3.Notethatwedonot
observe an enhancement of TC at the surface probed by XMCD14
. The
magneticfieldwasappliedeitherparallel(out-of-plane)orperpendicular
(in-plane) to the c axis of the films. The diamagnetic contribution
of the BaF2(111) substrate was determined from the slope of the M(H)
curve recorded at 300 K in high magnetic fields, and was subtracted
fromthe raw data. Identicalsample pieces were used for in-planeand
out-of-plane measurements. The sample size was 4 × 4 mm2
.
Scanningtransmissionelectronmicroscopy
Atomic resolution HRSTEM images were obtained with a FEI Titan G2
60-300 STEM equipped with a Cs probe corrector and a FEI Titan
60-300 Themis equipped with a Cs image corrector, which were 
operated at 300 keV. The HRSTEM data were recorded with a HAADF
detector and the images processed using a Wiener filter for noise
minimization36
. Thin cross-sectional lamellae from Mn-doped Bi2Te3
and Bi2Se3 films with Mn concentrations of 10% and 6%, respectively,
were prepared by focused ion beam (FIB) milling (ZEISS Crossbeam
XB 1540 and FEI Helios NanoLab 660) along two different crystallographic
directions of the BaF2(111) substrate ([211]and[011], respectively).
Owing to the epitaxial relationship between the films and the
BaF2(111)substrate,thisyields[1100]and[1210]zoneaxeswithrespect
totheBi2Te3 andBi2Se3 layers.Pre-characterizationofthelamellaeand
overview STEM images were obtained with a JEOL JEM-2200FS STEM
operated at 200 keV. Shortly before the HRSTEM images were taken,
thelamellaewereadditionallythinnedtoremovetheamorphoussur-
facelayersanddamagedregionscausedbytheinitialFIBpreparation
using a Fischione 1040 NanoMill. To map the element distribution
(ExtendedDataFig. 4c),wecarriedoutenergy-dispersiveX-rayanalysis
using a Bruker Super-X detector.
XANESandEXAFSmeasurementsandsimulations
The XANES and EXAFS spectra at the Mn K-edge were recorded at,
respectively, the ID12 and BM23 beamlines of the European Synchrotron
Radiation Facility in total fluorescence yield37
. The isotropic
XANES spectrum was derived from a weighted average of two XANES
spectra recorded with two orthogonal linear polarizations parallel
Reprinted page 7 of paper [69] “Magnetic band gap in MnBi2Te4-Bi2Te3 heterostructures”.
Article
and perpendicular to the c axis of the film. The resulting X-ray linear
dichroismspectracorroboratethefindingsofXANESandEXAFSwith
regard to Mn incorporation.
ForXANESsimulations,weusedtheFDMNEScode38
withamultiple
scatteringapproachonamuffin-tinpotential,forasupercellcomprising
the nominal bulk Bi2Te3 or Bi2Se3 lattices with a Mn atom replacing
one Bi atom within the quintuple layers (substitutional Mn), and
withMnincorporatedinthecentrallayersoftheseptuples(Extended
Data Fig. 6). Note that placing Mn as an octahedral interstitial within
thevan derWaals (vdW)gapleadstosomewhatsimilarresultsaswith
Mn in the central position of the septuple layer, while tetrahedral Mn
interstitialswereinlesseragreementwithexperiment(Fig. 3c–f).Concerning
the pre-edge features in the XANES data, it is known that the
FDMNEScodeusingthemultiplescatteringformalismhasdifficulties
inreproducingthe3d–4phybridizedstatesatthepre-edgefeaturewell;
neverthelessthemainabsorptionfeaturesarewellreproducedandwe
draw conclusions only from that spectral region.
WeusedidenticalinputgeometriesfortheEXAFSandXANESsimulations.WemeasuredEXAFSspectraforaseriesofMn-dopedBi2Te3
and
Bi2Se3 samples with Mn concentrations ranging from 4% to 13%. We
fittedtheEXAFSdataattheMnK-edgeusingtheFEFF9code,assuming
Mnatdifferentlatticesites.ThespectrawithamodelofMnatomsinthe
centrepositionoftheseptuplelayerareshowninExtendedDataFig. 7.
Thefirstcoordinationshellincludessixanionatomsintheoctahedral
environment. We note again that the substitutional position and the
interstitialpositioninthevan derWaalsgaphaveoctahedralcoordina-
tion.Thedistancesofthenearestneighboursinthefirstcoordination
shell derived from the fits are listed in Extended Data Fig. 7e. We note
that Mn atoms substituting Bi, Te(1) or Se(1) atoms in the quintuple
layers (using the notation of Extended Data Fig. 6) have two different
neighbours with different distances.
X-raydiffractionandsimulationwithrandomstackingmodel
WedeterminedthecrystalstructureusingsymmetricX-raydiffraction
scansandreciprocalspacemapsinthevicinityofthe(101.20)reciprocal
lattice point. The measurements were performed using a Rigaku
SmartLab diffractometer with a copper X-ray tube and channel-cut
Ge(220)monochromator.Symmetricscansalongthe[000.1]recipro-
calspacedirection(c axis)werefittedwithamodifiedone-dimensional
paracrystal model39
, in which random sequences of Bi2Te3 (or Sb2Te3
or Bi2Se3) quintuple segments alternate with MnBi2Te4 (or MnSb2Te4
or MnBi2Se4) septuples along the c axis. For the samples doped with
X = Pb,SnorGe(Fig. 4e),theseptuplesconsistofXBi2Te4.Forthequin-
tuples,thespacingsofatomicplanesweresettothenominalvaluesof
Bi2Te3 and Bi2Se3, and for the septuples the distance of the Mn (or Pb,
SnorGe)planetothenearestneighbourTe(orSe)wassettocorrespond
to the nearest-neighbour distances determined by EXAFS.
The random sequences of quintuple and septuple layers are generated
using the following assumptions. First, the length of the individual
quintuple segments, NQL, is given by the gamma distribution
withacertainmeanvalue, N⟨ ⟩QL ,andar.m.s.deviation,σ(r.m.s.d.);we
showitsrelativevalue,σ N/⟨ ⟩QL .Theseptuplesegmentsalwaysconsist
ofonlyonesingleseptuplelayer—thatis,septuplelayersarenotposi-
tionednexttoeachother.Notethatwecarriedoutadditionaltestfits
assumingavariablelengthofseptuplesegments,butthebestfitstend
to the result with just one septuple layer embedded in the blocks of
quintuple layers. Thus, we fixed the length of the septuple segments
to one, in order to keep the number of fitting parameters as small as
possible.
Second, we set the distances of the individual atomic planes in the
quintuples to the values of the pure Bi2Y3 phases (Y = Te, Se), as we
described previously39
. For the septuples we have set the distances
of the next Te or Se anion sites to the Mn in the central planes to correspond
to the distances determined by EXAFS. The total thickness
of the septuple equals approximately 4/3 of dQL: that is, dSL = 4/3dQL.
This relation is almost exactly satisfied for Bi2Te3, whereas for Bi2Se3
dSL = 1.02 × 4/3dQL.
For the random sequences generated in this way, we calculated the
XRDdiffractionspectrausingtheone-dimensionalparacrystalmodel
described before39
, and compared the spectra to the experimental
data. Examples of simulated profiles with various parameter values
areshowninExtendedDataFig. 8a–d.ExtendedDataFig. 8a,bdepict
theinfluenceoftheaveragenumberofquintuples, N⟨ ⟩QL ,betweenthe
septuplesforafixeddisorder,thatis,σ N/⟨ ⟩QL  = 0.5.Highvaluesof N⟨ ⟩QL
correspondtoanalmostpureBi2Y3 latticewithjustfewseptuplespresent
in the stack. Such a system corresponds to samples with low Mn
doping. Smaller values of N⟨ ⟩QL lead to a multilayer system, in which
additional satellite diffraction peaks appear. The limiting case of
N⟨ ⟩ = 1QL  , which is on average one quintuple alternating with one septuple,
corresponds to the top blue line, with the peak positions corresponding
to an average periodicity P = dQL + dSL along the growth
direction. Extended Data Fig. 8c, d show the influence of the randomness(r.m.s.)onthediffractionspectraforaconstant
N⟨ ⟩QL of5.Asmall
r.m.s.correspondstoaperiodicmultilayerofquintupleandseptuple
segments,withcorrespondingsharpsuperlatticemaxima,whilelarge
r.m.s. values correspond to a disordered system with accordingly
smearedprofiles.ForthesamplesdopedwithX = Pb,SnorGe(Fig. 4e),
the fitted paracrystal parameters are listed in Extended Data Fig. 9g.
We note that the relation dSL = 4/3dQL has quite an important conse-
quenceforthediffractionspectra,becausethereisasingleperiodicity
that is common to both quintuples and septuples. The simulated and
experimental diffraction profiles shown in Fig. 4 have sharp peaks
corresponding to such a periodicity independently of the statistical
orderingofquintupleandseptuplesegments.Thecorrespondingpeaks
appear at the positions (000.9) and (000.18) of the Bi2Y3 structure.
The average interplanar distance in the septuples is smaller than in
thequintuples,becausetheseptuplehas7/5 = 1.4moreatomicplanes
but is only thicker by a factor of 4/3 = 1.33.
WehavealsodeterminedtheMn-concentrationdependenceofthe
in-plane lattice parameter a of the Mn-doped Bi2Y3 layers from asymmetric
reciprocal space maps recorded in the vicinity of the (101.20)
reciprocal lattice point of the Bi2Y3 structure. These results, as well as
those for the average interplanar distance in the c axis direction, d ,
areplottedinExtendedDataFig. 8e,f.InMn-dopedBi2Te3,weobserve
adecreaseinbothlatticeparameterswithincreasingMncontent.This
can be explained by the fact that a higher concentration of septuple
layers leads to a smaller average interplanar distance, while for Mndoped
Bi2Se3 the Mn content has less influence on d owing to the
smaller number of septuple layers formed. In fact, in Bi2Se3 we do not
observeanyconcentrationdependenceoftheinterplanardistance d
up to Mn concentrations of 8%. This is in agreement with the finding
from X-ray diffraction that, for low Mn contents in Bi2Se3, only a very
lownumberofseptuples(Fig. 4)ispresent.Mnatomsalsocauseasmall
shrinkingofthein-planelatticeparameteraforbothBi2Te3 andBi2Se3
(Extended Data Fig. 8e, f).
DFTcalculationofmagneticanisotropy
TogetareliablevalueforthemagneticanisotropyofMn-dopedBi2Y3
(Y = Se, Te) with septuple/quintuple layer structure, we carry out ab
initiocalculationsusingthewellestablishedfull-potentiallinearized
augmented plane wave (FLAPW) method, as implemented in the
WIEN2kcode40
.Ourcalculationsarebasedonthelocaldensityapprox-
imation.Hereweusedexperimentallatticeparametersforthemultilayer
system with alternating septuple/quintuple layers, which
corresponds to an Mn concentration of 8%. One part of the magnetic
anisotropy energy, known as magnetocrystalline anisotropy (MCA),
arises from spin–orbit coupling; the other part, the so-called shape
anisotropy,Eshape,comesfromthemagneticdipole–dipoleinteraction
oftheindividualmagneticmoments.Itiswellknownthatasufficiently
densemeshintheBrillouinzoneisimportantfork-spaceintegration.
Reprinted page 8 of paper [69] “Magnetic band gap in MnBi2Te4-Bi2Te3 heterostructures”.
Onthebasisofthisinsight,weuseda45 × 45 × 7Monkhorst–Packgrid
in the full Brillouin zone41
. In our benchmark calculation for FePt42
we
showedthat,inadditiontotheconvergenceofk-points,itisimportant
toincorporateallFLAPWeigenfunctionswhenspin–orbitcouplingis
included as an additional term to the scalar-relativistic Hamiltonian,
the so-called second variational step43
. This basis set is controlled by
energy parameters (Emin and Emax). To achieve a high accuracy, we set
Emin tobe−10 RyandEmax tobe5 Ry.ToobtainastablevaluefortheMCA,
the energy parameters, ℓE , used for calculating radial wavefunctions,
ℓ ℓu r E( , ),aredeterminedveryprecisely—thatis,tobetterthan0.1 mRy.
AstheWIEN2kcodesolvestheDiracequationinanapproximateway,
it is necessary to check the reliability of these sensitive calculations.
Forcross-checkingweusedthemultiple-scatteringKKRGreenfunction
methodasimplementedintheSPRKKRcode44,45
.Thisschemesolvesthe
properDiracequation;hencetherelativisticeffectsarefullyincluded
in SPRKKR, unlike with the second variational step.
ObtainingtheMCAenergybysubtractingthetotalenergiesiscompu-
tationallyverycostly.Theneedforself-consistentcalculationsfortwo
magnetizationdirectionscanbeavoidedifonereliesonthemagnetic
force theorem. In this approach the MCA energy is calculated using a
frozen spin-dependent potential46
. The MCA energy is then obtained
by subtracting the band energies. Eshape is calculated using classical
electromagnetic theory. Good agreement has been found between
WIEN2kandSPRKKRcodesfortheMCAenergycalculation.Forthesake
ofsimplicitywepresentonlytheWIEN2kresults(ExtendedDataFig. 3g).
Ge-,Sn-andPb-dopedBi2Te3 andMn-dopedSb2Te3
Natural formation of quintuple/septuple layer heterostructures is a
generic and universal feature in Bi- and Sb-based tetradymite chalcogenide
topological insulators doped with elements that prefer a 2+
state. This is demonstrated by a series of complementary thin film
samples consisting of Bi2Te3 doped with Ge, Sn, and Pb, as well as
of Sb2Te3 doped with Mn, using similar growth conditions to those
described above. In all cases, two-dimensional growth was observed
under the given growth conditions, as shown by the RHEED patterns
recordedin situduringgrowthanddepictedinExtendedDataFig. 9a–f.
The structure of the films was analysed by X-ray diffraction, and the
measureddiffractionspectrawerefittedwiththesamerandomstacking
paracrystal model described in the section ‘X-ray diffraction and
simulationwithrandomstacking’,assumingthattheadditionaldoping
element (X = Pb, Ge, Sn, Mn) induces the same type of septuple layer
formationinwhichanadditionalXTedoublelayerisinserted.Asshown
inFig. 4e,inallcasesanexcellentfitofthediffractionspectraisobtained
withourparacrystalstructuremodel.Moreover,forthesameconcentration
of dopant elements, the average number of quintuple layers,
N⟨ ⟩QL ,betweentheseadditionallyinsertedseptuplelayersanditsr.m.s.
variation,σQL,derivedfromthemodelfits(see ExtendedDataFig. 9g)
turn out to be nearly the same for each dopant element.
Dataavailability
The data sets generated and analysed here are available from the
corresponding authors on reasonable request.
Codeavailability
The code for the paracrystal model is available from the correspond-
ingauthorsuponrequest.TheelectronicstructurecodesWien2Kand
SPR-KKRandX-rayabsorptionfinestructurecodesFDMNESandFEFF9
canbedownloadedafterthecorrespondinglicencerequirementsgiven
on the respective webpages are fulfilled.
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Acknowledgements ARPES experiments were performed at BESSY II of HelmholtzZentrum
Berlin and the EXAFS and XANES experiments at the European Synchrotron
Radiation Facility. We thank B. Henne, F. Wilhelm and A. Rogalev for support with XANES
and EXAFS measurements; W. Grafeneder and G. Hesser for TEM sample preparation; V.
Holý for advice on the paracrystal model; and G. Bihlmayer and A. Ernst for helpful
discussions. This project was supported by the Austrian Science Fund (FWF, project
P30969-N27 and P28185-N27); the Austrian Federal Ministry for Digital and Economic
Affairs, the National Foundation for Research, Technology and Development in the frame
of the Christian Doppler Laboratory for Nanoscale Phase Transformations; the Deutsche
Forschungsgemeinschaft (grants SPP 1666, SFB 1143 project C4, SFB 1277 project A2);
the Central European Institute of Technology (CEITEC) Nano research infrastructure
(ID LM2015041, MEYS CR, 2016-2019) and Computational and Experimental Design of
Advanced Materials with New Functionalities (CEDAMNF; grant CZ.02.1.01/0.0/0.0/15_00
3/0000358) of the Czech Ministerstvo Školství Mládeže a Telovýchovy (MSMT); the
Impuls- und Vernetzungsfonds der Helmholtz-Gemeinschaft (Virtual Institute
New States of Matter and their Excitations and Helmholtz-Russia Joint Research
Group no. HRSF-0067); and the European Union Horizon 2020 programme (grant
823717–ESTEEM3).
Author contributions Samples were grown by S.W., H.S., V.V.V. and G.S. X-ray analysis was
carried out by S.W., H.S., G.S., J.R. and O.C. O.C. performed paracrystal modelling and
magnetotransport measurements. XANES and EXAFS measurements were made by A.N., O.C.,
H.S. and G.S., and the simulations by O.C., A.N., J.R. and J. Minár. SQUID was carried out by
A.N., and HR-STEM by M.A., H.G., S.W., G.K., O.C. and J. Michalička. DFT calculations were done
by S.A.K., J. Minár and H.E. ARPES was carried out by E.D.L.R. and P.S.M., and spin-resolved
ARPES by J.S.-B., F.F. and A.V. The work was coordinated by G.S., G.B. and O.R. The manuscript
was written by O.R. and G.S. with input from all authors.
Competing interests The authors declare no competing interests.
Additional information
Supplementary information is available for this paper at https://doi.org/10.1038/s41586-019-
1826-7.
Correspondence and requests for materials should be addressed to O.R. or G.S.
Peer review information Nature thanks Alexander Balatsky, Jacek Furdyna and the other,
anonymous, reviewer(s) for their contribution to the peer review of this work.
Reprints and permissions information is available at http://www.nature.com/reprints.
Reprinted page 9 of paper [69] “Magnetic band gap in MnBi2Te4-Bi2Te3 heterostructures”.
Article
ExtendedDataFig.1|ARPESmeasurements.a, Dataforan additionalMndopedBi2Te3
film withMn concentration of10%.The normal emissionspectra
shownonthe left, recordedat 1 Kand 30 K,show a substantialredistributionof
spectralweight aroundthebinding energyofapproximately180 meVwhen
crossingtheferromagnetic transition at TC = 12 K.The shifts intheregions
markedS1andS2, shownon theright on a magnifiedscale, areofsimilar
magnitudetothatseenfor the 6% Mn-doped case in Fig. 1. Theshiftsmarked by
arrowsarecompatiblewitha 100 meVgap opening at theDiracpoint.ARPES
wasmeasuredwithp-polarized light and hν = 50 eV.b, c, ARPESmeasurements,
showingthat the gapin 6%-Mn-doped Bi2Se3 isindependentoftemperature.
b,ARPES E(k)maprecordedat 1 K, with theangle-dependent bindingenergies
oftheupperDiracconeand bulkvalencebandindicated withblueandorange
lines,obtainedfromLorentzianfitstoenergy-distributioncurves.
c,TemperaturedependenceofthebindingenergiesoftheupperDiraccone
minimum(bluecircles),thebulkvalencebandatΓ¯(orangesquares)andtheir
difference(blackdiamonds).TheferromagneticCurietemperatureis6 Kas
obtainedbySQUID.Thisanalysisrepresentsanalternativeto thatinFig. 1g,
whichwasbasedonfitsoftheupperandlowerDiraccones.Inbothcases,the
datadonotprovideanyindicationofarelativeorabsoluteshiftoftheband
edges,orofagapoftheorderseeninMn-doped Bi2Te3 whencrossingthe
ferromagnetictransitiontemperature.
Reprinted page 10 of paper [69] “Magnetic band gap in MnBi2Te4-Bi2Te3 heterostructures”.
ExtendedDataFig.2|Spin-resolvedARPESofMn-dopedBi2Te3.a,Geometry
ofthespin-resolvedARPESexperiments,including themagnetization
directionsindicatedbyM+
andM−
.Hor. Pol., horizontallightpolarization.
b,Plotofthe fit resultsfromspin-up and spin-down spectra ofthetopological
surfacestate(TSS) at the Dirac point (ED), anddetermination ofthemagnetic
exchangesplitting,Δ = 56 ± 4 meV,at 6.5 K.c, d, Fit to the spin-resolved
spectraat6.5 K,including a transition from thebulk conductionband(BCB).
e,Demonstration thatthe spin polarization reverseswhen themagnetization,
M,isreversed.Thisreversalwasachievedbyfieldcooling in anapplied field of
10 mT.f,Temperature-dependent magnetization,M(T), measuredbySQUID on
areferencesample thatwasidentical to that usedto determinethemagnetic
fieldnecessaryfor fieldcoolingandmagnetization reversal.g, h,Beforethe
spin-resolvedARPESmeasurement, the reversible temperature-dependent
broadeninginARPES wasverifiedbycoolingfrom14 K to6.5 K andwarmingup
againto14 K.Ataphotonenergyof30 eV,mostoftheintensityneartheFermi
energystemsfromthebulkconductionband.i,Reversiblebroadeningofthe
energy-dispersioncurvesuponcoolingfromaboveto belowTC andwarmingup
again. j,TSSgap attheDiracpointΔderived byARPESandspin-resolvedARPES
(redsquares),plotted againsttemperature,togetherwiththetemperature-
dependentout-of-planemagnetization(bluecrosses),showingthatthe
magneticexchangesplittingattheDiracpointΔfaithfullyfollowsthe
magnetizationperpendiculartothesamplesurface.Dataat1 K and20 Kare
fromFig. 1c,d.Datafromspin-resolved photoemission(at6.5 Kand300 K)
havethesmallesterror.Datafor14 Kwerederivedfromi,takingthespin-
resolveddatafrom6.5 Kasareferencepoint.
Reprinted page 11 of paper [69] “Magnetic band gap in MnBi2Te4-Bi2Te3 heterostructures”.
Article
ExtendedDataFig.3|MagneticpropertiesofMn-dopedBi2Se3 andBi2Te3.
a, d,Temperature-dependentmagnetization,M(T), usedtodeterminethe
ferromagnetic Curie temperature, TC, Mn-dopedBi2Se3 (a) andBi2Te3 (d).The
magnetization wasmeasured after fieldcooling (FC)at10 mT.Asindicated,
belowTC the magnetization ofthe samplesrisessteeplybymorethantwo
ordersofmagnitude. b, e, In-plane(ip) versusout-of-plane (oop)hysteresis
loopsat300 Kand2 K, showing the absence of ferromagnetismatroom
temperature.c, f, Magnetization versus applied field, M(H), forsampleswith
differentMnconcentrations,xMn, asindicated.For all Mn-dopedBi2Se3 films,
theeasyaxisofmagnetizationisfound to beinplane,whereasforallMn-doped
Bi2Te3 filmsitisperpendiculartothesurface.TheinsetsshowtheCurie
temperature,TC,plottedagainstMnconcentration.Forallmeasurements,the
diamagneticcontributionofthesubstratemeasuredat300 Kwassubtracted.
g,Magnetocrystallineanisotropyenergy,EMCA,obtained throughDFTfor
Bi2Se3/MnBi2Se4 and Bi2Te3/MnBi2Te4 bysubtractingbandenergiesfortwo
orientationsofthemagnetization.Shownaremagnetocrystallineanisotropy
EMCA = E(M∥x)
 − E(M∥z)
,shapeanisotropyEshape and totalmagneticanisotropy
Eaniso = EMCA + Eshape.
Reprinted page 12 of paper [69] “Magnetic band gap in MnBi2Te4-Bi2Te3 heterostructures”.
ExtendedDataFig.4|STEMofpureandMn-dopedBi2Se3 andEDXmapsof
Mn-dopedBi2Te3. a, b, Comparison of HR-STEM HAADF cross-sectionsof
Bi2Se3 (a)and Mn-dopedBi2Se3 (xMn = 6%)(b) filmsgrown underidentical
growthconditions, showing the highstructuralperfectionandthatadditional
septuplelayersare formedonlywith Mndoping, whereasthe pureBi2Se3 film
consistsonlyofquintuple layers.These STEMcross-sectionswererecorded
alongtwo different zoneaxes. c, Atomic-layer-resolved distributionoftheBi,
Teand MnatomsofaMn-dopedBi2Te3 film(xMn = 10%)obtained bySTEM-EDX
mapping.TheMnatomsarepredominantlyincorporatedinthecentreofthe
septuplelayersandtoalesserextentintheouterlayersoftheseptupleunits.
NoMnisseeninthevan derWaalsgaps.Notethatinthissample,becauseofthe
higherMnconcentration,twosubsequentseptuplesareobservedintheSTEM
cross-section.
Reprinted page 13 of paper [69] “Magnetic band gap in MnBi2Te4-Bi2Te3 heterostructures”.
Article
ExtendedDataFig.5|AnomalousHalleffect. Data forMn-dopedBi2Te3 and
Bi2Se3 withrespectively6% and 8% Mn. a, b, Raw data for Hall resistanceasa
functionof magnetic fieldapplied perpendicularlytothesurface,measured at
differenttemperaturesabove andbelowTC as indicated.c, d, Temperature
dependenceofthecarrierconcentrationandHallmobility.NotethataboveTC
thecontributionoftheanomalousHalleffecttotheHallvoltageisnegligible
andthereforedoesnotaffectthecarrierconcentrationandmobility
measurements.
Reprinted page 14 of paper [69] “Magnetic band gap in MnBi2Te4-Bi2Te3 heterostructures”.
ExtendedDataFig.6|PossibleMn-incorporationsitesinBi2Te3 andBi2Se3.
a,Structuremodels for,left to right: Mn inthe centre of septuplelayers;Mn
substituting for Biinquintuple layers; and interstitial Mn in thevan derWaals
gapsonoctrahedalsitesandtetrahedral sites.b,Nominalnearest-neighbour
(NN) distancesofMnatomslocatedinvariouspositionsasderivedbyEXAFS
analysis,includingalsopossibleMn onTe(Se) antisitesinthequintuples.Index
‘1’ referstoTe(Se)sitesnexttothevan derWaalsgaps,index‘2’ tothoseinthe
centreofthequintuple.
Reprinted page 15 of paper [69] “Magnetic band gap in MnBi2Te4-Bi2Te3 heterostructures”.
Article
ExtendedDataFig.7|FitsofEXAFSoscillationsfordifferentamountsofMn
doping.a, b, Bi2Te3;c, d,Bi2Se3. Experimental datapointsarerepresentedby
theredorblue circles;black linesdenote fitted curves(unlikethesimulations
inFig. 3).a, c are plottedwith respect to the wavevector kandthebackgroundsubtractedEXAFSabsorptionχ(k)
isk-weighted;b, dshowthemagnitude,that
is,theabsolutevalueofχ(R)afterFouriertransformation.e,EXAFS-fitted
nearest-neighbourdistancesofMnatomsinBi2Te3 andBi2Se3 asafunctionof
Mnconcentration.
Reprinted page 16 of paper [69] “Magnetic band gap in MnBi2Te4-Bi2Te3 heterostructures”.
ExtendedDataFig.8|Simulateddiffractionpatterns.a–d, Varying
paracrystal parametersof theseptuple/quintuple heterostructuresof:
a, c,Mn-dopedBi2Te3 andb, d, Mn-doped Bi2Se3.a, b depict theinfluenceof
differentaverage numbersofquintuples, N⟨ ⟩QL , between the septupleswitha
fixedrelative r.m.s.deviation (r.m.s.d.) of its distribution, setto0.5.Athigh
N⟨ ⟩QL ,thesystemapproaches the pure Bi2Y3 (Y = Te, Se) phase. c, dshow
simulations for different r.m.s.d.ofthe statisticaldistributionofthenumberof
quintuplesbetweenthe septuplesbut constantaverage separation, N⟨ ⟩QL  = 5.
Thelimitofr.m.s.d. = 0 correspondstoa perfectlyperiodic multilayeroffive
quintuplesalternatingwithoneseptuple;theadditionalmaximaarethe
resultingsuperlatticesatellitepeaks.Alargerr.m.s.d.meansamoredisordered
multilayer.Dashedlinesareplottedatpositionsofthe(000.ℓ)peaksofthepure
Bi2Y3 structure. eshowstheaverage vertical(0001)latticeplanespacing⟨d⟩ asa
functionofMnconcentrationdeterminedbythefitoftheexperimental
diffractionspectrapresented inFig.4a,b,andpanelfthecorrespondingin-
planelatticeconstantsdeterminedfromreciprocalspacemapsaroundthe
(101.20)reciprocallatticepoint. 
Reprinted page 17 of paper [69] “Magnetic band gap in MnBi2Te4-Bi2Te3 heterostructures”.
Article
ExtendedDataFig.9|RHEED.a–f, Comparison ofRHEEDpatternsfor:
aMn-doped Bi2Te3;b,Mn-doped Bi2Se3;c, Mn-doped Sb2Te3;d,Pb-doped
Bi2Te3;e,Sn-dopedBi2Te3; and f, Ge-dopedBi2Te3, recordedduringepitaxial
growth,showing perfecttwo-dimensionalgrowth in allcases.Thelayer
thicknesswas200 nm andthe dopant concentrationwas around 10%inall
cases.ThecorrespondingX-raydiffraction curvesofthe samplesareshownin
Fig. 4,and thevaluesderivedfromthefitsusingtheseptuple/quintuple
paracrystalstackingmodelarelisteding. N⟨ ⟩QL istheaveragenumberof
quintuplesbetweenconsecutiveXBi2Te4 septuplelayers;σQL istherelative
r.m.s.d.ofthedistribution; and %SListheoccupancyofMnsitesintheseptuple
layers.
Reprinted page 18 of paper [69] “Magnetic band gap in MnBi2Te4-Bi2Te3 heterostructures”.
ExtendedDataFig.10|ElectronicandmagneticpropertiesofMn-doped
Sb2Te3.a,Angle-resolvedphotoemission spectrum recordedatatemperature
of38 Kand aphoton energyof 23 eVphoton energy,showing p-typebehaviour
andthattheFermi level,EF,is close to the Dirac point, thelatterbeingonly
slightlyabovethetopofthevalenceband.b,In-planeand out-of-plane
hysteresiscurves,M(H),recordedthrough SQUID at2 K(blue) and300 K(red),
showingthesameperpendicularmagneticanisotropywitheasyaxisnormalto
thesurfaceasforMn-dopedBi2Te3 (Fig. 2andExtended DataFig. 3).
Reprinted page 19 of paper [69] “Magnetic band gap in MnBi2Te4-Bi2Te3 heterostructures”.
CHAPTER 4. REPRINTED PAPERS 139
4.7 Ferromagnetic transition in magnetic topological insulators
MnSb2Te4
The layers of MnSb2Te4 with a slight excess of Mn were studied. We have found the concentration
of Mn in the substitutional and central septuple layer positions. The magnetic Currie
temperature is relatively high for a magnetic topological insulator, almost 50 K. Contrary
to bismuth selenide and bismuth telluride, antimony telluride is p-doped. Thus photoemission
study of the band gap. Instead, we have used scanning tunneling spectroscopy to show
magnetic band gap opening correlating with magnetic order.
www.advmat.de
2102935  (1 of 11) © 2021 The Authors. Advanced Materials published by Wiley-VCH GmbH
Research Article
Mn-Rich MnSb2Te4: A Topological Insulator with Magnetic
Gap Closing at High Curie Temperatures of 45–50 K
Stefan Wimmer, Jaime Sánchez-Barriga, Philipp Küppers, Andreas Ney, Enrico Schierle,
Friedrich Freyse, Ondrej Caha, Jan Michalička, Marcus Liebmann, Daniel Primetzhofer,
Martin Hoffman, Arthur Ernst, Mikhail M. Otrokov, Gustav Bihlmayer, Eugen Weschke,
Bella Lake, Evgueni V. Chulkov, Markus Morgenstern, Günther Bauer,
Gunther Springholz,* and Oliver Rader*
S. Wimmer, A. Ney, G. Bauer, G. Springholz
Institut für Halbleiter- und Festkörperphysik
Johannes Kepler Universität
Altenberger Straße 69, Linz 4040, Austria
E-mail: Gunther.Springholz@jku.at
J. Sánchez-Barriga, E. Schierle, F. Freyse, E. Weschke, B. Lake, O. Rader
Helmholtz-Zentrum Berlin für Materialien und Energie
Albert-Einstein-Straße 15, 12489 Berlin, Germany
E-mail: rader@helmholtz-berlin.de
P. Küppers, M. Liebmann, M. Morgenstern
II. Institute of Physics B and JARA-FIT
RWTH Aachen Unversity
52074 Aachen, Germany
F. Freyse
Institut für Physik und Astronomie
Universität Potsdam
Karl-Liebknecht-Straße 24/25, 14476 Potsdam, Germany
O. Caha
Department of Condensed Matter Physics
Masaryk University
Kotlářská 267/2, Brno 61137, Czech Republic
J. Michalička
Central European Institute of Technology
Brno University of Technology
Purkyňova 123, Brno 612 00, Czech Republic
D. Primetzhofer
Department of Physics and Astronomy
Universitet Uppsala
Lägerhyddsvägen 1, Uppsala 75120, Sweden
M. Hoffman, A. Ernst
Institute for Theoretical Physics
Johannes Kepler Universität
Altenberger Straße 69, Linz 4040, Austria
DOI: 10.1002/adma.202102935
1. Introduction
The quantum anomalous Hall effect
(QAHE) offers quantized conductance
and lossless transport without the need for
an external magnetic field.[1] The idea to
combine ferromagnetism with topological
insulators for this purpose[2–4] has fuelled
the materials science.[5,6] It led to the
experimental discovery of the QAHE in
Cr- and V-doped (Bi, Sb)2Te3
[7–11]
with precise
quantized values of the Hall resistivity
down to the sub-part-per-million level.[12–15]
The stable 3+ configuration of V or Cr
substitutes the isoelectronic Bi or Sb[3,16,17]
enabling ferromagnetism by coupling the
magnetic moments of the transition metal
atoms. Hence, time-reversal symmetry is
broken enabling - through perpendicular
magnetization - a gap opening at the Dirac
point of the topological surface state.[2–5]
This gap hosts chiral edge states with precisely
quantized conductivity. However, the
Ferromagnetic topological insulators exhibit the quantum anomalous Hall
effect, which is potentially useful for high-precision metrology, edge channel
spintronics, and topological qubits.  The stable 2+ state of Mn enables intrinsic
magnetic topological insulators. MnBi2Te4 is, however, antiferromagnetic with
25 K Néel temperature and is strongly n-doped. In this work, p-type MnSb2Te4,
previously considered topologically trivial, is shown to be a ferromagnetic topological
insulator for a few percent Mn excess. i) Ferromagnetic hysteresis with
record Curie temperature of 45–50 K, ii) out-of-plane magnetic anisotropy, iii)
a 2D Dirac cone with the Dirac point close to the Fermi level, iv) out-of-plane
spin polarization as revealed by photoelectron spectroscopy, and v) a magnetically
induced bandgap closing at the Curie temperature, demonstrated by scanning
tunneling spectroscopy (STS), are shown. Moreover, a critical exponent of
the magnetization β ≈ 1 is found, indicating the vicinity of a quantum critical
point. Ab initio calculations reveal that Mn–Sb site exchange provides the ferromagnetic
interlayer coupling and the slight excess of Mn nearly doubles the
Curie temperature. Remaining deviations from the ferromagnetic order open
the inverted bulk bandgap and render MnSb2Te4 a robust topological insulator
and new benchmark for magnetic topological insulators.
The ORCID identification number(s) for the author(s) of this article
can be found under https://doi.org/10.1002/adma.202102935.
© 2021 The Authors. Advanced Materials published by Wiley-VCH
GmbH. This is an open access article under the terms of the Creative
Commons Attribution License, which permits use, distribution and
reproduction in any medium, provided the original work is properly
cited.
Adv. Mater. 2021, 2102935
Reprinted page 1 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
www.advmat.dewww.advancedsciencenews.com
2102935  (2 of 11) © 2021 The Authors. Advanced Materials published by Wiley-VCH GmbH
experimental temperatures featuring the QAHE are between
30 mK[7,13] and a few K[18,19] only, significantly lower than the
ferromagnetic transition temperatures TC in these systems.[20]
If the temperature of the QAHE could be raised, applications
such as chiral interconnects,[21] edge state spintronics,[22,23] and
metrological standards[14,15] become realistic.
One promising approach is the so-called modulation doping
in which the magnetic dopants are located only in certain
parts of the topological insulator. This implies strong coupling
of the topological surface state to the magnetic moments at a
reduced disorder level.[18,24] Most elegantly, this has been realized
for Mn-doped Bi2Te3 and Bi2Se3. The tendency of Mn to
substitute Bi is weak, such that Mn doping leads to the spontaneous
formation of septuple layers with MnBi2Te4 stoichiometry.
These septuple layers are statistically distributed
among quintuple layers of pure Bi2Te3 or Bi2Se3 at low Mn
concentration[25,26] and increase in number with increasing
Mn concentration.[25] Eventually, only septuple layers remain
when the overall stoichiometry of MnBi2Te4 or MnBi2Se4
[26,27]
is reached. Density functional theory (DFT) calculations found
that MnBi2Te4 forms ferromagnetic layers with antiferromagnetic
interlayer coupling[28,29] as confirmed by experiments
at low temperatures.[29–32] As a result, MnBi2Te4 is an antiferromagnetic
topological insulator[29,33–36] that can exhibit axion
states.[5] The QAHE, however, has only been realized in a limited
way: ultra thin flakes consisting of odd numbers of septuple
layers exhibited an anomalous Hall effect (AHE) that is
nearly quantized. This is caused by the uncompensated ferromagnetic
septuple layer without partner. Nevertheless, exact
quantization still required a magnetic field.[37] A ferromagnetic
AHE has also been observed for systems with either a larger
amount of quintuple layers[38–40] or via alloying of Sb and Bi in
MnBi2−xSbxTe4
[31,32,41] or both.[42,43] Most notably, a nearly quantized
AHE has been observed up to 7 K for a MnBi2Te4/Bi2Te3
heterostructure after unconventional counter doping inducing
vacancies by electron bombardment.[19]
A central drawback of the Bi2Te3 and Bi2Se3 host materials is
their strong n-type doping. In contrast, Sb2Te3 is p-doped and
much closer to charge neutrality.[44] Indeed, mixtures of Bi2Te3
and Sb2Te3 with stoichiometries close to Sb2Te3 have been
employed for the QAHE using Cr and V doping.[7–11] Magnetism
of dilute Mn-doped Sb2Te3 has initially been studied by Dyck
et al. obtaining TC ≃ 2 K and perpendicular anisotropy.[45] Later,
a higher TC = 17 K was reported for 1.5% Mn doping.[46] Stoichiometric
bulk MnSb2Te4 provided antiferromagnetism (Néel
temperature TN = 20 K)[31,32,47], ferromagnetism[48] as well as ferrimagnetism[47,49]
(TC  = 25–34 K), depending on the composition
and synthesis conditions. By comparison with scattering
methods, it has been conjectured that this is related to Mn–Sb
site exchange within the septuple layers[42,47,50] which could
even lead to spin glass behaviour.[51] DFT calculations found
that the perfectly ordered MnSb2Te4 is antiferromagnetic[28]
but topologically trivial,[47,52–55] while Mn–Sb site exchange can
render the interlayer coupling ferromagnetic.[47,50]
Here, epitaxial MnSb2Te4 is studied using spin- and angleresolved
photoemission spectroscopy (ARPES), scanning tunneling
microscopy (STM) and STS, magnetometry, X-ray magnetic
circular dichroism (XMCD) and DFT. All experiments
were performed as a function of temperature to pin down the
intricate correlation between magnetism and non-trivial band
topology essential for the QAHE. It is revealed that the material
unites the favorable properties of a topological insulator with its
Dirac point close to the Fermi level EF with that of a ferromagnetic
hysteresis with out-of-plane anisotropy and record-high
TC, twice as high as the TN previously reported for antiferromagnetic
MnBi2Te4 and MnSb2Te4.[31,32] Moreover, temperature
dependent STS finds a magnetic gap of 17 meV at EF for 4.3 K
that closes exactly at TC as expected for a ferromagnetic topological
insulator. Moreover, by combining DFT, STM, Rutherford
backscattering, and X-ray diffraction (XRD) it is uncovered that
a partial substitution of Sb atoms by Mn is decisive to render
MnSb2Te4 both ferromagnetic and a topological insulator.
2. Structure
Epitaxial MnSb2Te4 films with 200 nm thickness were grown
by molecular beam epitaxy (MBE) using an Mn:Sb2Te3 flux
ratio of 1:1 in order to obtain the desired 1:2:4 stoichiometry
of the MnSb2Te4 phase (Note S1, Supporting Information).
Figure 1a shows the cross section of the MnSb2Te4 lattice structure
revealed by high-resolution high-angle annular dark-field
scanning transmission electron microscopy (HAADF-STEM). It
consists of septuple layers (SL) with stacking sequence Te–Sb–
Te–Mn–Te–Sb–Te, Figure 1c, that corresponds to the MnSb2Te4
stoichiometry. The composition was verified by Rutherford
backscattering spectrometry (RBS), indicating a small excess
of Mn of 6% in the layers (composition of Mn1.06Sb1.94Te4, see
Figure S1, Supporting Information), which is attributed to the
fact that a small amount of Sb2Te3 desorbs from the surface
during growth. Like with MnBi2Te4/Bi2Te3,[56] the exchange
A. Ernst
Max Planck Institute of Microstructure Physics
Weinberg 2, 06120 Halle, Germany
M. M. Otrokov
Centro de Física de Materiales (CFM-MPC)
Centro Mixto CSIC-UPV/EHU, San Sebastián/Donostia 20018, Spain
M. M. Otrokov
IKERBASQUE
Basque Foundation for Science
Bilbao 48011, Spain
G. Bihlmayer
Peter Grünberg Institut and Institute for Advanced Simulation
Forschungszentrum Jülich and JARA
52425 Jülich, Germany
E. V. Chulkov
Donostia International Physics Center (DIPC)
San Sebastián/Donostia 20018, Spain
E. V. Chulkov
Departamento de Polímeros y Materiales Avanzados: Física, Química y
Tecnología, Facultad de Ciencias Químicas
Universidad del País Vasco UPV/EHU
San Sebastián/Donostia 20080, Spain
E. V. Chulkov
Saint Petersburg State University
Saint Petersburg 198504, Russia
E. V. Chulkov
Tomsk State University
Tomsk 634050, Russia
Adv. Mater. 2021, 2102935
Reprinted page 2 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
www.advmat.dewww.advancedsciencenews.com
2102935  (3 of 11) © 2021 The Authors. Advanced Materials published by Wiley-VCH GmbH
coupling is strongly enhanced in these septuple layers relative
to a disordered system where Mn substitutes Bi randomly.
The nearly exclusive formation of septuple layers in the
entire MnSb2Te4 samples is confirmed by high-resolution XRD
(Figure  S2, Supporting Information), revealing only a minute
number of residual quintuple layers. In contrast, STEM and
XRD of V-doped (Bi, Sb)2Te3 shows quintuple layers only.[57] This
highlights that septuple layers are unfavorable for V3+ incorporation
but very favorable for Mn as this requires the addition of a
charge neutral transition metal2+/Te2− bilayer to each quintuple
layer, which is possible for Mn2+ but not for V3+. In addition,
detailed XRD analysis reveals a 10% Mn–Sb site exchange within
the septuple layers (see Figure  S2, Supporting Information),
meaning that Mn does not reside exclusively in the center of the
septuple layers but also to a small extent on Sb sites in the adjacent
cation layers. The amount of Mn–Sb site exchange is, however,
significantly smaller as compared to single crystals reported
to be of the order of 30–40%.[47,49] This is due to the much lower
growth temperature of our epilayers of 290 °C compared to 600–
650 °C for single crystals. Indeed, STM images of the atomically
flat and Te-terminated surface of our MnSb2Te4 epilayers
(Figure  1b) exhibit triangular features, pointing to defects in
the cation layer beneath the surface.[58,59] These defects occur
with an atomic density of 5–10%. Since this is larger than for
undoped Sb2Te3 films,[58] the triangles are most likely caused by
subsurface Mn atoms on Sb sites, in line with the XRD and RBS
results. As shown by DFT below, these defects turn out to be
decisive for the ferromagnetic interlayer coupling in MnSb2Te4.
Similar conjectures have been raised previously.[42,47,50,51,60]
3. Magnetic Properties
Figure  1d displays the temperature-dependent magnetization
M(T) measured by superconducting quantum interference
device (SQUID) magnetometry. The measurements
were recorded while cooling the sample from 300 K to 2 K in
a field of 10 mT perpendicular (blue) or parallel (red) to the
film surface. Most strikingly, the MnSb2Te4 epilayers show
pronounced ferromagnetic behavior by M(H) hysteresis
loops (Figure 1e) with record high TC of 45–50 K (Figure 1d),
revealed independently for several samples (Figure  S3, Supporting
Information). This is significantly higher than the
antiferromagnetic or ferromagnetic transition temperatures
of bulk crystals (Table I, Supporting Information). Moreover,
it is twice as large as the TN ≤ 25 K of MnBi2Te4 films grown
under the same conditions. It has been crosschecked that the
displayed magnetization in M(T) curves is identical to the corresponding
hysteresis loops. In particular, the large remanent
magnetization observed by the bulk sensitive SQUID measurements
excludes that it is caused by uncompensated antiferromagnetically
coupled septuple layers only.[37] However,
the M(H) hysteresis curve (Figure 1e) shows a rounded shape
that persists up to fields much higher than those typical for
domain reversals and it does not saturate up to ±5 T where
the average magnetic moment per Mn atom is of the order of
1–1.5μB, similar to that of bulk MnSb2Te4 single crystals.[31,47,49]
This is because very high fields of 60 T are required to fully
polarize the system[61] and is in line with a similar rise of the
Hall resistance with applied field in Figure S10, Supporting
Adv. Mater. 2021, 2102935
Figure 1.  Structural and magnetic properties of epitaxial MnSb2Te4. a) Cross-sectional HAADF-STEM image of the septuple layer sequence formed in
the MnSb2Te4 films on BaF2 substrates. For clarity, one of the septuple layers is highlighted by red color and denoted as SL. The weak van-der-Waals-like
bond between the Te-terminated septuple layers is the natural surface termination. b) STM image of the flat topography of this surface, recorded at T =
4.3 K, sample voltage of 500 mV and current of 200 pA. c) Sketch of the ideal crystal structure as side view and top view. d) SQUID magnetometry as a
function of temperature while cooling the sample in 10 mT from 300 K down to 2 K. e) Hysteresis loops probed by SQUID. The insets show a larger H
range and the temperature dependence. Perpendicular anisotropy can be deduced from the larger out-of-plane signal. f) Temperature-dependent XMCD
signal at the Mn L3-edge and the (0001) Bragg peak position recorded in X-ray scattering geometry at 0 T after field cooling in 0.5 T. g) Corresponding
full XMCD spectra recorded with opposite circular polarizations at 10 K. h) Difference of the spectra in (g). Linear extrapolation in (d,f) (green lines)
reveals a ferromagnetic Curie temperature TC = 46 ± 2 K for both experimental probes.
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Information. This suggests additional types of competing
magnetic orders. Indeed, a small kink in M(T) is observed at
20–25 K (Figure S3, Supporting Information), close to the Néel
temperature reported earlier for antiferromagnetic MnSb2Te4.[31]
This implies that the high-temperature ferromagnetism is
most likely accompanied by ferrimagnetism as also supported
by the relatively large in-plane hysteresis and magnetization,
Figure  1e, in line with observations of competing ferro- and
antiferromagnetic order in bulk MnSb2Te4.[40,42,47,48,50,51,61]
Ferromagnetism is fully confirmed by element specific zerofield
XMCD recorded in diffraction geometry (see Note S7,
Supporting Information). For these measurements, the sample
was remanently magnetized at ≈0.5 T and 10 K. From spectra
recorded with oppositely circularly polarized light at the (0001)
Bragg peak, the intensity difference C+  − C− (Figure  1h) was
deduced for 0 T with the photon energy tuned to the Mn-L3
resonance (Figure  1g). The asymmetry (C+  − C−)/(C+  + C−)
directly yields the magnetization of the Mn atoms. Its temperature
dependence (Figure 1f) impressively confirms the SQUID
data with high TC ≃ 46 K and unambiguously attributes the
ferromagnetism to the Mn atoms. (For magnetotransport data,
see Figure S10, Supporting Information.) The record-high TC
with magnetic easy axis perpendicular to the surface (crystallographic
c-axis) as well as the large coercivity (≈0.2 T) render
the samples very robust ferromagnets. Note that the spin-orbit
interaction is crucial for both out-of-plane easy axis and large
coercivity.[25] While it is sufficiently strong to turn the magnetization
out of plane in Mn-doped Bi2Te3, the effect in Mndoped
Bi2Te3 is too weak.[25,62] The present data reveals that
Sb2Te3 is sufficiently heavy, that is, spin-orbit coupling sufficiently
large, to maintain the perpendicular anisotropy for high
Mn content.
To elucidate the origin of the ferromagnetism, DFT calculations
are employed (Section S11, Supporting Information).
They firstly highlight the differences between MnSb2Te4 and
MnBi2Te4. In both cases, the in-plane Mn coupling within each
septuple layer is ferromagnetic. It is unlikely that the observed
difference between antiferromagnetic interlayer coupling in
MnBi2Te4 and ferromagnetic interlayer coupling in MnSb2Te4 is
caused by the lowered spin-orbit interaction, since it obviously
remains large enough to induce a strong out-of-plane anisotropy
in both cases. However, the in-plane lattice constant a of
MnSb2Te4 is ≈2% smaller than for MnBi2Te4. Hence, we calculated
the exchange constants of MnSb2Te4 for a determined
by XRD in comparison to those for a expanded to the value of
MnBi2Te4 (see Table III, Supporting Information). Although
the smaller in-plane lattice constant of MnSb2Te4 increases the
in-plane exchange constant J between nearest neighbors by
almost a factor of three, TN remains barely changed because
the enlarged in-plane overlap of the Mn d states concomitantly
weakens the already small perpendicular interlayer coupling.
However, the energy gain of antiferromagnetism against ferromagnetism
becomes as low as 0.6 meV per Mn atom at the
XRD lattice constant. This suggests that already small structural
changes along the interlayer exchange path can easily
induce the transition to ferromagnetic order.
Indeed, a small degree of Mn–Sb site exchange occurs in
the setpuple layers, meaning that a small fraction of Mn actually
resides on Sb sites. Including this site exchange, our DFT
calculations reveal that already 2.5% of Mn on Sb sites and, in
turn, 5% of Sb on Mn sites is sufficient to swap the sign of the
interlayer exchange constant (see Table III, Supporting Information).
This renders MnSb2Te4 ferromagnetic for a degree of
site exchange that agrees well with our XRD analysis and the
density of subsurface defects observed by STM (Figure 1b). An
even stronger site exchange has been recently reported for bulk
MnSb2Te4
[47,49,51]
and MnSb1.8Bi0.2Te4 single crystals,[32] which
corroborates that the Mn–Sb site exchange easily occurs. Thus,
we conjecture that MnSb2Te4 single crystals remain antiferromagnetic[32]
only for negligible Sb–Mn intermixing. It is noted
that Mn on Sb sites tends to couple antiferromagnetically to
the Mn in the central layer of the septuple layer, while the Mn
moments in the center of the septuple layers always couple ferromagnetically
to each other.
According to our DFT calculations, however, Mn–Sb
site exchange barely increases the transition temperature
(TN = 18 K → TC = 25 K, see Table III, Supporting Information).
This can only be achieved by incorporation of excess Mn in the
DFT calculations, while keeping the Mn concentration in the
central layer constant. In fact it turns out that already a small
Mn excess of 5% residing on the Sb sites strongly increases TC
to 44 K, which well reproduces the experimental TC = 45–50 K
values. The strong enhancement is caused by the simultaneous
strengthening of the intra- and interlayer exchange constants
(see Table III, Supporting Information). The conclusion is
robust toward charge doping by up to 0.2% Te or Sb vacancies
that negligibly changes TC (Note S11, Supporting Information).
Note that the excess Mn in the Sb layers is perfectly in line with
our RBS results (Figure S1, Supporting Information) indicating
a Mn excess of 6% in our samples.
4. Topology and Magnetic Gap
Next, we probe the topological properties of the epitaxial
MnSb2Te4 layers, recalling that perfectly stoichiometric
MnSb2Te4 has been predicted to be topologically trivial.[47,52–54]
In particular, it could be turned into a topological insulator only
by replacement of more than half of the Sb by Bi[53] or by compressing
the lattice by as much as 3%.[52] However, as shown by
Figure 2, our ARPES data from the MnSb2Te4 epilayers reveal
the existence of a topological surface state with the dispersion
of a Dirac cone along the wave vector parallel to the surface k∥.
Varying the photon energy (Figure  2a,b and Figure S5, Supporting
Information) to tune the electron wave number kz perpendicular
to the surface once through the whole bulk Brillouin
zone (Table II, Supporting Information) reveals no dispersion,
evidencing the 2D character of the Dirac cone, contrary to the
lower-lying 3D bulk bands that strongly disperse with photon
energy (Figure 2f, arrows). Moreover, spin-resolved ARPES of
the 2D Dirac cone showcases a helical in-plane spin texture at
k∥ away from the Γ zone center, that is, it exhibits the characteristic
reversal of spin orientation with the sign of k∥ (Figure 2g,i,
Figure  S4, Supporting Information). This spin chirality is a
key signature of a topological surface state. In addition, a pronounced
out-of-plane spin polarization of about 25% occurs
in the remanently magnetized sample at the Γ zone center in
the vicinity of EF, which reverses its sign when the sample is
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magnetized in the opposite direction (Figure 2j). Such out-ofplane
spin texture at Γ is evidence for a magnetic gap opening
at the Dirac point.[63] Combined, the ARPES results demonstrate
that MnSb2Te4 is a ferromagnetic topological insulator
with clear fingerprints of a magnetic gap at Γ. Favorably, the
Dirac point of the topological surface state is rather close to EF.
Indeed, extrapolation of the observed linear bands, deduced by
Lorentzian peak fitting (Figure  2d,h), yields a position of the
Dirac point ED of 20 ± 7 meV above EF at 300 K (Note S8, Supporting
Information).
Since a Dirac point above EF is not accessible for ARPES,
here we employ low temperature STS to directly probe the ferromagnetic
gap expected to open up at T < TC. Figure 3a shows
a topography STM image of the MnSb2Te4 epilayer at 4.3 K
together with six STS spectra recorded at different locations on
the surface. All spectra consistently reveal a gap at EF varying,
however, significantly in size. Attributing the energy region
where dI/dV≈0 as gap (Note S9, Supporting Information),
a full map of the gap size Δ is obtained for a larger surface
region (Figure 3b),[64,65] with the corresponding gap histogram
displayed as inset. The gap size varies in the range 0–40 meV
with a mean value of 17 meV and a spatial correlation length of
2 nm observed consistently in three distinct areas (Figure S7,
Supporting Information). A corresponding set of dI/dV curves
recorded along the dashed line in Figure  3b is depicted in
Figure 3c and showcases the small-scale bandgap fluctuations.
Likely, the spatial variation of Δ is caused by the spatially varying
subsurface defect configurations, that is, by the Mn atoms
on Sb lattice sites. Indeed, the gap fluctuations appear on the
same length scale as the topographic features in Figure 1b. The
average gap center position is only 0.6 meV above EF (Figure S7,
Supporting Information), which compares well to the value of
Adv. Mater. 2021, 2102935
Figure 2.  Topological properties of MnSb2Te4 revealed by ARPES. a) ARPES maps along E(k∥x) for five different photon energies hν displayed at the
deduced kz values. b) Same data as (a) displayed as (k∥x, kz) maps via interpolation featuring negligible dispersion along kz. The kz range covers the
whole Brillouin zone. c) Full 3D representation of the surface Dirac cone with k∥x pointing along the Γ – K direction. d) Energy-momentum dispersion
of the Dirac cone (left) and corresponding momentum-distribution curves (right) recorded at hν = 23 eV. The dashed, red lines along maxima result
from fits to the data (Note S8, Supporting Information). They extrapolate to a Dirac point 20 meV above the Fermi level. e) Constant-energy cuts of the
Dirac cone. f) ARPES maps along E(k∥,x) at different photon energies featuring a strong dispersion of a bulk valence band (blue arrows) with photon
energy (i.e., kz). g,i) Spin-resolved ARPES at k∥ as marked in (h), hence, crossing the surface Dirac cone. Left: spectra for the two spin channels at one
k∥,x. Right: spin polarization for both k∥,x, that is, ±k∥,x. g) In-plane spin direction Sy perpendicular to k∥. i) Out-of-plane spin direction Sz. Data for Sx:
Figure S4, Supporting Information. h) Left: surface Dirac cone with marked k∥ of the spectra in (g,i) and dashed line along intensity maxima as deduced
by fitting (Note S8, Supporting Information). Right: energy distribution curves showing where (g,i,j) were measured. j) Spin-resolved ARPES recorded
at Γ and 30 K, and showcasing an out-of-plane spin polarization that reverses sign with reversal of the sample magnetization (M+
and M−
, right).
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ED − EF = 20 meV determined by ARPES on another sample.
The small difference most likely arises from small differences
in the growth and surface conditions, but may also be caused
by the different measurement temperatures (4.3 K vs 300 K) or
larger-scale potential fluctuations.[66,67]
To prove that the energy gap is of magnetic origin,[25] the
temperature dependence Δ(T) is probed by STS. This has not
been accomplished yet for any magnetic topological insulator
because at higher temperatures kBT ≥ Δ/5 the STS gap Δ
is smeared by the broadening of the Fermi–Dirac distribution,
leading to a small non-zero tunneling current at voltages
within the bandgap.[68] A direct deconvolution of the local
density of states (LDOS) and the Fermi distribution function
would require an assumption on the LDOS shape as function
of energy. Such an assumption is impeded due to the significant
spatial variation of the dI/dV curves at 4.3 K (Figure 3a–c),
as also found consistently for other magnetic topological insulators.[64,69]
Therefore, we developed a new method to derive Δ
at elevated temperatures using the ratio between dI/dV at V =
0 mV and dI/dV at V well outside the region of the 4.3 K
bandgap (Note S9, Supporting Information). Figure 3d displays
the ratio R = [dI/dV(0 mV)]/[dI/dV(−50 mV)] for a large number
of dI/dV spectra recorded at temperatures varying between
4.3 K and 50 K (small dots). Selected dI/dV spectra at 10, 21 and
47 K are shown as insets (more dI/dV data in Figure S8, Supporting
Information).
One can see that up to 20 K, the STS ratio R is zero and thus
dI/dV = 0 nS at zero bias, directly evidencing the persistence of
the gap. At higher temperatures the R values gradually increase,
which is due to the convolution of the temperature broadening
effect along with the decreasing magnetic gap size that goes to
zero at T = TC. To separate these two effects, we model the temperature
dependence of the STS ratio for fixed gap sizes Δ(4.3K)
= 0, 5, 10, 15 and 20 meV by convolving the dI/dV curves
recorded at 4.3 K (Figure 3a–c) with the Fermi–Dirac distribution
(Figure  S9, Supporting Information). The corresponding
model results are represented by solid gray lines in Figure 3d,
where the red line marked with 0 meV indicates how the STS
ratio R would evolve with temperature when the gap is zero.
Clearly, up to T = 47 K, the experimental STS data points R are
Adv. Mater. 2021, 2102935
Figure 3.  Spatial variation of the magnetic energy gap and its closing at TC. a) Center: STM image of MnSb2Te4 recorded at T= 4.3 K after ultrahigh
vacuum sample transfer from the MBE system, V = 0.5 V, I= 0.2 nA. Surrounding: dI/dV spectra recorded at the crosses as labelled. The dashed line
in the upper left spectrum is the noise threshold used for determination of gap size Δ (Note S9, Supporting Information). b) Spatial map of gap size
Δ. Inset: histogram of Δ resulting from three distinct areas, average gap size ∆ and standard deviation σ are marked. c) dI/dV spectra (color code)
along the magenta dashed line in (b). The yellow line at the bottom of the color code bar marks the threshold for gap determination in (a,b). d) Small
dots: Ratio [ / ( 0 mV)] /[ / ( 50 mV)]= = = −R dI dV V dI dV V deduced from dI/dV(V) curves recorded at different T. The different gray shades correspond
to different cooling cycles. Each point belongs to a single position on the sample surface within 1 nm. The error bars represent the standard deviation
resulting from multiple curves measured at the same position. Large gray dots: average values of all data at corresponding T implying spatially averaged
gap sizes ∆ (21 K) = 11 ± 5 meV, ∆ (31 K) = 6 ± 1 meV, and ∆ (36 K) = 4 ± 1 meV (Note S9, Supporting Information). Gray lines: T-dependence of
the ratio R for the marked gap sizes ∆ as deduced by convolving the measured dI/dV data at 4.3 K with the Fermi distribution function (Figure S9b,
Supporting Information). The area above Δ = 0 meV exhibits such a large R that the existence of a gap can be excluded. The error bars marked on the
right result from the variation of the dI/dV curves at 4.3 K and represent a standard deviation (Figure S9b, Supporting Information). Colored squares:
gap values deduced from XMCD (yellow, Figure 1f) and SQUID (red, violet, Figure S3, Supporting Information) via ( ) ( )∆ ∝T M T .[70] Insets: selected
dI/dV curves belonging to the points with blue arrows. For additional curves see Figure S8, Supporting Information.
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below this line. This evidences that the gap remains open up
to TC whereas for higher temperatures the gap is closed. This
directly demonstrates the magnetic origin of the gap[25]
due to
the ferromagnetism of the MnSb2Te4 system.
Comparing the actual experimental data points with the calculated
lines reveals that the gap size continuously decreases
as the temperature increases and that it closes rather precisely
at TC  = 45–50 K in line with the TC obtained by XMCD and
SQUID. As described above, the gap size varies spatially across
the surface (Figure  3a–c) due to local disorder. Accordingly, at
higher temperatures the STS ratios also exhibit a considerable
variation depending on where the STS spectra were recorded.
For this reason, larger ensembles of data points were recorded
at four selected temperatures T = 10, 21, 31, and 36 K within an
area of 400 nm2
. From this, the average gap sizes were deduced
as ∆(21 K) = 11 ± 5 meV, ∆(31 K) = 6 ± 1 meV, and ∆(36 K) =
4 ± 1 meV, represented by the large gray and white dots in
Figure 3d. Thus, the gap indeed gradually shrinks as the temperature
approaches TC and is closed above, fulfilling precisely
the expectations for a ferromagnetic topological insulator.[25]
Note that the different gray shades of the small data points
mark different cooling runs starting from an initial elevated
temperature. Hence, during cooling the tip slowly drifts across
the sample surface while measuring at varying temperature,
thus exploring the variations of Δ versus T and spatial position
simultaneously. Accordingly, the visible trend of Δ(T) relies on
the sufficient statistics of probed locations to obtain reliable
spatially averaged ∆ (large dots).
The conclusion that the gap closes at TC is corroborated by
comparing the experimental ( )∆ T gap evolution with the M(T)
magnetization, based on the relation ( ) ( )∆ ∝T M T derived by
theory[70] and previous experiments.[25] Combining the M(T)
data from SQUID and XMCD (Figure 1d,f and Figure S3, Supporting
Information) and the low temperature gap ∆(4.3 K) =
17 meV from STS (Figure  3b), ( ) (4.3 K)· ( )/ 0∆ = ∆T M T M is
obtained and, thus, straightforwardly ( )R T from the magnetization
data. The results are presented as yellow, blue, and red
dots in Figure 3d, demonstrating nice agreement with the STS
experiments. This further demonstrates the magnetic origin
of the gap. Since the center of the gap (Figure S7, Supporting
Information) is close to the Dirac point position observed by
ARPES (Figure  2e,h), the gap is attributed to the topological
surface state, consistent with the out-of-plane spin polarization
near the Dirac point observed in Figure 2j. Such a magnetic
gap of a topological surface state close to EF is highly
favorable for probing the resulting topological conductivity and
its expected quantization.
5. DFT Calculations
To clarify the origin of the discovered ferromagnetic topological
insulator, the electronic band structure of MnSb2Te4 was calculated
by various DFT methods, considering different magnetic
configurations, including chemical as well as magnetic disorder
(Note S11, Supporting Information). As a general result,
the ferromagnetic topological insulator phase is only formed
by introducing magnetic disorder. Calculating the bulk band
structure, the perfect ferromagnetic system without disorder
emerges as a topological Weyl semimetal with a zero bulk
bandgap and a Weyl crossing point located along ΓZ at about
5% of the Brillouin zone away from Γ (Figure 4f,g, Figures S11
and S12, Supporting Information). While this is in agreement
with recent calculations,[49,54]
it obviously disagrees with our
STS and ARPES results. On the other hand, the disorder-free
antiferromagnetic system is found to be a topological insulator
with a bulk bandgap of 120 meV (Figure 4k). This is evidenced
by the band inversion at Γ in Figure 4k indicated by the color
coding of the spectral function difference between cationic and
anionic sites [red (blue): dominating anion (cation) character,
see Note S11, Supporting Information]. This color code is also
used in Figure 4f–k. Slab calculations of the antiferromagnetic
surface band structure (Figure 4d) indeed reveal the topological
surface state with a gap at the Dirac point due to time reversal
symmetry breaking. Discrepancies to earlier calculations[52,53]
are discussed in Note S11, Supporting Information.
For a more realistic modelling, complex magnetic orders
have to be taken into account, deviating from perfect ferromagnetic
or antiferromagnetic order as implied by our magnetometry
results (Figure  1e, Figure  S3, Supporting Information).
The extreme case of completely disordered local magnetic
moments, without net magnetization, showcases a bulk
bandgap of 135 meV with nontrivial topology (Figure 4j) as seen
from the band inversion around the gap close to Γ. Varying
the degrees of magnetic disorder (Figure 4g–i, Figure S12, Supporting
Information) shows that already 20% of magnetic disorder
breaks up the Weyl point of ferromagnetic MnSb2Te4 and
opens an inverted bandgap. This topological insulator induced
by magnetic disorder is robust against chemical disorder such
as the Mn–Sb site exchange that proved to be essential for
inducing ferromagnetic order in the system. While a Mn–Sb
site exchange of 5% does not affect the band topology, 20% site
exchange renders the system trivial (see Figure S11, Supporting
Information). The reason is the lowered spin-orbit interaction
in the Sb layers. We have also simulated 7–10% Mn–Sb
site exchange plus Mn excess and find that the system is still
topological. Our results imply that, contrary to previous conclusions,[47]
defect engineering can accomplish simultaneously a
nontrival band topology and ferromagnetism with high Curie
temperature for the MnSb2Te4 system.
To further assess the robustness of the magnetic gap, slab
calculations are employed for various magnetic disorder configurations.
The simplest case of a purely ferromagnetic slab
does not lead to a Dirac cone, since the bulk bandgap vanishes
(Figure 4b). The pure antiferromagnetic order, on the other hand,
creates a pronounced Dirac cone with magnetic gap of 16 meV,
Figure 4d,e, matching the gap size found by STS (Figure 3b). The
magnetic gap size turns out to be a rather local property caused
by the exchange interaction in near-surface MnSb2Te4 septuple
layers. As such, the gapped Dirac cone also forms when the surface
of an antiferromagnet is terminated by a few ferromagnetic
layers (see Figure  S13d, Supporting Information). A relatively
strong out-of-plane spin polarization at the gap edges (≈60%)
is found in that case, matching the results of the spin-resolved
ARPES measured at 30 K (≈25%) nicely, if one takes into account
the temperature dependence of the magnetization (Figure 1d,f).
For more random combinations of antiferromagnetic and ferromagnetic
layers, the Dirac cone with magnetic gap persists,
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albeit the bulk bandgap vanishes due to the more extended
ferromagnetic portions in the structure (see Figure  S13a, Supporting
Information). Finally, for a system where the magnetic
moments of adjacent septuple layers are continuously tilted with
respect to each other, a gapped Dirac cone was also observed (see
Figure  4c). Likewise, alternate rotations of adjacent collinearly
coupled Mn layers by relative angles ≥40° open a gap in the Weyl
cone (Figure  S12, Supporting Information). Hence, magnetic
disorder turns out to be a decisive tool to accomplish topological
insulator properties for MnSb2Te4.
Last but not least, it is noted that the slope of the temperature
dependent M(T) shows a remarkable linear behavior toward
TC, described by an effective critical exponent β  = 0.7−1.2.
This large β apparently persists for about half of the range
between T = 0 K and TC (Figure 1d,f). Such large β values do
not exist in any classical model ranging from β ≃ 0.125 for the
2D Ising model to the mean-field value of 0.5. The behavior at
the classical critical point may, however, strongly change due
to quantum fluctuations, which can lead to β = 1 in the presence
of disorder[71] as experimentally observed.[72,73] Note that
such disorder is witnessed in our samples by the spatial gap
size fluctuations (Figure 3). Moreover, the magnetic phases of
MnSb2Te4 are energetically very close to each other (Table III,
Supporting Information)[28] which may lead to changes as a
function of temperature as suggested by the kink in the M(T)
curve (Figure S3, Supporting Information).
Adv. Mater. 2021, 2102935
Figure 4.  Theoretical predictions for MnSb2Te4. a) Brillouin zone of the bulk (bottom) and the surface (top) of MnSb2Te4 with high symmetry points
marked. b–e) Band structure from DFT calculations of slab geometries for various magnetic configurations as marked on top. b) Ferromagnetic
interlayer coupling calculated for a thick slab. Blue dots: surface states identified via their strength in the top septuple layer. c) Non-collinear interlayer
coupling as sketched to the right by a vector model and calculated for a thin slab. The color code marks the out-of-plane spin polarization of the gapped
surface-localized Dirac cone on the background of uncolored bulk-like states. d) Antiferromagentic interlayer coupling calculated for a slab (blue lines)
on top of the projected bulk band structure (gray lines). A gapped Dirac cone appears at Γ in the slab calculation. e) Zoom into (d) with marked size
of the magnetic gap in the Dirac cone (topological surface state). f–k) Band structures from DFT calculation of a bulk geometry for magnetic configurations
as marked on top. Color represents the spectral function difference between anion and cation sites for each state with red (blue) representing
dominating anion (cation) character (Note S11, Supporting Information). f) Ferromagnetic interlayer coupling exhibiting a topologically protected Weyl
cone around Γ. g) Zoom into (f). h,i) same as (g) but with magnetic disorder modelled via overlap of collinear spin-up and spin-down states at each
Mn site (Note S11, Supporting Information). j) Same as (f), but with full magnetic disorder. (k) Antiferromagnetic interlayer coupling. Note that (h–k)
feature an inverted bandgap at Γ as visible by the exchanged colors of the two bands surrounding EF rendering these structures topological insulators.
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6. Summary and Conclusion
Epitaxial MnSb2Te4 with regularly stacked septuple layers and
a slight Mn excess features a robust nontrivial band topology
at record-high Curie temperatures up to TC = 50 K. DFT band
structure calculations, ARPES and STS experiments showcase
a 2D Dirac cone of a topological surface state with a magnetic
gap of ≈17 meV close to the Fermi level. The gap disappears at
TC and above, signifying its magnetic origin. This is corroborated
by the out-of-plane spin polarization at the Dirac point
observed by spin-resolved ARPES. Ferromagnetism is triggered
by the modifications of the exchange interactions induced by
Mn–Sb site exchange in combination with a slight in-plane contraction.
Most importantly, excess Mn on Sb sites significantly
enforces the ferromagnetic interactions, leading to a factor of
two increase of the Curie temperature. Last but not least, the
spin-orbit interaction in MnSb2Te4 compared to MnBi2Te4 turns
out to be still sufficiently large to maintain both the band inversion
and the perpendicular magnetic anisotropy. This renders
MnSb2Te4 highly favorable for the quantum anomalous Hall
effect and other topology-based device applications as the critical
temperature is twice as large as for MnBi2Te4 and the Dirac
point is close to EF with small spatial variations. Altogether, our
results underline that the magnetic properties and interlayer
couplings are highly sensitive to the structural disorder in the
material and that magnetic disorder is essential to sustain the
magnetic topological insulator phase. Indeed, the magnetization
features an exotic critical exponent β ≈ 1, which indicates
the influence of a quantum critical point, likely merging ferromagnetic
and antiferromagnetic order.
7. Experimental Section
Details on the sample growth, STEM, RBS, XRD, SQUID magnetometry,
resonant scattering and XMCD, ARPES with spin polarimetry, STM
and STS, electrical transport measurements, and DFT calculations are
provided in the Supporting Information.
Supporting Information
Supporting Information is available from the Wiley Online Library or
from the author.
Acknowledgements
The authors thank Ondrej Man for help with lamella preparation
for STEM and gratefully acknowledge financial support from the
Austrian Science Funds (FWF, I4493-N: P30960-N27), the Impuls- und
Vernetzungsfonds der Helmholtz-Gemeinschaft (Grant No. HRSF-
0067, Helmholtz-Russia Joint Research Group), the CzechNanoLab
project LM2018110 funded by MEYS CR, the CEITEC Nano Research
Infrastructure, the Swedish Research Council (Project No. 821-2012-5144),
the Swedish Foundation for Strategic Research (Project No. RIF14-0053),
the Spanish Ministerio de Ciencia e Innovación (Project No. PID2019-
103910GB-I00), Tomsk State University (Project No. 8.1.01.2018), and
Saint Petersburg State University (Project No. 73028629). The work was
also funded by the Deutsche Forschungsgemeinschaft within SPP1666
Topological Insulators and Germany’s Excellence Strategy—Cluster
of Excellence Matter and Light for Quantum Computing (ML4Q) EXC
2004/1 — 390534769, and the Graphene Flagship Core 3. G.Bihlmayer
gratefully acknowledges computing resources on the supercomputer
JURECA at the Jülich Supercomputing Centre.
Open access funding enabled and organized by Projekt DEAL.
Conflict of Interest
The authors declare no conflict of interest.
Author Contributions
P.K., J.S.-B., and S.W. contributed equally to this work, which was
coordinated by M.M., G.S., and O.R.
Data Availability Statement
The data that support the findings of this study are available from the
corresponding author upon reasonable request.
Keywords
magnetic bandgap, magnetic topological insulators, magnetization,
MnSb2Te4, Mn–Sb site exchange, molecular beam epitaxy
Received: April 18, 2021
Revised: June 29, 2021
Published online:
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Supporting Information
for Adv. Mater., DOI: 10.1002/adma.202102935
Mn-Rich MnSb2Te4: A Topological Insulator with
Magnetic Gap Closing at High Curie Temperatures of
45–50 K
Stefan Wimmer, Jaime Sánchez-Barriga, Philipp
Küppers, Andreas Ney, Enrico Schierle, Friedrich
Freyse, Ondrej Caha, Jan Michalička, Marcus Liebmann,
Daniel Primetzhofer, Martin Hoffman, Arthur Ernst,
Mikhail M. Otrokov, Gustav Bihlmayer, Eugen Weschke,
Bella Lake, Evgueni V. Chulkov, Markus Morgenstern,
Günther Bauer, Gunther Springholz,* and Oliver Rader*
Reprinted supplement page 1 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
Supporting Information
Mn-rich MnSb2Te4: A topological insulator with magnetic gap
closing at high Curie temperatures of 45–50 K
S. Wimmer,1
J. S´anchez-Barriga,2
P. K¨uppers,3
A. Ney,1
E. Schierle,2
F. Freyse,2, 4
O. Caha,5
J. Michaliˇcka,6
M. Liebmann,3
D. Primetzhofer,7
M. Hoffmann,8
A.
Ernst,9, 10
M. M. Otrokov,11, 12
G. Bihlmayer,13
E. Weschke,2
B. Lake,2
E. V.
Chulkov,14, 15, 16, 17
M. Morgenstern,3
G. Bauer,1
G. Springholz,1
and O. Rader2
1
Institut f¨ur Halbleiter- und Festk¨orperphysik,
Johannes Kepler Universit¨at, Altenberger Straße 69, 4040 Linz, Austria
2
Helmholtz-Zentrum Berlin f¨ur Materialien und Energie,
Albert-Einstein-Straße 15, 12489 Berlin, Germany∗
3
II. Institute of Physics B and JARA-FIT,
RWTH Aachen University, 52074 Aachen, Germany∗
4
Institut f¨ur Physik und Astronomie, Universit¨at Potsdam,
Karl-Liebknecht-Straße 24/25, 14476 Potsdam, Germany
5
Department of Condensed Matter Physics, Masaryk University,
Kotl´aˇrsk´a 267/2, 61137 Brno, Czech Republic
6
Central European Institute of Technology, Brno University of Technology,
Purkyˇnova 123, 612 00 Brno, Czech Republic
7
Department of Physics and Astronomy, Universitet Uppsala,
L¨agerhyddsv¨agen 1, 75120 Uppsala, Sweden
8
Institute for Theoretical Physics, Johannes Kepler Universit¨at,
Altenberger Straße 69, 4040 Linz, Austria
9
Institute for Theoretical Physics, Johannes Kepler Universit¨at,
Altenberger Straße 69, 4040 Linz, Austria
10
Max Planck Institute of Microstructure Physics,
Weinberg 2, 06120 Halle, Germany
11
Centro de F´ısica de Materiales (CFM-MPC),
Centro Mixto CSIC-UPV/EHU, 20018 San Sebasti´an/Donostia, Spain
12
IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain
1
Reprinted supplement page 2 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
13
Peter Gr¨unberg Institute and Institute for Advanced Simulation,
Forschungszentrum J¨ulich and JARA, 52425 J¨ulich, Germany
14
Donostia International Physics Center (DIPC),
20018 San Sebasti´an/Donostia, Spain
15
Departamento de F´ısica de Materiales,
Facultad de Ciencias Qu´ımicas, Universidad del Pa´ıs Vasco,
Apdo. 1072, 20080 San Sebasti´an/Donostia, Spain
16
Saint Petersburg State University, 198504, Saint Petersburg, Russia
17
Tomsk State University, Tomsk, 634050, Russia
(Dated: June 29, 2021)
2
Reprinted supplement page 3 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
CONTENTS
S1. Sample Growth 4
S2. Electron Microscopy 5
S3. Rutherford Backscattering Spectrometry 5
S4. X-ray Diffraction 5
S5. Magnetometry by SQUID 8
S6. Comparison with Magnetic Properties of Other MnSb2Te4 Samples 9
S7. Resonant Scattering and X-ray Circular Dichroism 10
S8. ARPES and spin-resolved ARPES 11
S9. Scanning Tunneling Microscopy and Spectroscopy 15
A. Measurement Details 15
B. Band Gap Determination at 4.3 K 16
C. dI/dV (V ) Curves at Different Temperatures 17
D. Determination of Band Gaps at Elevated Temperature 19
S10. Electric Transport Measurements 22
S11. Density Functional Theory Calculations 22
A. Details of the Calculations 22
B. Magnetic Ground State for Different Disorder Configurations 25
C. Topological Properties for Different Disorder Configurations 26
D. Influence of Charge Doping on the Magnetic Interactions 29
References 32
∗
These authors contributed equally to this work
3
Reprinted supplement page 4 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
The following Supporting Notes are ordered according to the methods applied. Each Supporting
Note describes both the details of the experiment or the calculations and additional
data supporting the conclusions from the main text.
S1: SAMPLE GROWTH
MnSb2Te4 films were grown by molecular beam epitaxy (MBE) on BaF2(111) substrates
using a Varian GEN II system. Compound Sb2Te3 and elemental Mn and Te sources were
employed for control of stoichiometry and composition. The Mn:Sb2Te3 flux ratio was set
to 1:1 in order to obtain the nominal 1:2:4 stoichiometry of the MnSb2Te4 phase. The
corresponding Mn and Sb2Te3 flux rates were 0.1 monolayers (ML)/s and 0.1 quintuple
layers/s, respectively, determined by the quartz microbalance method with precision of ±5%.
In addition, an excess Te flux of 1.5 ML/s was used. Typical sample thicknesses were 200
nm. Deposition was carried out at a sample temperature of 290◦
C at which perfect 2D growth
is sustained independently of the Mn concentration, as verified by in situ reflection high
energy electron diffraction and atomic force microscopy. At the given substrate temperature
of 290°C, the incorporation coefficient is unity for Mn due to its very low vapour pressure, but
for Sb2Te3 a small fraction desorbs during growth and is thus, not incorporated. This leads
to a slightly Mn rich composition of the epilayers as revealed by Rutherford backscattering
spectrometry (RBS) described in Supporting Note S3. The composition was further checked
by x-ray diffraction analysis described in Supporting Note S4. Only samples exhibiting the
diffraction spectra of the MnSb2Te4 phase were used for further investigations.
For angle-resolved photoelectron spectroscopy (ARPES) performed at BESSY II and
scanning tunneling microscopy (STM) performed at RWTH Aachen University, samples
were transferred from the MBE system using an ultrahigh vacuum (UHV) suitcase operated
in the low 10−10
mbar pressure range that allowed transportation without breaking UHV
conditions. Samples used for magnetometry and x-ray magnetic circular dichroism (XMCD)
were capped in situ after MBE growth with amorphous Se and Te capping layers to protect
the surface against oxidation.
4
Reprinted supplement page 5 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
S2: ELECTRON MICROSCOPY
High-resolution scanning transmission electron microscopy (TEM) was performed with
a FEI Titan 60-300 Themis instrument equipped with a Cs image corrector. The TEM
data were recorded with a high-angle annular dark field (HAADF) detector and the images
processed using a fast Fourier transform and Fourier mask filtering technique for noise minimization.
Thin cross-sectional lamellae from MnSb2Te4 films were prepared by focused ion
beam milling (FEI Helios NanoLab 660).
S3: RUTHERFORD BACKSCATTERING SPECTROMETRY
The chemical composition of the samples was determined by Rutherford backscattering
spectrometry (RBS) employing a primary beam of 2 MeV 4
He+
ions provided by the 5 MV
15SDH-2 Pelletron accelerator at Uppsala University. A solid-state detector was placed in
backscattering geometry under an angle of 170◦
with respect to the primary beam. The
beam incidence angle was randomized in a 3◦
angular interval around an equilibrium angle
of 18◦
with respect to the surface normal to counteract potential channeling effects. The
resulting spectra (Fig. S1) were fitted by the SIMNRA software package [1] to obtain the
film composition and confirm its uniformity over the film cross section. Analysis of the RBS
data as shown in Fig. S1 yields an excellent fit (blue line in Fig. S1) for atom concentrations
of 57.0% Te, 27.7% Sb and 15.3% Mn with a high uniformity throughout the film cross
section. The obtained composition of Mn1.06Sb1.94Te4 is close to the nominal MnSb2Te4
stoichiometry, but features a slight Mn excess of ∼ 6% and a slight Sb deficiency of ∼ 3% ,
indicating a small amount of substitution of Sb atoms by additional Mn atoms in addition
to Mn-Sb site exchange, as corroborated by x-ray diffraction analysis shown in Supporting
Note S4.
S4: X-RAY DIFFRACTION
The crystalline structure was determined by x-ray diffraction (XRD) scans and reciprocal
space maps recorded in the vicinity of the (101.20) reciprocal lattice point. The measurements
were performed using a Rigaku SmartLab diffractometer with Cu x-ray tube and
channel-cut Ge(220) monochromator. The results are shown as red lines in Fig. S2. The
5
Reprinted supplement page 6 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
1 3 0 0 1 4 0 0 1 5 0 0 1 6 0 0 1 7 0 0 1 8 0 0
0
1 0 0 0
2 0 0 0
3 0 0 0
4 0 0 0
5 0 0 0
6 0 0 0
7 0 0 0
8 0 0 0
M n
S b
2 M e V 4
H e +
i o n s
E x p e r i m e n t
S i m u l a t i o n
T e ( 5 7 . 0 % )
S b ( 2 7 . 8 % )
M n ( 1 5 . 2 % )
s u b s t r a t e
Counts
I o n E n e r g y ( k e V )
R B S s p e c t r u m o f M n 1 . 0 6 S b 1 . 9 4 T e 4 e p i l a y e r
o n B a F 2 ( 1 1 1 ) s u b s t r a t e
T e
Figure S1. Chemical composition and depth profile. Rutherford backscattering spectrum
measured in random geometry. The simulation of the total backscattering signal using SIMNRA
(blue line) is in excellent agreement with the experimental data (open circles). The corresponding
contributions of the film constituents (Te, Sb and Mn) are indicated by the green, orange and red
lines and correspondingly shaded areas. The data reveal a slight Mn excess of ∼ 6 % and an Sb
deficiency of ∼ 3 % with respect to the ideal MnSb2Te4 stoichiometry, suggesting a partial Mn
replacement of Sb atoms in the Sb layer. This yields a composition of Mn1.06Sb1.94Te4 of the films.
symmetric scans along the [000.1] reciprocal space direction (c-axis) were fitted with a modified
one dimensional paracrystal model [2, 3] (black lines in Fig. S2). We have fitted the
data of two samples and obtained consistent results of a = 4.23 ˚A and c = 40.98 ˚A.
The Mn-Sb site exchange was modelled by assuming various fractional occupancies of
Mn on Mn sites CMn/Mn in the central cation lattice plane of the septuples, ideally occupied
by Mn only, the rest of these sites being occupied by Sb atoms. This accordingly leads to
6
Reprinted supplement page 7 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
10
0
10
2
104
10
6
108
10
10
10
12
10
14
10
16
1018
0 1 2 3 4 5 6 7 8 9
a
b
Intensity(arb.u.)
Qz (1/Å)
l=3 6 9 12 15 18 21 24 27 30 33 36 39 42 45
10
0
10
2
10
4
10
6
108
1010
10
12
10
14
1016
1018
10
20
0 0.5 1 1.5 2
Intensity(arb.u.)
Qz (1/Å)
CMn/Mn
Mn Sb Te1.06 1.94 4
Mn Sb Te1.06 1.94 4
CMn/Sb
1.0 0.06
0.9 0.16
0.8 0.26
0.7 0.36
0.6 0.46
0.5 0.56
0.4 0.66
CMn/Mn CMn/Sb
1.0 0.06
0.9 0.16
0.8 0.26
0.7 0.36
0.6 0.46
0.5 0.56
0.4 0.66
l=3 6 9 12
BaF2
BaF2 BaF2 BaF2 BaF2
Figure S2. X-ray diffraction spectra with fits. (a) Experimental x-ray diffraction spectrum of
the MnSb2Te4 epilayer (red lines) compared with simulations (black lines) using a one-dimensional
paracrystal model [2, 3] while assuming different Mn occupation in the central layer (CMn/Mn)
and in the adjacent nominal Sb layers (CMn/Sb) of the septuple. Blue lines denote positions of (0
0 0 l) reciprocal lattice points. (b) Zoom into (a) showcasing the strong sensitivity of the peak at
Qz ≈ 0.9 ˚A−1 (black arrow in (a)) to the Mn-Sb site exchange. The concentration pairs CMn/Mn
and CMn/Sb are chosen to correspond to the Mn1.06Sb1.94Te4 stoichiometry determined by RBS.
Peaks of the BaF2 substrate are indicated.
7
Reprinted supplement page 8 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
a partial occupancy of the Sb sites in the outer cation lattice planes by Mn atoms with
CMn/Sb = (Ctot − CMn/Mn)/2 where Ctot is the total number of Mn atoms in each septuple.
The factor 1/2 arises from the fact that the exchanged Mn from the center of the septuple
is evenly distributed between the two outer Sb layers. In the case of excess Mn in the layers
as seen by RBS, the sum (CMn/Mn + CMn/Sb) > 1.
With these definitions, the structure factor of MnSb2Te4 reads
F(Qz) =
n
Cnfn(Qz) exp(−iQzzn), (1)
where fn(Qz) is the atomic form factor of the n-th atom in the unit cell, zn its coordinate,
Cn its occupancy, Qz its position in reciprocal space and the summation runs over all atoms
in the septuple layer. For Sb, Te, and Mn the atomic form factors at Qz = 0.9 ˚A−1
are 48.9,
49.9 and 23.6, respectively.
The comparison of the measured diffraction spectrum with the simulation for different
amounts of Mn-Sb site exchange are shown in Fig. S2, taking into account the small Mn
excess in the layers (CMn/Mn + CMn/Sb = 1.06 ) as derived by RBS (Fig. S1). CMn/Mn =
0.4 and CMn/Sb = 0.66 at the top of the figure corresponds to 40% Mn atoms in the center
and 66% in the outer two cation layers of the septuple. Figure S2(b) highlights the low
Qz region, evidencing the strong sensitivity of the [000.6] peak at Qz = 0.9 ˚A−1
to the Mn
and Sb exchange. For this peak, the two different cation layers contribute to the structure
factor with almost exactly opposite phase, while the contribution of the Te layers almost
cancels. Because of the different Mn and Sb atomic form factors, the intensity of this peak
rapidly diminishes with increasing Mn-Sb exchange and completely vanishes for complete
intermixing, i.e., CMn/Mn CMn/Sb. The best fit to the experiment is found for CMn/Mn
between 0.9 and 0.8 and CMn/Sb ∼ 0.2, evidencing a non-ideal distribution of Mn and Sb in
the respective layers.
S5: MAGNETOMETRY BY SQUID
The magnetic properties were determined by a superconducting quantum interference
device (SQUID) magnetometer (Quantum Design MPMS-XL) as a function of temperature
from 2 K to 300 K. The external field H was applied either parallel (in plane) or perpendicular
(out of plane) to the epilayer surface, that itself is oriented perpendicular to the
8
Reprinted supplement page 9 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
crystallographic c axis. The diamagnetic contribution of the substrate was determined from
the slope of the magnetization M(H) recorded at high magnetic fields and 300 K well above
the Curie temperature TC of MnSb2Te4, where the magnetic contribution of the thin film
is completely superseded by that of the thousand times thicker substrate. The derived substrate
contribution was then subtracted from the raw data recorded at lower T. Identical
sample pieces were used for in-plane and out-of-plane measurements.
Figure S3 shows out-of-plane M(T) data while field cooling at 10 mT for three different
samples. They reveal a quite similar TC and consistently display a ferromagnetic behavior
via its remanence. Data for sample 1 are also shown in Fig. 1 (main text) where they give
a slightly smaller TC within the error bars.
Figure S3 (top) features a small kink at 20–25 K that indicates deviations from pure
ferromagnetic order possibly indicating a second phase transition that might contribute to
the large critical exponent β 1 as discussed in the main text and attributed there to the
vicinity to a quantum critical point.
S6: COMPARISON WITH MAGNETIC PROPERTIES OF OTHER MNSB2TE4
SAMPLES
Table I compares the results of our three MnSb2Te4 samples with data from the literature.
The comparison highlights the exceptionally large Curie temperature of the Mn-rich epitaxial
films.
9
Reprinted supplement page 10 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
0 . 0
0 . 5
1 . 0
1 . 5
2 . 0
2 . 5
0 2 0 4 0 6 0
3 0 4 0 5 0 6 04 0 5 0 6 0
0 . 0
0 . 5
1 . 0
4 0 5 0 6 0 7 0
1 0 0 2 0 0
0
0 . 0 4
t e m p e r a t u r e ( K )
M(x10
-5
emu)
M n S b 2
T e 4
/ B a F 2
( 1 1 1 )
t e m p e r a t u r e ( K )
M(x10
-5
emu)
s a m p l e 1
s a m p l e 3
S Q U I D
F C i n 1 0 m T , o o p
d i a m a g n e t i s m s u b t r a c t e d
T C
T C
= 4 5 ( 3 ) K
s a m p l e 2
T C
= 4 8 ( 2 ) K
s a m p l e 1
T C
= 5 0 ( 3 ) K
s a m p l e 3
Figure S3. Magnetometry by SQUID. Magnetization M(T) of three individual MnSb2Te4
epilayers measured by SQUID. M(T) was measured in out-of-plane (oop) direction while field
cooling (FC) in a field of 10 mT. Linear extrapolation to M = 0 emu was used to estimate TC as
marked. Notice the small kink in M(T) around 20 K in the top panel which indicates deviations
from pure ferromagnetic order. Inset: Full temperature dependence of the magnetization M(T) up
to 300 K on a vertical scale enlarged by a factor of 40. From the SQUID raw data, the diamagnetic
contribution from the BaF2 substrate of 0.0205 µemu/Oe was substracted.
S7: RESONANT SCATTERING AND X-RAY CIRCULAR DICHROISM
Resonant scattering and XMCD were measured at the extreme ultraviolet (XUV) diffractometer
of the UE46-PGM1 undulator beam line of BESSY II at Helmholtz-Zentrum Berlin.
The XMCD signal was obtained by measuring the difference of the (0001) Bragg peak intensities
for incident photons with opposite circular polarization and the photon energy tuned
to the Mn-L3 resonance. In this setup, the sample was field cooled down to 10 K in an
external field of about 0.5 T provided by a removable permanent magnet. Subsequent po-
10
Reprinted supplement page 11 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
nominal growth magnetism critical reference
stoichiometry temperature
MnSb2Te4 epitaxial film FM TC=46-48 K sample 1, this work
MnSb2Te4 epitaxial film FM TC=45 K sample 2, this work
MnSb2Te4 epitaxial film FM TC=50 K sample 3, this work
MnSb2Te4 single crystal AFM TN= 19 K J.-Q. Yan et al. a
)
MnSb2Te4 single crystal AFM TN=19.5 K Y. Chen et al. b
)
MnSb1.8 Bi0.2Te4 single crystal FM TC=26 K Y. Chen et al. b
)
MnSb2Te4 polycrystal FM TC=25 K Murakami et al. c
)
Table I. Magnetic properties of MnSb2Te4 for epitaxial films, bulk crystals and polycrystals,
comparing the ferromagnetic (FM) Curie temperatures TC determined in the present work to TC
and antiferromagnetic (AFM) N´eel temperatures TN from the literature. a) J.-Q. Yan et al., Phys.
Rev. B 100, 104409 (2019); b) Y. Chen et al., Phys. Rev. Mat. 4, 064411 (2020); c) T. Murakami
et al., Phys. Rev. B 100, 195103 (2019).
larization dependent and wave-vector dependent measurements were performed in zero field
at various temperatures. The recorded XMCD data are thus a direct measurement of the
remanent ferromagnetic polarization of the Mn moments in MnSb2Te4.
S8: ARPES AND SPIN-RESOLVED ARPES
ARPES measurements were performed at 30 K with a Scienta R4000 hemispherical analyzer
at the RGBL-2 end station of the U125/2 undulator beamline at BESSY II. Light
is incident under an azimuthal angle of 45◦
and a polar angle of 90◦
with respect to the
sample surface. The light polarization is linear and horizontal. Photon energies between 19
and 70 eV were employed. Spin-resolved ARPES spectra were acquired with a Mott-type
spin polarimeter operated at 25 kV, capable of detecting both in-plane and out-of-plane spin
components. Samples were transported to the RGBL-2 setup in a UHV suitcase to always
maintain pressures below 1 · 10−10
mbar. Overall resolution of ARPES measurements was
10 meV (energy) and 0.3 ◦
(angular). Resolutions for spin-resolved ARPES were 45 meV
11
Reprinted supplement page 12 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
(energy) and 0.75 ◦
(angular).
For the measurement in Fig. 2j, main text, the sample was magnetized in situ at 30 K
by applying a pulsed magnetic field from a removable coil of ∼ ±0.5 T in the direction
perpendicular to the surface. As usual, the spin-resolved ARPES experiment is conducted
in remanence. The movement between the ARPES chamber and the preparation chamber,
where the coil is situated, is a vertical movement of the cryostat so that the sample is always
at 30 K.
Figure S4 shows a complete set of spin-polarized ARPES data featuring all three orthogonal
spin directions for a finite k = ±0.15 ˚A−1
. Only in-plane spin polarization perpendicular
to the electron wave vector k appears and reverses sign with a sign change of k . This evidences
a spin texture that rotates anti-clockwise (right-handed) around the measured Dirac
cone (Fig. 2g,i, main text) with the electron spin locked to the electron momentum. Such
helical in-plane spin texture is a key signature of the topological character of the Dirac cone.
Note that the ferromagnetism of MnSb2Te4 exhibits out-of-plane anisotropy such that bulk
states cannot have in-plane spin polarization, which fully supports the assignment to the
Dirac cone surface state. To deduce the Dirac point energy ED, the peaks within momentum
distribution curves are fitted by two Lorentzians (Fig. S4e) and the energy dependent peak
maxima are connected via two fitted lines (Fig. S4d and Fig. 2d,h, main text) that cross at
ED −EF = 20±7 meV. The binding energy range of the fit was determined by the possibility
to fit separate Lorentzians, see Fig. S4d,e. Since we do not observe any surface band bending
by residual gas adsorption (prominent for the n-doped systems such as Bi2Se3 and Bi2Te3),
the Dirac point can be regarded as a rather good measure of the chemical potential.
Figure S5 shows that the Dirac cone surface state has no dispersion with the wave vector
perpendicular to the surface plane, in contrast to the bulk valence band. Figure S5 is the
input for Fig. 2b, main text, with linear interpolation between the 9 photon energies. Table
II shows the momentum values in kinetic energy.
12
Reprinted supplement page 13 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
+k
In-plane
Sx
Spin-resolved
Intensity(arb.units)
-0.2 0.0
E-E (eV)F
40
20
0
-20
-40
Px(%)
-0.2 0.0
E-E (eV)F
IIx-k
+kIIx
IIx
Spin up
Spin down
b
Spin up
Spin down
Sy
-0.2 0.0
E-E (eV)F
Spin-resolved
Intensity(arb.units)
+kIIx
In-plane
-0.2 0.0
E-E (eV)F
40
20
0
-20
-40
Py(%)
+kIIx
IIx-k
a
+kIIx
Out-of-plane
Sz
Spin-resolved
Intensity(arb.units)
-0.2 0.0
E-E (eV)F
40
20
0
-20
-40
Pz(%)
-0.2 0.0
E-E (eV)F
IIx-k
+kIIx
Spin up
Spin down
c
Intensity(arb.units)
E-E(eV)F
-0.15 0.150
-0.14
-0.12
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
-0.15 0.150-0.30 0.30
d e
E(k)
Fit
MDCs
Fit
kIIx(Å–1
) kIIx(Å–1
)
ED
-0.13
eV
-0.12
eV
-0.10
eV
-0.08
eV
-0.07
eV
-0.06
eV
-0.03
eV
Figure S4. Spin-resolved ARPES data and fit of Dirac cone. All three spin polarization
components are shown for k ,x ±0.15 ˚A−1 (indicated in Fig. 2h, main text). Left hand side of
each subfigure shows the ARPES data for the two opposite spin channels at k ,x +0.15 ˚A−1,
while the right hand side shows the resulting spin polarization Pi for both k ,x ±0.15 ˚A−1. (a)
In-plane spin components perpendicular to k ,x (same as Fig. 2g, main text). (b) In-plane spin
components parallel/antiparallel to k ,x. (c) Out-of-plane spin components. The symbols for spin
direction and orientation are relative to panel (d). (d) The Dirac energy ED is determined by the
crossing of two lines given by fits to experimental data points which, in turn, were determined
by Lorentzians fitted to momentum distribution curves (MDC). These fits are shown in panel (e).
hν = 25 eV.
13
Reprinted supplement page 14 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
-0.4-0.20.0
-0.5 0.0 0.5
E-E(eV)FE-E(eV)FE-E(eV)F
-0.4-0.20.0
-0.5 0.0 0.5
kIIx(Å–1
) kIIx(Å–1
) kIIx(Å–1
) kIIx(Å–1
) kIIx(Å–1
) kIIx(Å–1
) kIIx(Å–1
) kIIx(Å–1
) kIIx(Å–1
)
kIIx(Å–1
) kIIx(Å–1
) kIIx(Å–1
) kIIx(Å–1
) kIIx(Å–1
) kIIx(Å–1
) kIIx(Å–1
) kIIx(Å–1
) kIIx(Å–1
)
kIIx(Å–1
) kIIx(Å–1
) kIIx(Å–1
) kIIx(Å–1
) kIIx(Å–1
) kIIx(Å–1
) kIIx(Å–1
) kIIx(Å–1
) kIIx(Å–1
)
19.5 eV19 eV 20 eV 21 eV 22 eV 23 eV 24 eV 25 eV 26 eV
28 eV27 eV 29 eV 30 eV 31 eV 35 eV 36 eV 37 eV 38 eV
61 eV60 eV 62 eV 63 eV 64 eV 65 eV 66 eV 67 eV 68 eV
Figure S5. Photon-energy-dependent ARPES data. Energy-momentum dispersions for photon
energies from 19 to 68 eV showing a 2D Dirac cone and the dispersion of 3D bulk states with
photon energy. The periodicity in the bulk dispersion demonstrates that the bulk Brillouin zone
is probed completely.
14
Reprinted supplement page 15 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
h (eV) kz(Å-1
)
60 4.341
61 4.371
62 4.401
63 4.431
64 4.460
65 4.490
66 4.519
67 4.548
68 4.576
Table II. Perpendicular momentum. Determination of the perpendicular momentum for the
data shown in Fig. 2a,b, main text. Distance from Γ to Z corresponds to 0.1327 ˚A−1. An inner
potential of 11.8 eV was used.
S9: SCANNING TUNNELING MICROSCOPY AND SPECTROSCOPY
A: Measurement Details
STM measurements were conducted in a home built UHV-STM operating down to
T = 4.3 K. Cr tips were firstly etched ex-situ and additionally prepared in UHV by field
emission on clean W(110). Topography images were recorded in constant-current mode at
a tunneling current I and bias voltage V applied to the sample. The dI/dV (V ) spectra for
scanning tunneling spectroscopy (STS) were recorded after firstly stabilizing the tip-sample
distance at voltage VStab = −0.1 V and current IStab = 0.1 nA, if not mentioned differently
in the captions. Afterwards, the feedback loop was opened and dI/dV was recorded
using standard lock-in technique with modulation frequency f = 1219 Hz and amplitude
Vmod = 1.4 mV while ramping V . The spectra were normalized to account for remaining
vibrational noise during stabilization by equilibrating the integral between VStab and
V = 0 mV. We crosschecked that dI/dV curves barely depend on the chosen Istab and,
hence, on the tip-surface distance (Fig. S6).
For measurements above the base temperature of 4.3 K, the STM body was exposed
15
Reprinted supplement page 16 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
-100 -50 0 50 100
Voltage [mV]
0
2
4
6
8
10
dI/dV[arb.u.]
20pA
50pA
100pA
200pA
400pA
800pA
Figure S6. STS curves recorded at different set points. dI/dV (V ) curves recorded at the
same position after stabilizing the tip at Vstab = −100 mV and various Istab as marked, T = 4.3 K.
to thermal radiation via opening of a radiation shield until a maximum T 60 K was
achieved. Then, the shield was closed, and dI/dV (V ) curves were recorded while the sample
temperature slowly decreased back to 4.3 K. Measurements at constant T > 4.3 K were
performed with partly open shield. A more frequent stabilization between subsequent dI/dV
curves was necessary due to the remaining thermal drift of the tip-sample distance during
the cooling process. This implies shorter recording times that have been compensated by a
more intense averaging of subsequently recorded curves.
B: Band Gap Determination at 4.3 K
The band gaps at T = 4.3 K were determined as follows. First, the noise level of the
dI/dV curves was reduced by averaging 3 × 3 curves covering an area of (1.2 nm)2
. Subsequently,
an averaging of dI/dV (V ) across ±2 mV in bias direction was employed. Then,
we estimated the remaining dI/dV noise level as the maximum of |dI/dV | that appears
with similar strength positively and negatively. For that purpose, we employed about 50
randomly selected dI/dV (V ) curves. Afterwards, the threshold was chosen slightly above
the determined noise level. This threshold is marked in Fig. 3a #1 as dashed line and in
Fig. 3c as yellow line in the color code bar. The voltage width, where the dI/dV (V ) spectra
stayed below this threshold, defines the measured gap ∆ as used in Fig. 3a–c, main text.
16
Reprinted supplement page 17 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
We crosschecked that dI/dV values below the noise level appeared exclusively close to the
determined band gap areas. The resulting gap size ∆ turned out to barely depend on details
of the chosen noise threshold.
Figure S7a and b display two additional ∆(x, y) maps like the ones in Fig. 3b, main text,
but recorded on different areas of the sample surface. They exhibit a similar range of spatial
fluctuations of ∆ as shown in Fig. 3b, main text. Sometimes, ∆ could not be determined
from the dI/dV (V ) curves as, e.g., in the bright area marked by a black circle in Fig. S7a.
There, the spectra stayed below the threshold on the positive V > 0 mV side up to 100 mV
while a gap edge is observed only on the negative side, for an unknown reason. These spectra
(∼ 5 % of all spectra) are discarded from further analysis including the histogram of Fig. 3b,
main text. The correlation length ξ of ∆(x, y) is calculated as FWHM of the correlation
function resulting in ξ 2 nm as given in the main text.
The central energy within the gap, E0, is deduced as the arithmetic mean of all voltages
where the dI/dV signal remains below the threshold. Figure S7c–f displays maps E0(x, y)
for the three studied areas as well as a resulting E0 histogram. Favorably, the average of
E0 is rather precisely at EF showing only small spatial fluctuations in the meV range. The
small discrepancy of the average E0 EF found by STS to the Dirac point determined by
ARPES (20 meV above EF) might be due to the different recording temperatures (4.3 K vs.
300 K) or to sample to sample variations.
C: dI/dV (V ) Curves at Different Temperatures
Figure S8 displays dI/dV (V ) spectra recorded at various temperatures as used for the
band gap evaluation displayed in Fig. 3d, main text. An obvious band gap with a voltage
region of dI/dV 0 nS is only found up to about 30 K. At larger T, the curves partly stay
close to dI/dV = 0 nS around EF, but partly strongly deviate from dI/dV = 0 nS. This
varying behaviour requires a more detailed analysis to determine ∆, since a small deviation
from dI/dV = 0 nS might also be caused by Fermi level broadening of the tip that probes a
local density of states (LDOS) of the sample with a small band gap.
17
Reprinted supplement page 18 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
Figure S7. Maps of gap size ∆ and gap center E0 at 4.3 K. (a,b) Spatial maps of the gap size
∆(x, y) as obtained from dI/dV (V ) curves recorded at T = 4.3 K. Two additional surface areas
named area 1 and area 2 are shown, while area 3 is displayed in Fig. 3b, main text. The black
circle marks a region, where the determination of a band gap was not possible (see text). (c)-(e)
Spatial maps of the center of the gap E0(x, y) with respect to the Fermi level EF for the 3 different
areas. (f) Histogram of E0 for all three maps with marked mean and standard deviation σ.
18
Reprinted supplement page 19 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
Figure S8. STS spectra recorded at different temperatures. Selected dI/dV (V) curves
ordered with increasing T as marked on top. The dot in the upper left is colored identically to the
extracted band gap from the same curve as displayed in Fig. 3d, main text.
D: Determination of Band Gaps at Elevated Temperature
The requirement of a more detailed analysis is demonstrated in Fig. S9a. A dI/dV (V )
spectrum exhibiting a gap size ∆ = 17 meV is displayed (blue line) as recorded at 4.3 K.
This spectrum is then convolved with the derivative of the Fermi-Dirac distribution function,
proportional to 1/ cosh2
(eV/2kBT) [4] (other colored lines in Fig. S9a). By this convolution,
we mimick the expected appearance of the same spectrum at elevated T. Obviously, the
previously introduced method of gap determination would obtain ∆ = 0 meV for all T ≥
31 K, albeit the LDOS of the sample still exhibits ∆ = 17 meV.
In order to deduce the correct ∆ from dI/dV (V ) curves recorded at such large T, we introduce
the ratio R = [dI/dV (0 mV)]/[dI/dV (−50 mV)] that turns out to be monotonously
19
Reprinted supplement page 20 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
Figure S9. Gap size determination at elevated T. (a) dI/dV (V ) spectrum with gap ∆ =
17 meV recorded at 4.3 K (blue) and the same spectrum after convolution with the derivative of the
Fermi-Dirac distribution function for T = 31 K (red), T = 40 K (yellow) and T = 50 K (violet). The
Fermi level broadening leads to an apparently ungapped dI/dV curve, albeit the sample LDOS
features a gap of 17 meV. (b) Relation between the measured gap size ∆ of dI/dV (V ) curves
recorded at 4.3 K and the ratio R = [dI/dV (V = 0 mV)]/[dI/dV (V = −50 mV)] of the same
dI/dV (V ) curves deduced after convolution with the derivative of the Fermi-Dirac distribution
function at 40 K. Different circle colors: different areas (Fig. S7). Colored lines: median (violet)
surrounded by the standard deviation ±σ (green, blue). (c,d) Same as Fig. 3d, main text, but
using a different reference voltage Vref to determine R. (c) Vref = 40 mV, (d) Vref = 60 mV.
20
Reprinted supplement page 21 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
anticorrelated with the gap size ∆. This is demonstrated in Fig. S9b for T = 40 K. All
dI/dV (V ) curves recorded at 4.3 K (area 1–3, 8000 curves) are convoluted with the derivative
of the Fermi-Dirac distribution of 40 K (as in Fig. S9a, yellow curve) before R is determined.
Subsequently, each R is related to its corresponding ∆ (same dI/dV (V ) curve) as deduced
via the method described in subsection S9 B. The anticorrelation of R and ∆ appears in
Fig. S9b and is similarly found for all T = 25 − 50 K (not shown). We used the resulting
median of the simulated R values (violet line in Fig. S9b) to deduce ∆ from a measured R
for each dI/dV (V ) curve recorded at elevated T. The required simulated R(T) curves for
constant ∆ are displayed as full lines in Fig. 3d, main text, for the sake of comparison with
the R values of the measured dI/dV curves. The error of R(∆) at given T is taken as the
2σ width of the simulated R(∆), marked by colored lines in Fig. S9b. For gap sizes below
10 meV, one observes an error of 2–4 meV only. Overall, the R(∆) relation reaches a relative
accuracy for ∆ determination of ±30 %, as long as ∆ remains below 20 meV. This error is
displayed exemplarily on the very right of Fig. 3d, main text.
In addition, we determined errors for the measured R values. They are deduced as
the standard deviation of subsequently recorded 25 dI/dV (V ) data sets (averaged from
10 subsequent dI/dV curves each and smoothed by box averaging of width 3 mV). The
measurement errors are displayed as error bars at the data points in Fig. 3d, main text
(circles). Interestingly, these measurement errors increase significantly around T 45 K,
i.e., close to TC, where they get as large as 10 meV. Since the spatial drift during recording
of the 25 data sets is below 1 nm, as deduced by comparing the long term development of
dI/dV data during cooling to the spatial fluctuations recorded at 4.3 K, these relatively large
errors cannot be caused by a lateral drift of the tip with respect to the sample only. Likely,
they are caused by enhanced temporal fluctuations of the gap close to TC during recording
of the 25 data sets. Thus, the increased error bars around TC corroborate the relation of the
band gap evolution to the magnetic properties additionally.
Error bars of the spatially averaged data points in Fig. 3d, main text, indicate the width
of the R histograms obtained at the corresponding T.
The reference voltage Vref = −50 mV used to determine R is chosen such that it is not
influenced by temperature (|eVref| 5kBT) or gap size (|eVref| max(∆)/2) and not
influenced by spectroscopic features that might spatially vary due to disorder. We crosschecked
that the exact value of Vref barely influences the deduced ∆. This is demonstrated
21
Reprinted supplement page 22 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
in Fig. S9c–d displaying the same data set as Fig. 3d, main text, but using two different
Vref.
S10: ELECTRIC TRANSPORT MEASUREMENTS
Transport invstigations were performed in the van der Pauw geometry with applied magnetic
fields ranging from -3 T to +3 T oriented parallel to the rhombohedral axis of the
epilayers. A mini cryogen-free system was employed for the magnetotransport measurements
at temperatures between 2 K and 300 K. The results are shown in Fig. S10, where
the Hall and anomalous Hall effect as well as the magnetoresistance are shown as a function
of applied field and temperature. Evidently, the anomalous Hall effect appears at temperatures
below about 50 K where a pronounced hysteresis appears in the transport data at
fields less than about 1 T. This perfectly agrees with the onset of ferromagnetism detected
by SQUID and XMCD at temperatures of 45 – 50K. The carrier concentration in the films
was determined from the Hall resistance above 1 T, i.e., well above the coercive field. The
deduced hole concentrations of the MnSb2Te4 samples range from 1 to 3 · 1020
cm−3
, similar
to values reported in the literature [5, 6].
S11: DENSITY FUNCTIONAL THEORY CALCULATIONS
A: Details of the Calculations
The electronic and magnetic structures were calculated by two different methods based
on density functional theory (DFT). Most of the bulk-type calculations (Figs. 4f–k, main
text, Fig. S11, Fig. S12a,b) used a Green function method within the multiple scattering
theory [7, 8]. To describe both localization and interaction of the Mn 3d orbitals appropriately,
Coulomb U values of 3–5 eV were employed within a GGA+U approach [9]. During
these calculations, we confirmed that different topological phases of MnSb2Te4 arise, if one
uses either GGA+U or LDA+U, indicating that LDA+U is not sufficient. To account for
antiferromagnetic configurations of MnSb2Te4, a double unit cell consisting of two septuple
layers was used such as for Fig. 4k, main text, and Fig. S11a and c. In these structures,
the Mn atoms couple ferromagnetically within the Mn planes and antiferromagnetically between
neighboring Mn layers in adajacent septuple layers. For the determination of TN and
22
Reprinted supplement page 23 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
a
R (B)SR (T)S
TC
Hall effect
-4
-2
0
2
4
-3 -2 -1 0 1 2 3
Hallresistance(
5K
10K
20K
30K
40K
-4
-2
0
2
4
-3 -2 -1 0 1 2 3
b
Hallresistance(W)
50K
60K
100K
620
640
660
680
700
720
740
760
780
0 50 100 150 200 250 300
c
Sheetresistance(W)
Temperature (K)
B=0.0 T
B=0.1 T
640
660
680
700
720
740
760
780
800
-3 -2 -1 0 1 2 3
d
Sheetresistance(W)
Magnetic field µ H (T)0
Magnetic field µ H (T)0
T=2K
5K
10K
-4
-3
-2
-1
0
1
2
3
4
-3 -2 -1 0 1 2 3
AnomalousHallresistance(
T=2KT=2K
5K
10K
20K
30K
40K
-4
-3
-2
-1
0
1
2
3
4
-3 -2 -1 0 1 2 3
AnomalousHallresistance(W)
50K
AHE
60K
100K
Magnetic field µ H (T)0
20K
30K
40K
50K
60K
100K
Figure S10. Electrical transport of ferromangetic MnSb2Te4 films. (a) Hall resistance,
(b) anomalous Hall resistance and (d) magnetoresistance as a function of applied magnetic field
recorded at various temperatures between 2 and 100 K, as indicated. Also shown in (c) is the sheet
resistance as a function of temperature. All measurements clearly indicate ferromagnetic behavior
with a TC close to 50 K, in agreement with SQUID and XMCD measurements.
TC, exchange constants Jij were obtained by mapping the DFT calculations onto a classical
Heisenberg model [10].
Different types of disorder were treated within a coherent potential approximation (CPA)
[11, 12]. Chemical disorder is modelled by mixing various atomic species on the same atomic
site (substitutional alloys). The elemental unit cell was used in this case such that only
ferromagnetic order could be described. We simulated three types of chemical disorder,
namely site exchange, i.e., placing as much Mn on Sb sites as Sb on Mn sites, Sb excess, i.e.,
additional, substitutional Sb in the Mn layers, and Mn excess, i.e., additional, substitutional
Mn in the Sb layers. Electron (hole) doping was also modeled by CPA via mixing Te (Sb)
23
Reprinted supplement page 24 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
vacancies, that were simulated as empty spheres, with Te (Sb) atoms on the same site.
Magnetic moment disorder was modeled by CPA via mixing two Mn atoms with opposite
magnetic moment on the same atomic site. This approach has been proven to be very
successful in mimicking spin moment fluctuations, e.g., to account for elevated temperatures.
The 50 : 50 mixing represents the paramagnetic state, while smaller spin fluctuations are
described by, e.g., 95 : 5 or 98 : 2 mixings.
The calculations in Fig. S12c–f were performed with the full-potential linearized augmented
plane-wave method as implemented in the FLEUR code. Also here, GGA [13] with
a Hubbard U correction using U = 6 eV and J = 0.54 eV was used and spin-orbit coupling
was included self-consistently in the non-collinear calculations [14]. Thin film calculations
were also performed with the FLEUR code (Fig. 4c, main text, and Fig. S13b–e). These
calculations are restricted to relatively small and simple unit cells in order to retain high
enough accuracy to derive the Dirac cone dispersion and the size of its magnetic gap by
DFT. Instead, the surface band structure for the antiferromagnetic ground state in Fig. 4d–
e, main text, for the ferromagnetic ground state in Fig. 4b, main text, and for the mixed
state in Fig. S13a was calculated by the projector augmented-wave method [15] using the
VASP code [16, 17]. The exchange-correlation energy was treated using the GGA [13]. The
Hamiltonian contained scalar relativistic corrections and the spin-orbit coupling was taken
into account by the second variation method [18]. In order to describe the van der Waals
interactions, we made use of the DFT-D3 [19, 20] approach. The Mn 3d states were treated
employing the GGA+U approximation [9] within the Dudarev scheme [21]. The Ueff = U −J
value for the Mn 3d states was chosen to 5.34 eV as in previous works [22–25].
For all three methods, the crystal structure of ideal MnSb2Te4 was fully optimized to
obtain the equilibrium lattice parameters, namely cell volume, c/a ratio as well as atomic
positions. Using this structure yields the antiferromagnetic topological insulator state for
MnSb2Te4 within both the projector augmented-wave and full-potential linearized augmented
plane-wave methods (VASP and FLEUR, respectively). For the Green function
method both the experimental crystal structure as determined by XRD (Fig. S2) and the
theoretically optimized one result in the antiferromagnetic topological insulator phase.
In order to visualize the topological character within bulk-type band structure calculations,
we analyze the spectral function difference between anion and cation contributions
of each state: Ai
k(E) = Aanion
k (E) − Acation
k (E). The resulting Ai
k(E) are displayed as color
24
Reprinted supplement page 25 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
MnSb2Te4 MnSb2Te4 with lattice
0% disorder 5% disorder 5% extra Mn constants of MnBi2Te4
TN=18 K TC=25 K TC=44 K TN=20 K
direction r (Å) J (meV) J (meV) J (meV) r (Å) J (meV)
|| 4.23 0.519 0.458 0.674 4.34 0.180
|| 7.36 -0.024 0.034 0.024 7.51 -0.007
|| 8.52 0.016 0.025 0.033 8.68 0.025
 16.8 -0.02 0.002 0.04 16.4 -0.035
Table III. Magnetic structure, critical temperature, and Mn exchange integrals of
MnSb2Te4 for four different crystal configurations (DFT). The exchange integrals J for
the four smallest distances r between the contributing Mn ions are additionally marked by (⊥)
for intralayer (interlayer) Mn pairs. The model with 0% disorder refers to ideal MnSb2Te4 with all
Mn atoms in the central plane of the septuple layers at the experimental lattice constants a = 4.23
˚A, c = 40.98 ˚A (XRD). In the second model (5% disorder), a Mn-Sb site exchange leads to an
occupancy of 95% Mn and 5% Sb in the central lattice plane and 2.5% Mn and 97.5% Sb in each
of the two outer cationic lattice planes of the septuple layer. In the third case, 2.5% extra Mn was
substitutionally introduced in the Sb layers, such that the outer cationic planes contain 2.5% Mn
and 97.5% Sb, while a 100% Mn occupancy appears in the central layer. The fourth model features
ideal MnSb2Te4 with 0% disorder, but laterally expanded to the lattice constants of MnBi2Te4,
i.e., a = 4.34 ˚A, c = 40.89 ˚A.
code in Fig. 4f–k, main text, Fig. S11, and Fig. S12a,b with red color for Ai
k(E) > 0 and
blue color for Ai
k(E) < 0. Band inversion can, hence, be deduced from a mutually changing
color within adjacent bands.
B: Magnetic Ground State for Different Disorder Configurations
Table III summarizes the magnetic properties for four different crystallographic configurations
as obtained by bulk-type DFT calculations. The ideal MnSb2Te4 septuple layer
configuration is antiferromagnetic with low TN = 18 K (third row). To probe the role of
the lattice constant for the magnetic properties, we slightly expanded the lattice within the
25
Reprinted supplement page 26 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
planes towards the lattice constant of MnBi2Te4 (last row). This led to a reduced nearest
neighbor exchange constant J, but barely to a change in TN. Introducing 5 % Mn-Sb site
exchange, in line with the XRD and STM data, turned the interlayer coupling ferromagnetic,
but still with a TC= 25 K only, i.e., significantly lower than the experimental value (fourth
row). However, adding 2.5 % Mn to each Sb layer in the septuple without removing Mn
from the central layer of the septuple, i.e., incorporation of 5 % excess Mn, yields TC= 44 K,
very close to the experimental value (fifth row). Hence, we conclude, in line with RBS, STM
and XRD data, that an excess Mn in combination with an Sb deficiency is responsible for
the high ferromagnetic Curie temperature via Mn substitution in the Sb layers.
C: Topological Properties for Different Disorder Configurations
Figure S11 shows bulk band structure calculations for antiferromagnetic MnSb2Te4
with ideal stoichiometric order (a,c), ideal, ferromagnetic MnSb2Te4 (e) and ferromagnetic
MnSb2Te4 with increasing Mn-Sb site exchange (b,d,f). Antiferromagnetic MnSb2Te4 is a
topological insulator with inverted band gap at Γ, if spin-orbit coupling is considered (c).
This is contrary to previous calculations that have suggested antiferromagnetic MnSb2Te4
to be trivial [26–29]. We assume that the topological insulator state of antiferromagnetic
MnSb2Te4 was missed because structural optimization was either not performed in favor of
experimental lattice constants [27, 29] or performed without van der Waals forces [26, 28]
which both gave by ∼ 3% larger c parameters than in the structurally optimized equilibrium
lattice. Ferromagnetic MnSb2Te4 instead, is a Weyl semimetal without band gap that
remains a Weyl semimetal for moderate Mn-Sb site exchange (Fig. S11b,d), but becomes
topologically trivial at large site exchange (Fig. S11f). Hence, site exchange alone does not
reveal the experimentally observed ferromagnetic topological insulator in contrast to the
magnetic disorder as presented in Fig. 4g–j, main text.
Figure S12 corroborates the gap opening by magnetic disorder. Figure S12b displays the
complete band structure at maximum spin mixture (50 % spin-up, 50 % spin down) for each
Mn lattice site as partially presented in Fig. 4j, main text. An inverted band gap of about
100 meV is found at Γ. Note that the purely ferromagnetic phase in Fig. S12a is calculated
for a unit cell of a single septuple layer only and, hence, differs from Fig. S11e employing a
unit cell with two septuple layers, due to backfolding.
26
Reprinted supplement page 27 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
a antiferromagnetic (nonrelativistic calculation) b ferromagnetic, 5% Mn and Sb exchanged
c antiferromagnetic d ferromagnetic, 5% Mn and Sb exchanged
e ferromagnetic f ferromagnetic, 20% Mn and Sb exchanged
Figure S11. Band Structure at Different Strength of Mn-Sb Site Exchange (DFT). Color
represents the difference between anionic and cationic spectral function for each state, red: more
anionic, blue: more cationic. (a) Antiferromagnetic, ideal MnSb2Te4 in a nonrelativistic (more
precisely scalar relativistic) calculation. No band inversion occurs. (c) Antiferromagnetic, ideal
MnSb2Te4 in a fully relativistic calculation yielding a band inversion. Only one inversion appears
in the Brillouin zone (at Γ) evidencing a Z2 topological insulator. (Also shown as Fig. 4k, main
text, for the ferromagnetic unit cell.). (e) Same as (c) but for ferromagnetically ordered, ideal
MnSb2Te4 with perfect out-of-plane alignment of Mn moments. A 3D Weyl semimetal occurs.
The calculation used the antiferromagnetic unit cell for better comparison with (c). (b, d, f)
Ferromagnetic MnSb2Te4 with different Mn-Sb site exchange as labeled (ferromagnetic unit cell).
In (b) and (d), the Weyl point is preserved, while (f) shows a topologically trivial band gap.
27
Reprinted supplement page 28 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
a ferromagnetic
b disordered local moment
c ferromagnetic d ferrimagnetic e ferrimagnetic f
Figure S12. Inverted band gap by magnetic disorder (DFT). (a) Bulk band structure of
ideal, ferromagnetic MnSb2Te4 with Mn moments perpendicular to the septuple layers (single layer
unit cell). (Part of this figure is shown as Fig. 4f, main text.) (b) Same as (a), but with disordered
local magnetic moments (50% spin up, 50% spin down). An inverted band gap appears at Γ. (Part
of this figure is shown as Fig. 4j, main text.) (c–e) Alternative demonstration of gap opening at the
Weyl point (two septuple layer unit cell): one layer exhibits a collinear out-of-plane ferromagnetic
order, while the other is also collinear, but canted relative to the first one by an angle α as marked.
(f) Vector model of the collinearly canted two septuple layers.
28
Reprinted supplement page 29 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
The Weyl point observed for the ferromagnetic MnSb2Te4 can also be opened by rotating
the spins of adjacent Mn layers, while keeping a collinear spin order within each layer
(Fig. S12c–f). Thus, magnetic disorder renders a dominantly ferromagnetic MnSb2Te4 a
topological insulator as already discussed for Fig. 4g–j, main text.
Figure S13 shows the band structures of slab calculations for different magnetic disorder
configurations, such that surface states are captured. They are performed, e.g., for a combination
of ferromagnetic interior layers surrounded by a few antiferromagnetic layers on top
and bottom (Fig. S13a). This configuration reveals a Dirac-type surface state with a gap
around the Dirac point of 16 meV, very close to the average gap size observed by STS. The
opposite configuration with antiferromagnetic interior surrounded by ferromagnetic surfaces
also exhibits a gapped Dirac cone, here with 40 meV gap size, that might be enhanced by the
thickness of this slab of only 7 septuple layers (Fig. S13d). Indeed, the spin-polarized states
at the gap edge penetrate about 3 septuple layers into the bulk of the thin film (Fig. S13b).
The out-of-plane spin polarization near the Dirac point amounts to ∼ 60%, nicely matching
the experimentally found out-of-plane spin polarization in spin-resolved ARPES (Fig. 2j,
main text). The latter amounts to ∼ 25 % at 30 K in line with the reduced magnetization
at this elevated T (Fig. 1d,f, main text). Note that the band structure in Fig. S13d also
features an exchange splitting of bulk bands as visible by the different colors around −0.2 eV.
The pure antiferromagnetic configuration (Fig. S13e) shows a small band gap of the
topological surface state as well, while the pure ferromagnetic order leads to a gapped Weyl
cone (Fig. S13c), likely being an artifact of the finite slab size of 7 septuple layers only.
D: Influence of Charge Doping on the Magnetic Interactions
Finally, the influence of charge doping on the magnetic properties of MnSb2Te4 was studied.
For undoped, ideally stacked MnSb2Te4, the leading magnetic interaction between the
septuple layers is of a superexchange type, which is responsible for the antiferromagnetic
interlayer coupling. As shown above, chemical disorder by exchanging (replacing) Mn with
(by) Sb changes the magnetic order to ferromagnetic. The presence of Mn defects could
induce an additional Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction that might influence
the magnetic order, if mobile charges are present. However, our calculations show
only minor changes of exchange constants and the magnetic transition temperatures upon
29
Reprinted supplement page 30 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
a b
upper Dirac cone lower Dirac cone
charge spin charge spin
c d e
Figure S13. Influence of magnetic structure on topological surface states (DFT). (a)
Band structure for a ferromagnetic bulk surrounded by antiferromagnetic surface layers as marked
on top. Blue dots are surface states with dot diameter marking their strength at the surface
septuple layer. A gap appears in the topological surface state. (b) Charge density and spin density
of the states at the edges of the magnetically induced band gap in (d) displayed as thin film cross
section. The magnetic configuration is marked on top. (c–e) Band structure for various magnetic
configurations each marked on top. Colors denote the spin density in the out-of-plane direction.
(c) Ferromagnetic order with out-of-plane anisotropy. (d) Two ferromagnetic septuple layers on
both sides of three antiferromagnetic layers. Black arrows mark the states shown in (b). (e) Perfect
antiferromagnetic order as in Fig. 4d,e, main text.
30
Reprinted supplement page 31 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
charge doping. For n-type doping by 0.2% Te vacancies, EF shifts by 0.29 eV increasing TC
by 0.9 K only. For p-type doping by 0.2% Sb vacancies, EF shifts by −0.08 eV increasing
TC by 1.6 K. This indicates that the RKKY interaction is negligible in MnSb2Te4.
31
Reprinted supplement page 32 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
[1] M. Mayer, Nuclear Instrum. Methods B 2014, 332 176.
[2] H. Steiner, V. Volobuev, O. Caha, G. Bauer, G. Springholz, V. Hol´y, J. Appl. Cryst. 2014,
47, 6 1889.
[3] E. D. L. Rienks, S. Wimmer, J. S´anchez-Barriga, O. Caha, P. S. Mandal, J. R˚uˇziˇcka, A. Ney,
H. Steiner, V. V. Volobuev, H. Groiss, M. Albu, G. Kothleitner, J. Michaliˇcka, S. A. Khan,
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J. Zhu, C. Heikes, P. Quarterman, P. Zajdel, J. A. Borchers, W. Ratcliff, Phys. Rev. Mat.
2020, 4, 6 064411.
[7] B. L. Gyorffy, M. J. Stott, In D. J. Fabian, L. M. Watson, editors, Proc. of the Int. Conf. on
Band Structure and Spectroscopy of Metals and Alloys. Academic Press, 1973 385.
[8] M. Geilhufe, S. Achilles, M. A. K¨obis, M. Arnold, I. Mertig, W. Hergert, A. Ernst, J. Phys.:
Condens. Matter 2015, 27, 43 435202.
[9] V. I. Anisimov, J. Zaanen, O. K. Andersen, Phys. Rev. B 1991, 44, 3 943.
[10] A. Liechtenstein, M. Katsnelson, V. Antropov, V. Gubanov, J. Magn. Magn. Mat. 1987, 67,
1 65.
[11] P. Soven, Phys. Rev. 1967, 156, 3 809.
[12] B. L. Gyorffy, Phys. Rev. B 1972, 5, 6 2382.
[13] J. P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 1996, 77, 18 3865.
[14] P. Kurz, F. F¨orster, L. Nordstr¨om, G. Bihlmayer, S. Bl¨ugel, Phys. Rev. B 2004, 69 024415.
[15] P. E. Bl¨ochl, Phys. Rev. B 1994, 50, 24 17953.
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[18] D. D. Koelling, B. N. Harmon, Journal of Physics C: Solid State Physics 1977, 10, 16 3107.
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32
Reprinted supplement page 33 of paper [70] “Magnetic order and band gap in MnSb2Te4”.
CHAPTER 4. REPRINTED PAPERS 184
4.8 Doping induced topological phase transition of (Pb,Sn)Se
This paper deals with (Pb,Sn)Se topological crystalline insulator. Topological crystalline
insulators are merely protected by individual crystal symmetries and exist for an even number
of Dirac cones. We demonstrated that Bi-doping of (Pb,Sn)Se (111) epilayers induces a
quantum phase transition from a topological crystalline insulator to a Z2 topological insulator.
The transition occurs because Bi-doping lifts the fourfold valley degeneracy and induces a gap
at Γ, while the three Dirac cones at the ¯M points of the surface Brillouin zone remain intact.
We interpret this new phase transition as caused by a lattice distortion. Our findings extend
the topological phase diagram enormously and make strong topological insulators switchable
by distortions or electric fields.
ARTICLE
Topological quantum phase transition from mirror
to time reversal symmetry protected topological
insulator
Partha S. Mandal1,2, Gunther Springholz3, Valentine V. Volobuev3,4, Ondrej Caha5, Andrei Varykhalov1,
Evangelos Golias 1, Günther Bauer3, Oliver Rader 1 & Jaime Sánchez-Barriga 1
Topological insulators constitute a new phase of matter protected by symmetries. Timereversal
symmetry protects strong topological insulators of the Z2 class, which possess an
odd number of metallic surface states with dispersion of a Dirac cone. Topological crystalline
insulators are merely protected by individual crystal symmetries and exist for an even
number of Dirac cones. Here, we demonstrate that Bi-doping of Pb1−xSnxSe (111) epilayers
induces a quantum phase transition from a topological crystalline insulator to a Z2 topological
insulator. This occurs because Bi-doping lifts the fourfold valley degeneracy and induces a
gap at Γ, while the three Dirac cones at the M points of the surface Brillouin zone remain
intact. We interpret this new phase transition as caused by a lattice distortion. Our findings
extend the topological phase diagram enormously and make strong topological insulators
switchable by distortions or electric fields.
DOI: 10.1038/s41467-017-01204-0 OPEN
1 Helmholtz-Zentrum Berlin für Materialien und Energie, Albert-Einstein Strasse 15, 12489 Berlin, Germany. 2 Institut für Physik und Astronomie, Universität
Potsdam, Karl-Liebknecht Street 24/25, 14476 Potsdam, Germany. 3 Institute for Semiconductor and Solid State Physics, Johannes Kepler Universität,
Altenberger Strasse 69, 4040 Linz, Austria. 4 National Technical University “Kharkiv Polytechnic Institute”, Frunze Street 21, 61002 Kharkiv, Ukraine.
5 Department of Condensed Matter Physics, Masaryk University, Kotlářská 267/2, 61137 Brno, Czech Republic. Correspondence and requests for materials
should be addressed to J.S-B. (email: jaime.sanchez-barriga@helmholtz-berlin.de)
NATURE COMMUNICATIONS |8: 968 |DOI: 10.1038/s41467-017-01204-0 |www.nature.com/naturecommunications 1
Reprinted page 1 of paper [61] “Topological transition from TCI to TI via Bi doping”.
T
opological insulators are bulk insulators with a metallic
surface state1. Provided that the system stays in the same
symmetry class of the Hamiltonian2, it is fundamentally
impossible to follow a path from this topologically distinct phase of
matter to a trivial phase without closing the insulating bulk band
gap. For a strong topological insulator, metallic surface states are
necessarily present at the boundary to a trivial insulator as, for
example, air or vacuum. These topological surface states are protected
by time-reversal symmetry and their energy vs. momentum
dispersion mimics quasirelativistic, massless particles, with the
shape of a Dirac cone and a peculiar helical spin texture1–4. The
topological classification is given by the so-called Z2 invariant ν0,
which for odd number of Dirac cones is ν0 = 1, giving rise to strong
(Z2) topological insulators, but for even number of cones is zero,
characterizing weak topological or trivial insulators5, 6.
It is possible to transform a strong (Z2) topological insulator to
a trivial insulator by alloying as has been shown for Bi2Se3:In7, 8
and BiTl(S1−xSex)2
9. The fundamental principle of bulk-boundary
correspondence dictates again that this topological phase transition
proceeds through a transition point where the bulk band gap
closes. In this picture, it is supposed that the crystal symmetry is
maintained through the phase transition. However, the crystal
symmetry itself can protect topologically distinct phases as well,
termed topological crystalline insulators (TCIs)5, 10–14. For TCIs,
the decisive role of the crystal symmetry renders the topological
protection dependent on the specific crystal face10. The
topological invariants allow for an even number of Dirac cones,
which are, however, not robust against disorder5. Pb1−xSnxSe and
Pb1−xSnxTe represent such mirror-symmetry protected TCIs with
fourfold valley degeneracy5, 11 in which the trivial-to-TCI phase
transition is reached for sufficiently large Sn contents10, 15. Upon
cooling, the lattice contracts and the enhanced orbital overlap
leads to an inverted (i.e., negative) bulk band gap, which, via
bulk-boundary correspondence, gives rise to Dirac cone surface
states. This has impressively been shown by temperaturedependent
angle-resolved photoemission (ARPES)15.
On the other hand, there are crystals that are not necessarily
topological, but change their symmetry and their electronic
properties with temperature. Such phase-change materials have
been studied intensively for non-volatile data storage because
their properties can be altered dramatically at the structural phase
transition16. GeTe is such a prototypical material16, 17 that
transforms upon cooling from the cubic rock salt to a rhombohedral
structure characterized by a large relative sublattice
displacement. This gives rise to pronounced ferroelectricity of
GeTe18 and has recently been found to allow for an electrical
switching of electronic properties19. Symmetry changes are
potentially very interesting also for topological insulators. In fact,
it has been shown for the TCI Pb1−xSnxSe that by breaking of
mirror symmetries two out of the four Dirac cones at its (100)
surface can be gapped11, 20–22. In that case, the topological phase
remains, however, unchanged by the symmetry breaking and the
0 100 200 300
0.2
0.1
0.0
–0.1
–0.20.5
0.4
Electron-binding
energy(eV)
Electron-binding
energy(eV)
Electron-binding
energy(eV)
0.3
0.2
0.1
0.0
–0.2 –0.1 0 0.1 0.2
0.5
0.4
0.3
0.2
0.1
0.0
–0.2 –0.1 0 0.1 0.2
0.5
0.4
0.3
0.2
0.1
0.0
–0.2 –0.1 0 0.1 0.2
0.4
0.3
0.2
0.1
0.0
–0.2 –0.1 0 0.1 0.2
0.5
0.4
0.3
0.2
0.1
0.0
–0.2 –0.1 0 0.1 0.2
0.5
0.4
0.3
0.2
0.1
0.0
–0.2 –0.1 0 0.1 0.2
0.5
0.4
0.3
0.2
0.1
0.0
–0.2 –0.1 0 0.1 0.2
0.5
0.4
0.3
0.2
0.1
0.0
–0.2 –0.1 0 0.1 0.2
0.5
0.4
0.3
0.2
0.1
0.0
–0.2 –0.1 0 0.1 0.2
0.5
0.4
0.3
0.2
0.1
0.0
–0.2 –0.1 0 0.1 0.2
0.5
0.4
0.3
0.2
0.1
0.0
–0.2 –0.1 0 0.1 0.2
0.5
0.4
0.3
0.2
0.1
0.0
–0.2 –0.1 0 0.1 0.2
c
e
d
f
h
g
i
k
j
l
n
m
T = 305 K T = 210 K T = 110 K T = 22 K
T = 305 K T = 210 K T = 90 K T = 40 K
T = 305 K T = 200 K T = 130 K T = 50 K
10% Sn
20% Sn
28% Sn
Δ(eV)
0 100 200 300
0.2
0.1
0.0
–0.1
–0.2
Δ(eV)
0 100 200 300
0.2
0.1
0.0
–0.1
–0.2
Δ(eV)
o
q
p
Surface
Bulk
Surface
Bulk
Surface
Bulk
10 % Sn
20% Sn
28 % Sn
Low
High
Low
High
Low
High
a
b
–0.5
–0.5
0.0
0.0
k||y(Å–1
)
0.5
0.5
Γ
M1
M3 M2
kz
Γ
Γ
K
X
X
[111]
M2
M1


hv
p+ s
Low
High
M1
M3
M3
L4
L3
L2
L1
M2
T (K)k|| (Å
–1
) k|| (Å
–1
) k|| (Å
–1
) k|| (Å
–1
)
k|| (Å
–1
) k|| (Å
–1
) k|| (Å
–1
) k|| (Å
–1
)
k|| (Å
–1
)
k|| (Å–1
)
k|| (Å
–1
) k|| (Å
–1
) k|| (Å
–1
)
T (K)
T (K)
Fig. 1 Trivial to TCI phase transition induced by cooling. The phase transition into a topological crystalline insulator (TCI) is monitored for undoped
Pb1−xSnxSe (111) films by ARPES around the Γ point. a For (111) films, the four bulk L-points of the bulk Brillouin zone project onto the surface Γ-point for the
longitudinal L-valley along [111], whereas the three oblique valleys project on the M points. b At these momenta, Dirac points appear in ARPES. c–q ARPES
data measured at 18 eV photon energy as a function of temperature and Sn content. The xSn = 10% sample (c, f, i, and l) remains trivial down to low
temperature as seen from the persistence of a band gap. For xSn = 20% (d, g, j, and m) and 28% (e, h, k, and n), gapless Dirac cones develop at low
temperature due to the inversion of the bulk band gap. Panels o–q show the comparison of the measured surface (Dirac cone) band gap (red squares) with
the bulk band gap (blue line) from optical data27, evidencing that the surface gap closes when the bulk band gap changes sign. The error bars in the
measured surface band gap correspond to the uncertainty in determining the energy position of the band dispersions at the Γ-point (see Supplementary
Note 6 for details). The ARPES dispersions were acquired using linearly polarized p + s photons incident on the sample under an angle ϕ = 45° as shown in
a (see also Supplementary Note 5)
ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/s41467-017-01204-0
2 NATURE COMMUNICATIONS |8: 968 |DOI: 10.1038/s41467-017-01204-0 |www.nature.com/naturecommunications
Reprinted page 2 of paper [61] “Topological transition from TCI to TI via Bi doping”.
Z2 invariant stays even. It is crucial for the present work to note
that in principle the topological phase does not need to be preserved
by a distortion. Indeed, topological phase transitions have
recently been predicted for two-dimensional TlSe23 and threedimensional
SnTe by distortions24 and by finite-size effects25.
Here, we investigate the band topology of the (111) surface of
Pb1−xSnxSe by cooling through the complete trivial to topological
phase transition. We demonstrate a new type of phase transition
from crystal-symmetry-protected to time-reversal symmetryprotected
topology controlled by Bi incorporation. We show that
when Bi is introduced in the bulk making the system n-type, a
gap is opened up at the one Dirac cone at the center of the surface
Brillouin zone at Γ, while the three Dirac cones located at the M
points at the zone boundaries behave as in pure Pb1−xSnxSe, that
is, are gapless at low temperature. Our findings provide the first
experimental evidence for a topological phase transition from a
TCI with an even number of Dirac cones to a Z2 time-reversal
symmetry-protected strong topological insulator where the
0–0.1–0.2
0.6% Bi 1.1 % Bi 2.2% Bi0 % Bi
SS
BCB
SS
BCB
SSSS
BVB
BVB
BVBBVB
0.5
0.4
0.3
0.2
0.1
0.0
–0.1 0 0.1
k|| (Å–1
) k|| (Å–1
) k|| (Å–1
) k|| (Å–1
) k|| (Å–1
) k|| (Å–1
)
–0.1 0 0.1 –0.1 0 0.1 –0.1 0 0.1 –0.1 0 0.1 –0.1 0 0.1 –0.1 0 0.1
k|| (Å–1
)
Electron-binding
energy(eV)
18 eV 19 eV 20 eV 21 eV 22 eV 23 eV
SS
BCB
BVB
0.0
Electron-binding
energy(eV)
0.2
0.4
0.6
0.1
0.1
0.0
0.0–0.1
–0.1
Γ M
Γ K
Γ
Δ
Δ(meV)
160
140
120
100
80
60
40
20
0
300 250 200 150 100 50
T (K)
28% Sn
0 % Bi
0.6% Bi
1.1% Bi
2.2% Bi
Bulk
140
120
100
80
60
40
20
0
2.52.01.51.0
Bi content (%)
0.50.0
28% Sn
T = 30 K
Low
High
Low
High
Low
High
BVB
SS
2.2% Bi
T = 30K
0.0
0.1
0.2
0.3
0.4
Electron-binding
energy(eV)
0.5
0.0
0.1
0.2
0.3
0.4
0.5
0.20.10–0.1–0.2
0.0
0.1
0.2
0.3
0.4
0.5
0.20.10
k||y (Å–1
)
k||x (Å–1
)
–0.1–0.2
0.0
0.1
0.2
0.3
0.4
0.5
0.20.10
k|| (Å–1
) k|| (Å–1
) k|| (Å–1
) k|| (Å–1
)
–0.1–0.2 0.20.1
e f g
a b c d
nh i j k l m
23 eV
18 eV
Fig. 2 Doping effect and gap opening at Γ induced by Bi. Incorporation of Bi in Pb0.72Sn0.28Se (111) films leads to n-type doping and a gap opening at the Γ
point as revealed by ARPES. a–d ARPES data measured at a temperature of 30 K and 18 eV photon energy. e Corresponding full ARPES map around the Γ
point for nBi = 2.2%. f, g Dependence of the surface band gap Δ on temperature and nBi. The error bars correspond to the uncertainty in determining the
energy position of the band dispersions at the Γ-point (Supplementary Note 6). h–m Photon energy dependence for nBi = 2.2%, indicating that the gapped
surface state (SS) is two-dimensional. At high binding energies, the dispersion of the bulk-valence band (BVB) with photon energy (marked with horizontal
white arrows) can be distinguished from the lower half of the SS. The dispersion of the bulk-conduction band (BCB) can be observed between 18 and
20 eV, while the size of the surface gap remains qualitatively unchanged as indicated by horizontal dashed lines. n Energy-momentum dispersions of the
upper and lower part of the SS as extracted from fits to results shown in h–m (see Supplementary Fig. 8 and Supplementary Note 7 for details). The error
bars given in the legend represent the maximum uncertainty in determining the corresponding band dispersions
NATURE COMMUNICATIONS | DOI: 10.1038/s41467-017-01204-0 ARTICLE
NATURE COMMUNICATIONS |8: 968 |DOI: 10.1038/s41467-017-01204-0 |www.nature.com/naturecommunications 3
Reprinted page 3 of paper [61] “Topological transition from TCI to TI via Bi doping”.
number is odd (three). Following the recent prediction24, the
origin of the novel topological phase transition is interpreted as
due to a sublattice shift and rhombohedral distortion along the
[111] direction, which lifts the bulk band inversion only at the Zpoint
(L-point in the undistorted phase) projected onto Γ. At the
same time, we do not find any evidence for a bulk band gap
closing across the phase transition, most likely, because the
rhombohedral distortion does not leave the system in the same
symmetry class where the TCI is defined.
Results
Effect of temperature and Sn concentration. We have grown
both undoped and Bi-doped epitaxial (111) Pb1−xSnxSe films of
high quality by molecular beam epitaxy (see Supplementary
Fig. 1–6 and Supplementary Notes 1–4 for details). The samples
were capped in-situ by a thin Se layer to protect the surface
during transport to the ARPES setup, where the cap was desorbed
by annealing (see also “Methods” section and Supplementary
Note 5). ARPES measurements were performed using linearly
polarized light incident on the sample under the geometry shown
in Fig. 1a, which also depicts the bulk and (111) surface Brillouin
zones of rock salt Pb1−xSnxSe. In contrast to the natural (100)
cleavage plane of bulk crystals previously studied12, 13, 15, 26, for
the (111) orientation, the four bulk L-points project on the following
four time-reversal invariant surface momenta: Γ and three
equivalent M points27. This is seen in the ARPES data shown in
Fig. 1b, where the intensity from the Dirac cones at the three M
points is enhanced by a photoemission final-state effect. Due to
the sensitive dependence of the bulk band inversion on the lattice
d
SS
BCB
BVB
Δ
c
T = 305 K T = 30 K
Γ Γ
28% Sn
2.2 % Bi
28% Sn
2.2 % Bi
T = 305 K 28% Sn
2.2% Bi
SS
BVB
T = 30 K 28% Sn
2.2 % Bi
M1 M1
j k
High
0
k|| (Å–1
)
a
T = 305 K
Γ
28 % Sn
0 % Bi
b
T = 50 K
Γ
28% Sn
0% Bi
T = 50 K 28% Sn
0% Bi
T = 305 K 28 % Sn
0% Bi
Electron-bindingenergy(eV)
SS
BVB
SS
BVB
Low Low
High
T (K)
T = 50 K
SS
BVB
M2
28% Sn
2.2% Bi
T = 50 K
SS
BVB
M3
28% Sn
2.2 % Bi
i
150
100
50
0
300 250 200 150 100 50
28% Sn
2.2% Bi
Trivial Topological
insulator
Δ(meV)
Γ
M
0.0
0.1
0.2
0.3
0.4
0.5
0.0
0.1
0.2
0.3
0.4
0.5
–0.2 –0.1 0.20.1 0
k|| (Å–1
)
Electron-bindingenergy(eV)
0.0
0.1
0.2
0.3
0.4
0.5
–0.2 –0.1 0.20.1 0
k|| (Å–1
)
0.0
0.1
0.2
0.3
0.4
0.5
–0.2 –0.1 0.20.10
k|| (Å–1
)
–0.2 –0.1 0.20.1
0
k|| (Å–1
)
Electron-bindingenergy(eV)
0.0
0.1
0.2
0.3
0.4
0.5
0.0
0.1
0.2
0.3
0.4
0.5
–0.2 –0.1 0.20.1 0
k|| (Å–1
)
Electron-bindingenergy(eV)
0.0
0.1
0.2
0.3
0.4
0.5
–0.2 –0.1 0.20.1 0
k|| (Å–1
)
0.0
0.1
0.2
0.3
0.4
0.5
–0.2 –0.1 0.20.1
0
k|| (Å–1)
Electron-bindingenergy(eV)
0.0
0.1
0.2
0.3
0.4
0.5
–0.2 –0.1 0.20.1 0
k|| (Å–1)
0.0
0.1
0.2
0.3
0.4
0.5
–0.2 –0.1 0.20.1
0
k|| (Å–1
)
–0.2 –0.1 0.20.1
e f g h
M1M1
Fig. 3 TCI to Z2 topological phase transition induced by Bi. a–k ARPES data of Pb1−xSnxSe (111) films recorded using 18 eV photon energy at Γ and M
without (a, b, e, and f) and with high Bi doping (c, d, g, h, j, and k). Without Bi doping (b, f), the Dirac cones simultaneously close at Γ and M <150 K,
whereas for high Bi concentration, the Dirac cone is gapped at Γ (d) and intact at all three M points at low temperatures (h, j, and k). i Temperature
dependence of the gap Δ at Γ (red) and M (black). Solid lines are a guide to the eye, and the error bars correspond to the uncertainty in determining the
energy position of the band dispersions at Γ and M, respectively
ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/s41467-017-01204-0
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Reprinted page 4 of paper [61] “Topological transition from TCI to TI via Bi doping”.
constant, the trivial to topological phase transition can be
monitored during cooling by tracing the evolution of the bulk
band gap28 or by observation of the appearance of the
Dirac cones in ARPES15, 26. Indeed, as seen in Fig. 1c–q, for our
(111) films with low Sn concentrations and without Bi doping
(xSn = 10%, Fig. 1c, f, i, and l), the Dirac cone at the Γ point does
not form down to 22 K, while for xSn = 20% (Fig. 1d, g, j, and m)
and xSn = 28% (Fig. 1e, h, k, and n), the gapless Dirac cone
appears at around 90 and 130 K, respectively.
Impact of Bi incorporation in the bulk. Figure 2 shows the effect
of bulk Bi doping on the Γ Dirac cone of Pb0.72Sn0.28Se. When
substitutionally incorporated at cation (Pb, Sn—group IV) lattice
sites, the group V element Bi acts as electron donor due to its
excess valence electron29. Increasing the Bi concentration nBi thus
leads to a strong upward shift of the Fermi level by 200 meV for
nBi = 2.2% (Fig. 2a–e). Remarkably, while for undoped
Pb0.72Sn0.28Se, an intact Dirac cone is seen at 30 K, a surface
gap as large as ~100 meV opens up at the Γ Dirac cone upon
Bi doping and increases strongly with increasing Bi content
(see Fig. 2f, g, Supplementary Fig. 7, and Supplementary Note 6).
This leads to the general conclusion that for Bi concentrations
>~0.6%, the gap at Γdoes not close. Figure 2h–n demonstrates
that within the experimental error bars, this gapped surface state
does not disperse with the photon energy, i.e., momentum perpendicular
to the surface plane, pinpointing its two-dimensional
nature (see also Supplementary Fig. 8 and discussion in Supplementary
Note 7). This observation is important to rule out that
the probed state corresponds to the gapped bulk states.
The effect of Bi on the Dirac cones at the Γ and M points was
evaluated in dependence of the Bi and Sn contents as well as of
temperature. On the topologically trivial side (xSn < 16%), for Bi
doping nBi < 0.6%, no difference in the gaps Δ at Γ and M is
found, which remain open at all temperatures (Supplementary
Figs. 9, 10, and Supplementary Note 8). On the topologically
non-trivial side (xSn > 16%), the Dirac cones at Γ (Fig. 3a–d) and
M (Fig. 3e–h) close synchronously as a function of temperature
for low Bi concentrations. This is shown by Fig. 3a, b, e, and f,
where corresponding ARPES dispersions at 305 and 50 K are
presented. In contrast, for high Bi concentrations (Fig. 3c, d, g,
and h), the fourfold valley degeneracy is completely lifted such
that the gap is closed to zero at all three M points (Fig. 3h–k), but
opens as wide as 100 meV at the Γ point at 30 K (Fig. 3d). Thus,
we conclude that of the even numbered Dirac cones per surface
Brillouin zone, characteristic of a TCI, only three remain,
qualifying Pb1−xSnxSe:Bi as a strong Z2 topological insulator
already for moderate Bi doping. This is the central result of the
present work. While a TCI is protected by mirror symmetry,
the odd numbered Dirac cones of strong topological insulators
are protected by time-reversal symmetry and robust against
disorder. Figure 3i shows that the new Z2 phase, which has never
been observed before for this material class, exists in a wide
temperature range from ~150 K down to the lowest temperature
probed in our experiments.
Discussion
Due to the bulk-boundary correspondence, the formation of the
Dirac cones at the surface indicates a bulk band inversion at the
parent momenta in the Brillouin zone as indicated by Fig. 1a. The
band structures and shape of the Dirac cones corresponding to
the different topological phases are illustrated schematically in
Fig. 4a–c, where the open and closed Dirac cones are colored such
as to indicate the changes of the predominant charge density at
the anion (orange) and cation sites (blue) occurring during the
band inversion (see Supplementary Fig. 11 and Supplementary
Note 9). The topological phase transition so far reported for
Pb1−xSnxSe15, 26 occurs between trivial (Fig. 4a) and TCI phase
(Fig. 4b) where all bulk band inversions behave equally. For the
new topological phase transition into the Z2 topological insulator
phase (Fig. 4c), the bulk band inversion along the momenta
a b
c d
Γ
Γ
Γ
M1
M2
M3
M1
M2
M3 M1
M2
M3
M1
M2
M3
M1
Z2 topological insulator
M2
M3
M1
M2
M3
2.0
1.5
1.0
0.5
Bicontent(%)
0.0
30025020015010050
T (K)
TCI
Z2 Trivial insulator
Trivial insulator Topological crystalline insulator (TCI)
Fig. 4 Topological phase transition as a function of Bi doping and temperature. Schematic illustration of the transition from (a) trivial to (b) topological
crystalline insulator (TCI) and eventually to (c) strong Z2 topological insulator. d Topological phase diagram derived from our ARPES data for xSn = 28%.
The phase diagram contains a trivial phase at high temperature (positive gap Δ at all four L-points) with massive gapped cones at Γ and M; a TCI phase at
low temperature with even Z2 invariant (all bulk L-points have negative, i.e., inverted gaps) and closed Dirac cones at Γ and all M points; a Z2 topological
insulator phase with odd Z2 invariant due to a distortion along [111], giving three closed Dirac cones at the M points and an open gap at the Γ point
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normal to the surface does not occur, triggered by the Bi doping.
This means the discovery of two new topological phase transitions
in Pb1−xSnxSe: (i) from trivial to Z2 topological by cooling
and (ii) from topological crystalline to Z2 topological by adding
Bi. The resulting topological phase diagram (Fig. 4d) derived
from our data shows the interdependence of these two pathways.
The observed behavior resembles the predictions by Plekhanov
et al.24 for SnTe. SnTe is known for its ferroelectric phase transition
in which the anion and cation sublattices are shifted against
each other along the [111] direction17, connected to a transverse
optical phonon softening30. Plekhanov et al.24 tested small displacements
and theoretically predicted that for a certain range of
displacements a Z2 topological insulator can exist.
In general, all IV–VI compounds are close to such a structural
phase transition due to their mixed covalent-ionic bonding. They
belong to the family of 10 electron systems and crystallize either
in the cubic rock salt, rhombohedral, or orthorhombic structure.
As calculated by Littlewood31, 32, the type of structure in which a
IV–VI compound crystallizes critically depends on the values of
two bond orbital coordinates—one is a measure of the ionicity
and the other of covalency or s–p hybridization, and based on
these a phase diagram has been established31, 32. Due to the not
fully saturated p-bonds, the rock salt structure is inherently
unstable against rhombohedral distortions31–33, which reduces
the six nearest neighbors to three. The cubic/rhombohedral phase
boundary is determined by the electronegativity difference
between the constituting elements and as a physical explanation
of the instability the resonating bond model was invoked34. For
the six nearest neighbors, the number of available p-electrons (six
per atom pair) is not sufficient to stabilize the cubic bonds35.
Thus, SnTe and GeTe assume a rhombohedral structure and even
for PbTe minute addition of <0.5% of Ge suffices to drive Pb1xGexTe
into the rhombohedral phase, rendering it
ferroelectric36, 37. Thus, very small changes on the group IV
lattice sites give rise to structural phase transitions. Indeed, for
our Bi-doped films, we find a small Bi-induced rhombohedral
distortion along the [111] direction using x-ray diffraction
(Supplementary Figs. 4–6 and Supplementary Note 4). This
indicates a ferroelectric inversion symmetry breaking as the
underlying physical mechanism, which has been suggested to be
much enhanced at the surface21, 38. Because of the (111) orientation
of our films, this symmetry breaking lifts the even number
degeneracy of the Dirac cones such that a gap is opened only at
the Γ point. This leaves an odd number of Dirac cones intact at
the three M points, causing the topological phase transition.
Finally, we would like to address the role of Bi as decisive
ingredient for symmetry breaking even at small concentrations. Bi
is another 10 electron system33, covalently bonded and crystallizing
in a rhombohedral structure. Accordingly, when incorporated
at group IV lattice sites in Pb1−xSnxSe, it shifts the alloy
toward a more covalently bonded structure in the phase
diagram31, 32, 39. Moreover, on such lattice sites, Bi also reduces
the cation vacancy concentration and the latter strongly enhances
the ferroelectric Curie temperature TC of the cubic-torhombohedral
phase transition30, 35, 38, 40. Indeed, in SnTe thin
films with reduced vacancy concentration, ferroelectricity up to
room temperature was recently reported38. Thus, both effects of
the Bi, higher covalency, and lower vacancy concentration, contribute
to structural symmetry breaking and trigger the novel
TCI-to-Z2 topological phase transition discovered in the present
work.
Methods
Sample growth and characterization. Epitaxial growth of (111) Pb1−xSnxSe films
on BaF2 substrates was performed using molecular beam epitaxy (MBE) in ultrahigh
vacuum conditions better than 5 × 10−10 mbar at a substrate temperature of
380 °C. Effusion cells filled with stoichiometric PbSe and SnSe were used as source
materials, as well as a ternary Pb1−xSnxSe source with xSn = 25%. Bi-doping was
realized using a Bi2Se3 effusion cell. The chemical composition of the layers was
varied over a wide range from xSn = 0 to 40% by control of the SnSe/PbSe beam
flux ratio, and a two-dimensional growth was observed by in situ reflection highenergy
electron diffraction (Supplementary Fig. 1). The film thickness was in the
range of 1–3 µm.
High-resolution ARPES. For the ARPES measurements, the films were capped
in situ in the MBE chamber with a 200 nm thick amorphous Se layer at room
temperature to protect the surface against oxidation during transport to the BESSY
II synchrotron radiation source in Berlin, Germany. There the Se cap was completely
desorbed in the ARPES preparation chamber by annealing at about 230 °C
for 15 min in 3 × 10−10 mbar. ARPES measurements were performed at the UE112PGM2a
beamline of BESSY II at pressures better than 1 × 10−10 mbar using linearly
polarized p + s photons incident on the sample under an angle ϕ = 45°. We used
photon energies between 18 and 23 eV for the temperature-dependent ARPES
measurements of the band dispersions, and a photon energy of 90 eV for the core
levels (see Supplementary Fig. 12 and Supplementary Note 10). Emitted photoelectrons
were detected with a Scienta R8000 electron energy analyzer at the
ARPES 12 endstation. Overall resolutions of the ARPES measurements were 5 meV
(energy) and 0.3° (angular).
Composition and structural characterization. The composition of the epilayers
was determined using high-resolution x-ray diffraction and the Vegard’s law
(Supplementary Fig. 2 and Supplementary Note 2). We employed a Seifert diffractometer
equipped with primary and secondary monochromator crystals. Upon
Bi incorporation, the rhombohedral lattice distortion was determined from reciprocal
space maps recorded around the (513) reflection (see Supplementary
Figs. 4–6 and Supplementary Note 4).
Electrical characterization. The dopant concentration and transport properties
were assessed by Hall effect measurements at 77 K (Supplementary Fig. 3 and
Supplementary Note 3), evidencing carrier mobilities as high as 104 cm2 V−1 s−1 in
dependence of the carrier concentration.
Data availability. The authors declare that all data supporting the findings of this
study are available within the paper and its Supplementary Information files.
Received: 16 December 2016 Accepted: 24 August 2017
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Acknowledgements
This work was supported by SPP 1666 of DFG and the SFB-025 IRON of the Austrian
Science Funds. P.S.M. is supported by Helmholtz Virtual Institute “New states of matter
and their excitations.” We thank Andrzej Szczerbakow for providing the MBE source
material.
Author contributions
P.S.M., G.S., V.V.V., O.C., and J.S.-B. performed photoemission experiments with support
from A.V. and E.G.; G.S. prepared and characterized the samples; G.S., V.V.V., and
O.C. performed x-ray diffraction experiments; J.S.-B. and P.S.M. performed data analysis,
figure and draft planning; J.S.-B., O.R., G.S., and G.B. coordinated the project and wrote
the manuscript with input from all the co-authors.
Additional information
Supplementary Information accompanies this paper at doi:10.1038/s41467-017-01204-0.
Competing interests: The authors declare no competing financial interests.
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Reprinted page 7 of paper [61] “Topological transition from TCI to TI via Bi doping”.
1
Supplementary Figures
Supplementary Figure 1: Growth and Surface Characterization. Reflection high-energy electron
diffraction of Pb1-xSnxSe epilayers on BaF2 (111) substrates recorded during MBE growth for xsn = 0,
10, 20 and 28% from (a) to (d), respectively. (e) Atomic force microscopy image of the xsn = 28%
epilayer with 1 µm thickness. Horizontal scale bar, 1 µm (white-solid line).
d
PbSnSe (111)
a b
c
xSn =0%
xSn =28%
xSn =10%
xSn =20%
xSn =28%
PbSnSe (111)e
Reprinted supplement page 1 of paper [61] “Topological transition from TCI to TI via Bi doping”.
2
25.4 25.6 25.8 26.0 26.2 26.4
100
101
102
103
104
105
0 5 10 15 20 25 30 35 40 45 50
0
5
10
15
20
25
30
35
40
45
50
a
BaF2
(222)Intensity(arb.units)
Diffraction angle 2θ (°)
xSn= 0%
xSn= 10%
xSn= 20%
xSn= 33%
PbSnSe
b
Vegard
solubility limit
Composition
XRD
xSnfromXRD(%)
xSn (%) from MBE flux ratio
of Pb1-xSnxSe
Supplementary Figure 2: X-ray diffraction of Pb1-xSnxSe epilayers on BaF2 (111). (a) Radial (222)
diffraction scans for selected compositions varying from xSn = 0 to 33%. (b) Sn content derived from
Vegard’s law (dashed line) plotted versus the beam flux ratio of SnSe/(PbSe+SnSe) used for molecular
beam epitaxy (MBE). The boundary of the Sn solubility limit in single phase cubic Pb1-xSnxSe of about
42% is indicated. The error in xSn was derived from the 2% precision of the MBE flux measurements
using the microbalance technique.
Reprinted supplement page 2 of paper [61] “Topological transition from TCI to TI via Bi doping”.
3
300 320 340 360 380 400
1018
1019
1020
1017
1018
1019
1020
102
103
104
105
xSn
= 28%
PbSnSe:Bi
a Bi-doping calibration
Hall effect
at 77 K
nHall
-p0
(cm-3
)
BiSe cell temperature (°C)
g = 3Å/sec
PbSe:Bi
10-2
10-1
100
BismuthconcentrationnBi
(%)
xSn
= 24 - 28%
77K
PbSnSe:Bi
PbSe:Bi
b Hall mobility
Hallmobilityat77K(cm2
/Vsec)
Hall concentration (cm-3
)
Supplementary Figure 3: Bi doping and Hall effect transport measurements. The measurements are
obtained at 77 K for PbSe:Bi () and PbSnSe:Bi with xSn = 28% (). (a) Effective electron
concentration (nHall – p0) versus Bi2Se3 effusion cell temperature used during growth by molecular
beam epitaxy for a constant film deposition rate of 3 Ås-1
. The background carrier concentration of
undoped p-type reference layers due to cation vacancies was p0 = +2×1017
for PbSe and +8×1017
cm-3
for Pb0.72Sn0.28Se. The dashed line represents the values expected for unity doping efficiency. The
lower carrier concentration observed for Pb0.72Sn0.28Se indicates a reduction of the doping efficiency
with increasing Bi content, contrary to the behavior of PbSe. (b) Hall mobility of the epilayers versus
carrier concentration. For low carrier concentrations, a saturation mobility of µ77K = 32000 and 10500
cm2
V-1
s-1
is obtained for PbSe and Pb0.72Sn0.28Se, respectively.
Reprinted supplement page 3 of paper [61] “Topological transition from TCI to TI via Bi doping”.
4
49 50 51 52 53
b
0.5%
2%
(222)
2θ (°)
BaF2
PbSnSe:Bi
20 30 40 50 60 70 80 90 100 110 120 130
a
nBi=2%
nBi<0.5%
PbSnSe:Bi
BaF2
(444)(333)
(222)
Intensity(arb.units)
Diffraction angle 2θ (°)
(111)
BaF2
PbSnSe:Bi
Supplementary Figure S4: Structural effect of Bi-doping of Pb1-xSnxSe. (a) X-ray diffraction spectra
of two Pb0.72Sn0.28Se layers with high and low Bi dopant concentration (blue: nBi <0.5%, red: nBi =
2.2% ), evidencing a single phase structure without any traces of secondary phases. (b) Zoom-in on
the diffraction curves around the (222) Bragg reflection, evidencing no structural degradation due to
Bi incorporation.
Reprinted supplement page 4 of paper [61] “Topological transition from TCI to TI via Bi doping”.
5
Supplementary Figure 5: X-ray diffraction reciprocal space maps. Results of two Pb0.72Sn0.28Se:Bi
samples doped with nBi ~ 0.6% (a, c) and nBi = 2.2% (b, d), indicating a small rhombohedral lattice
distortion for the latter with the distortion angle α = 89.94°. The reciprocal space maps were recorded
around the symmetric (222) and asymmetric (513) reciprocal lattice points at room temperature.
a b c
PbSnSe
PbSnSe
BaF2
BaF2
nBi =0.6% nBi =2.2%
nBi =0.5% nBi =2.2%
α = 89.94°
α = 90°
d
Reprinted supplement page 5 of paper [61] “Topological transition from TCI to TI via Bi doping”.
6
Supplementary Figure 6: Rhombohedral distortion. (a) Sketch of a rhombohedral distortion with
rhombohedral angle α < 90°. This angle corresponds to an elongation along [111] direction. (b) A
sublattice shift (green atoms) is shown which is responsible for ferroelectricity. For simplicity, this is
shown for a cubic structure. The sublattice shift typically also leads to a rhombohedral distortion.
Reprinted supplement page 6 of paper [61] “Topological transition from TCI to TI via Bi doping”.
7
Supplementary Figure 7: Determination of the surface band gap. (a) Energy-momentum ARPES
dispersion measured at 30 K and 18 eV photon energy for Pb0.72Sn0.28Se doped with 0.6% Bi. (b)
Corresponding energy-distribution curves (EDCs) extracted from a. The EDC at zero momentum is
highlighted by a thick red solid line, and contains a double peak structure which is the signature of a
~45±10 meV gap. (d) Corresponding fit results (black solid lines) of the EDC at zero momentum (red
circles) considering a Shirley-like background [4]. The size of the surface band gap is determined from
the energy separation between the fitted Lorentzian peaks shown in blue (green) color, which are
located at the energy minimum (maximum) of the upper (lower) part of the surface state (SS). The
Lorentzian peaks shown in gray color as a thick solid line represent the contribution from the bulkvalence
band (BVB).
Reprinted supplement page 7 of paper [61] “Topological transition from TCI to TI via Bi doping”.
8
Supplementary Figure 8: Photon energy dependence of Pb0.72Sn0.28Se doped with 2.2% Bi. (a) Band
dispersion of the gapped surface state at 18 eV photon energy, with the peak positions extracted from
fits to momentum-distribution curves (MDCs) superimposed. (b) Fit results as shown in (a), with the
upper (USS) and lower (LSS) parts of the surface state indicated. (c) and (d): Analogous results for a
photon energy of 22 eV as in (a) and (b), respectively. (e-h) Fits (black solid lines) to the experimental
MDCs (red symbols) shown for selected binding energies across (e,g) the upper and (f,h) lower parts
of the surface state at (e,f) 18 eV and (g,h) 22 eV photon energy. The intensity contributions from the
surface state are marked with black filled circles on top of each fit. In (h), the intensity from the
opposite branches of the surface state is clearly resolved as shoulders around the intensity of the bulkvalence
band. (i-n) Photon-energy dependent ARPES spectra shown in Figs. 2h-m of the main text.
For each photon energy, we have superimposed the fit results to MDCs shown in Fig. 2n of the main
text. (o-t) MDCs extracted from the data shown in panels (i-n). Dashed lines are guides to the eye
qualitatively following the fitted band dispersions.
Reprinted supplement page 8 of paper [61] “Topological transition from TCI to TI via Bi doping”.
9
Supplementary Figure 9: ARPES spectra of a control sample in the trivial state. (a-d) Energymomentum
ARPES dispersions of a Pb1-xSnxSe (111) epilayer with 16% Sn and 0.6% Bi doping at
(a,b) Γ� and (c,d) M�, acquired at (a,c) room temperature and (b,d) 30 K. For this sample, the band gap
becomes smaller but remains open at the lowest measured temperature. The data show that the band
gaps at the Γ� and M� points exhibit similar behavior with decreasing temperature.
Reprinted supplement page 9 of paper [61] “Topological transition from TCI to TI via Bi doping”.
10
Supplementary Figure 10: Schematic of the surface Brillouin zone of Pb1-xSnxSe (111). The energymomentum
ARPES dispersions around the M� points have been acquired with k|| running perpendicular
to each individual Γ�M� direction as indicated by the black solid lines.
Reprinted supplement page 10 of paper [61] “Topological transition from TCI to TI via Bi doping”.
11
Supplementary Figure 11: Sketch of the different topological phases. (a-c) Relative position of the
band extrema and Dirac cones at the M� and Γ� points of Pb1-xSnxSe (111) in the (a) trivial insulator, (b)
topological crystalline insulator (TCI), and (c) Z2 topological insulator phases. The surface state Dirac
cones (red lines) together with the bulk conduction and valence bands are shown. In the trivial state,
all gaps at M� and Γ� are equal. In the TCI state the bulk bands are inverted and a topological surface
state is formed at all four symmetry points. In the Z2 topological insulator state, the Dirac cones are
closed at all three M� points but open at Γ�. The reversal of the color of the bulk bands indicates the
presence of the bulk band inversion.
Reprinted supplement page 11 of paper [61] “Topological transition from TCI to TI via Bi doping”.
12
Supplementary Figure 12: Core level spectra of Pb0.72Sn0.28Se:Bi film. (a) 2.2% Bi doping measured
after desorption of the Se cap at the ARPES setup. (b) Fitted spectra.
Reprinted supplement page 12 of paper [61] “Topological transition from TCI to TI via Bi doping”.
13
Supplementary Notes
Supplementary Note 1: Sample growth by molecular beam epitaxy
Epitaxial growth of (111) Pb1-xSnxSe films on BaF2 substrates was performed in a Riber 1000
system for molecular beam epitaxy (MBE) in ultrahigh vacuum conditions better than 5 × 10-
10
mbar. Effusion cells filled with stoichiometric PbSe and SnSe were used as beam flux
sources. Alternatively, also a ternary Pb0.75Sn0.25Se source was used. Bi-doping was realized
using a compound Bi2Se3 effusion cell. The chemical composition of the layers was varied
over a wide range from xSn = 0 to 40% by variation of the SnSe/PbSe beam flux ratio
measured using a quartz microbalance moved into the substrate position. The composition of
the layers determined from the beam flux ratio agrees within ±2% to the composition
determined independently determined by x-ray diffraction as described below. The growth
rates were around 1 µm h-1
(~1 monolayer s-1
) and the growth temperature was set to 380°C
as checked by an IRCON infrared pyrometer. The film thickness was in the range of 1–3 µm.
For all layers smooth two-dimensional (2D) growth occurs after few nanometer deposition on
BaF2 (111) as evidenced by Supplementary Figs. 1a-d that present the reflection high-energy
electron diffraction (RHEED) patterns recorded in situ during MBE growth for films with
various Sn compositions. The high quality of the layers is evidenced by sharp diffraction spots
on the Laue circle and intense Kikuchi lines arising from diffraction from subsurface bulk
lattice planes. No surface reconstruction was observed during deposition. The surface of the
films is atomically flat, exhibiting only single monolayer steps of 3.52 Å height as
exemplified by the atomic force microscopy (AFM) image presented in Supplementary Fig.
1e for xsn = 28%. At the given growth temperature, growth proceeds in a 2D step-flow mode.
Due to pinning of surface steps at screw type threading dislocations originating from the Pb1xSnxSe
/ BaF2 (111) lattice-mismatch of Δa/a ~ 1.6% a characteristic spiral step structure is
formed (cf. Supplementary Fig. 1e) similar as described in Ref. [1].
Supplementary Note 2: X-Ray diffraction and composition
The structural properties and composition of the Pb1-xSnxSe epilayers were characterized in
detail by high-resolution x-ray diffraction (XRD) using a Seifert diffractometer equipped with
primary and secondary monochromator crystals. Films with thicknesses larger than 1 µm are
generally fully relaxed as found by reciprocal space mapping of asymmetric Bragg
reflections. With increasing Sn content, the diffraction peaks shift to larger diffraction angles
as illustrated by Supplementary Fig. 2a for the (222) Bragg reflection, indicating a
corresponding decrease of the lattice constant a0. From the evaluation of the lattice parameter,
we find that the lattice constant closely follows the Vegard’s law given by:
a0 (xSn) = 6.124 – 0.123.
xSn [Å] (1)
in agreement with previous works [2]. Here, a0 = 6.124 Å is the lattice constant of pure PbSe.
Due to the sharp diffraction peaks and the high-resolution x-ray diffraction set-up the
precision of the lattice constant determination is ±0.001 Å, which translates into a precision
for xSn of ±0.01, i.e., of ±1%. Supplementary Fig. 2b shows the resulting composition of the
layers versus that obtained from in situ beam flux measurements using the quartz balance
method, evidencing a very good agreement without adjustable parameters. Films with Sn
content above 40% are found to be no longer single phase, resulting in a splitting of the
diffraction peaks. This is due to the fact that SnSe exhibits an orthorhombic crystal structure,
for which reason the solubility of Sn in cubic rock salt Pb1-xSnxSe is limited to about 42%.
Reprinted supplement page 13 of paper [61] “Topological transition from TCI to TI via Bi doping”.
14
Supplementary Note 3: Bi-doping and electrical characterization
Undoped Pb1-xSnxSe exhibits a p-type background carrier concentration due to cation (Pb/Sn)
vacancies formed during growth. These cation vacancies form resonant acceptor like energy
levels and thus induce a p-type hole conductivity. The p-type carrier concentration increases
with increasing Sn content from around 1017
cm-3
for PbSe to above 1018
cm-3
for xSn > 30%.
Incorporating Bi makes the system n-type and allows tuning the Fermi level into the
conduction band as required for studying the properties of the of the entire Dirac cones of the
topological surface states by angle-resolved photoemission (ARPES). We use a Bi2Se3
effusion cell for doping, which promotes substitutional incorporation of Bi on cation lattice
sites without the need of an additional Se flux. The solubility of Bi in PbSe and SnSe amounts
to several percent according to the quasi binary phase diagrams [1], however, for n-doping
only a small Bi2Se3 flux in the range of 10-5
-10-2
ML s-1
range is actually required, depending
on the desired doping level. This doping flux was calibrated as described in detail in Ref. [3].
Doping action of Bi and the resulting electrical properties of the films were evaluated by Hall
measurements of a large series of samples as shown in Supplementary Fig. 3. For Bi-doped
PbSe the measured electron concentration nH corrected for the background hole concentration
p0 increases linearly with Bi flux and therefore changes exponentially with Bi2Se3 effusion
cell temperature (cf. Supplementary Fig. 3a, ), indicating a unity doping efficiency in
agreement with previous results for Bi-doped PbTe films [3]. This therefore provides a
reliable calibration of Bi concentrations within a relative error of 10%.
For Pb1-xSnxSe films, the electron concentration nH - p0 (Supplementary Fig. 3b, ) is
generally found to be lower for the same growth conditions. This indicates a reduced doping
efficiency of Bi in PbSnSe compared to that in PbSe, in particular at higher doping
concentrations. As shown in Supplementary Fig. 3b, for small electron densities in the 1017
cm-3
range, the mobility of the epilayers at 77K is as high as µ77K = 32000 cm2
V-1
s-1
for PbSe
and 10.500 cm2
V-1
s-1
for Pb0.72Sn0.28Se . Due to the increased scattering the mobility rapidly
decreases with increasing Bi-content in particular above the 1018
cm-3
level, as we have also
previously reported for PbTe [3].
Supplementary Note 4: Structural effect of Bi-doping
The influence of Bi-doping on the structural properties of the epilayers was evaluated by
high-resolution x-ray diffraction as shown by Supplementary Fig. 4. For Bi-concentrations as
high as 2.2% (doping concentration of 3.5 × 1020
cm-3
) we do not find any indication of phase
separation or secondary phase formation and no broadening of the diffraction peaks occurs
(Supplementary Fig. 4b).
For further analysis of possible lattice deformations, reciprocal space maps were recorded
around the (222) and (513) reciprocal lattice points as shown in Supplementary Fig. 5 for two
Pb0.72Sn0.28Se epilayers with high (2.2%) and low (<0.5%) Bi-doping. From the fit of the peak
positions, the in-plane and out-of-plane lattice constants, as well as unit cell corner angle α
(rhombohedral distortion) was derived using the relation:
sin(α/2) = a//√3 (2a┴
2
+ 4 a//
2
)-1/2
(2)
For low Bi-concentration the layers exhibit a cubic lattice structure with a corner angle α =
90°. The experimental error in α is of ±0.01°, as derived from the errors in the lattice
parameter determination (±0.001 Å). For the high-Bi doped layers, however, a rhombohedral
lattice distortion is found with α ~ 89.94° for nBi = 2.2% as shown by Supplementary Fig. 5d.
This indicates that Bi-doping modifies the lattice structure and thus impacts the topological
surface state in the presence of a rhombohedral distortion. The visualization of the
rhombohedral angle α and the shift of anion and cation (111) planes that typically cause the
Reprinted supplement page 14 of paper [61] “Topological transition from TCI to TI via Bi doping”.
15
rhombohedral distortion is depicted in Supplementary Fig. 6. On the other hand, we point out
that for the sample with nBi = 1%, since the distortion is still too weak, from the XRD data we
cannot conclusively derive the exact point of the structural phase transition considering the
error bars.
Supplementary Note 5: Angle-resolved photoemission spectroscopy
Photoemission experiments were performed at the undulator beamline UE112-PGM2a of the
BESSY II synchrotron radiation source in Berlin, Germany. We used the endstation ARPES
12
which is equipped with a Scienta R8000 hemispherical analyzer allowing to detect emitted
photoelectrons up to acceptance angles of 30°. The base pressure during experiments was
better than 1 × 10-10
mbar. The epitaxial films were capped in situ after MBE growth with a
200 nm thick amorphous Se layer at room temperature to protect the surface against oxidation
during transport to the ARPES setup, where the Se cap was completely desorbed in the
preparation chamber by annealing at about 230°C for 15 min in 3×10−10
mbar. The
corresponding valence band ARPES data were collected in a wide range of temperatures
using linearly-polarized p+s photons with energies ranging from 18 to 23 eV. The ARPES
dispersions around the Γ� and M� points were acquired using the photon beam geometry shown
in Fig. 1a of the main text, where the light is incident on the sample under and angle of φ=45°
with respect to the surface normal. The light incidence and electron detection planes were
parallel to the M�-Γ�-M� and K�-Γ�-K� high symmetry directions of the surface Brillouin zone,
respectively. The corresponding energy and angular resolutions were set to 5 meV and 0.1°
,
respectively.
Supplementary Note 6: Determination of the surface band gap
To determine the size of the surface band gaps as a function of Bi and Sn concentrations as
well as of temperature, we have fitted the experimental energy-distributions curves (EDCs) at
zero momentum extracted from the ARPES spectra shown in the main text. In Supplementary
Fig. 7, we summarize the procedure used by taking a Pb0.72Sn0.28Se sample doped with 0.6%
Bi as an example. Supplementary Fig. 7a displays the corresponding energy-momentum
ARPES dispersion measured at 30 K and 18 eV photon energy. The intensity contributions
from the bulk-valence band (BVB) states at high binding energies are clearly distinguishable
from the dispersion of the upper and lower part of the surface state (SS) at lower binding
energies. In particular, we observe that in contrast to the undoped Pb0.72Sn0.28Se sample
measured under the same experimental conditions (see Fig. 2a of the main text), incorporating
Bi leads to an intensity dip at the energy position of the original Dirac point which is the
signature of a small gap. We also note that by increasing the Bi concentration, as also seen in
Figs. 2c,d of the main text, the intensity dip becomes more and more pronounced which is
related to the widening of the surface gap.
In Supplementary Fig. 7b we show the corresponding EDCs extracted from Supplementary
Fig. 7a, where the EDC at normal emission is highlighted with a thick red line. The
corresponding fit results (black solid lines) of the EDC (red circles) are shown in
Supplementary Fig. 7c. The error bars in the determination of the surface gap shown in the
main text correspond to the uncertainty of determining the energy position of the band
dispersions, and are estimated from the standard deviations of the peak positions over several
fitting cycles. Specifically, the size of the surface band gap is determined from the energy
separation between the fitted Lorentzian peaks shown in blue (green) color, which are located
at the energy minimum (maximum) of the upper (lower) part of the SS. We also point out that
a lower limit of the surface band gap can be obtained from the ARPES spectra after
considering the contribution from the linewidth broadening. The lower limit of the surface
Reprinted supplement page 15 of paper [61] “Topological transition from TCI to TI via Bi doping”.
16
band gap is approximately represented by horizontal dashed lines around the region of the gap
in Figs. 2a-d and Fig. 3 of the main text. In Supplementary Figs. 7c, other Lorentzian peaks
shown in gray color are contributions from the bulk-valence band (BVB). To extract the
energy positions, the experimental ARPES spectra were fitted by a sum of Lorentzian
functions plus a background. A typical spectrum containing N number of peaks was fitted by
a function involving a convolution of the form:
I(𝐸, 𝑘) = �f(𝐸, 𝑇) ∙ ∑ M𝑖
2
∙ A𝑖(𝐸𝑖, 𝑤𝑖
N
𝑖=1 ) + B(𝐸)� ⊗ G(𝐸) (3)
Where Ei, ωi, and the matrix elements Mi are fitting parameters corresponding to the binding
energy, width, and intensity of each Lorentzian peak, and f(E,T) is the Fermi function. The
spectral function Ai(Ei,ωi) is approximated by Lorentzian functions, and B(E) is assumed to
be a Shirley-like background [4]. The full width at half maximum (FWHM) of the Gaussian
slit function G(E) corresponds to the total energy resolution of the experiment, which is
photon-energy dependent.
Supplementary Note 7: Photon energy dependence of Pb0.72Sn0.28Se doped with 2.2% Bi
To analyze the energy-momentum band dispersions of the surface state as a function of
photon energy, we have fitted the experimental momentum-distribution curves (MDCs)
extracted from the ARPES measurements shown in Fig. 2h-m of the main text. In
Supplementary Figs. 8a-h, we summarize the procedure used by taking representative results
at 18 eV and 22 eV photon energy as an example. For the fitting procedure, we used a sum of
Lorentzian peaks plus a constant background convoluted with a Gaussian function
representing the momentum resolution, and thus a fit function which is similar to
Supplementary Eq. (3) but with the electron momentum parallel to the surface as the main
variable. Supplementary Fig. 8a shows the fit results of the upper and lower parts of the
surface state superimposed on the corresponding ARPES dispersion measured at 18 eV. The
fitted peak positions are also shown independently in Supplementary Fig. 8b. Analogous
results for measurements at 22 eV photon energy are displayed in Supplementary Figs. 8c,d.
From this comparison, we observe good agreement concerning both the energy positions of
the upper and lower parts of the surface state as well as their overall dispersion with
momentum parallel to the surface.
In Supplementary Figs. 8e-h, we show few-selected fits (black solid lines) to experimental
MDCs (red symbols) obtained at various binding energies across the upper and lower parts of
the surface state for photon energies of 18 eV (Supplementary Figs. 8e,f) and 22 eV
(Supplementary Figs. 8g,h). The intensity contributions from the surface state are marked
with black filled circles on top of each fit. Additional intensities from the bulk-conduction
band (BCB) near the Fermi level and from the bulk-valence band (BVB) at high binding
energies were fitted by extra Lorentzian peaks introduced into the analysis procedure. As seen
in Supplementary Figs. 8e-h, the obtained fits are in remarkable agreement with the
experimental MDCs. The intensity contributions from the upper part of the surface state
(Supplementary Figs. 8e,g) appear as distinct peaks in the corresponding MDCs. This is also
the case for the whole measured photon-energy range shown in Figs. 2h-m of the main text,
even for photon energies where the dispersion of the BCB is clearly observed. Similarly, as
seen in Supplementary Fig. 8f, the lower part of the surface state appears as pronounced peaks
around the BVB intensity, which becomes progressively smaller with decreasing binding
energy. This situation is more or less representative for fits to experimental MDCs up to
photon energies of 21 eV. At higher photon energies, despite the dispersion of the BVB with
momentum perpendicular to the surface kz, we clearly resolve the opposite branches of the
lower part of the surface state as pronounced shoulders around the BVB intensity (see
Reprinted supplement page 16 of paper [61] “Topological transition from TCI to TI via Bi doping”.
17
Supplementary Fig. 8h). This allows us to extract the energy positions of the lower surface
state with relatively good accuracy, despite the partial overlap with the BVB which
nevertheless introduces additional errors in the fitted band dispersions. The error bars in the
MDC fits were estimated from the standard deviations of the peak positions over several
fitting cycles. In particular, the error bars in ∆k|| (∆E) shown in Fig. 2n of the main text for
each photon energy were taken as the maximum error obtained for the whole fitted range, and
the corresponding error bars in energy were estimated from the obtained ∆k|| values. These
error bars represent the maximum uncertainty in determining the corresponding band
dispersions as extracted from the MDC fits. Supplementary Figs. 8i-n display the photonenergy
dependent ARPES spectra shown in Figs. 2h-m of the main text, where we have
superimposed the corresponding results of the MDC fits for each photon energy. By
comparing the maximum error bar obtained from the MDC fits to the maximum deviation
between the fitted results for different photon energies shown in Fig. 2n of the main text, we
derive a total accuracy representing the upper bound for the maximal kz dispersion of the
surface state of ±20 meV. This result strongly indicates that the gapped surface state is two
dimensional, in contrast to the three-dimensional character of the BCB or the BVB which
clearly disperse with photon energy as seen in Supplementary Figs. 8i-n.
Supplementary Note 8: ARPES of the surface state in the topologically trivial state
To determine whether in the topologically trivial phase the temperature dependence of the
band gaps is similar at the Γ� and at M� points, ARPES data were recorded for a ~0.6% Bidoped
Pb1-xSnxSe sample with a Sn content of 16% at temperatures ranging from 300 to 30 K.
This particular Sn content was chosen to be close to the quantum critical point of the phase
transition, but staying in the trivial phase for all investigated temperatures. The ARPES data
shown in Supplementary Fig. 9 reveal both the valence and conduction band states with an
open gap corresponding to the non-inverted band structure. At Γ�, we clearly observe the
contribution from topologically trivial surface states forming as precursor states of the
quantum-phase transition, which are also seen in Figs. 1-3 of the main text in agreement with
previous observations on undoped topological crystalline insulators [5]. We also point out that
the same precursor states have been observed in quantum-phase transitions between trivial
and Z2 topological insulators, which in addition preserve the helical spin texture despite their
trivial origin [6]. Note that the intensity from the precursor states at the M� points is less
resolved in our data most probably because of their tilted projection onto the (111) plane,
which corresponds to an electron emission angle of about 21° in the particular geometry
shown in Supplementary Fig. 10.
Supplementary Note 9: Band gaps and Dirac cones in the different topological phases
As described in the main text, Pb1-xSnxSe (111) exists in different topological states depending
on temperature, Sn and Bi content. For low xSn < 16%, Pb1-xSnxSe is topologically trivial with
an open and equal band gap at the M� and Γ� points of the surface Brillouin zone as shown
schematically in Supplementary Fig. 11a. For higher xSn, a bulk band inversion occurs at low
temperatures, which renders Pb1-xSnxSe as topological crystalline insulator, in which Dirac
cones are formed at all four high symmetry points, i.e., all M� and Γ� points. This is shown in
Supplementary Fig. 11b. Upon Bi-doping, the valley degeneracy is lifted and a gap opens up
at the Γ� point, while the Dirac cones remain closed, i.e., ungapped at all three M�-points
(Supplementary Fig. 11c). This makes Bi-doped Pb1-xSnxSe a Z2 topological insulator with
odd number of band inversions.
Reprinted supplement page 17 of paper [61] “Topological transition from TCI to TI via Bi doping”.
18
Supplementary Note 10: Core-level photoemission
Core-level spectra measured with 90 eV photons for Pb1-xSnxSe with 28% Sn concentration
and 2.2% Bi doping are shown in Supplementary Fig. 12a. The overlap of Bi 5d5/2 with Sn
4d5/2 emission is resolved by a fitting procedure, the results of which are shown in
Supplementary Fig. 12b. To further evaluate the stoichiometry from the core-level spectra, in
particular the Bi concentration, we analyzed the intensity ratios by taking into account the
peak areas and the corresponding photoemission cross sections of the individual elements [7].
Specifically, we used a similar fitting procedure as the one described in Supplementary Note
6. After normalizing the peak areas of individual elements by their photoemission cross
section, we derived the Bi concentration from the ratio nBi=ABi/(ABi+BPb+CSn), where A, B, C
denote the corresponding peak areas normalized with respect to the area under the Se peak.
For the core-levels shown in Supplementary Fig. 12, we derive ABi=0.0973, BPb=2.04129 and
CSn=0.84593, which yields an absolute value of nBi~3.2 % that is in fair agreement with the
more accurate result obtained using high resolution x-ray diffraction and the Vegard’s law
(see Supplementary Fig. 2 and Supplementary Note 2).
Supplementary References
1. Springholz, G., Ueta, A. Y., Frank, N. & Bauer, G. Spiral growth and threading
dislocations for molecular beam epitaxy of PbTe on BaF2 (111) studied by scanning
tunneling microscopy. Appl. Phys. Lett. 69, 2822-2824 (1996).
2. McCann, P. J., Fuchs, J., Feit, Z. & Fonstad, C. G. Phase equilibria and liquid-phaseepitaxy
growth of PbSnSeTe lattice-matched to PbSe. J. Appl. Phys. 62, 2994-3000
(1987).
3. Ueta, A. Y., Springholz, G., Schinagl, F., Marschner, G. & Bauer, G. Doping studies for
molecular beam epitaxy of PbTe and Pb1-xEuxTe. Thin Solid Films 306, 320-325 (1997).
4. Shirley, D. A. High-resolution x-ray photoemission spectrum of the valence bands of
gold. Phys. Rev. B 5, 4709 (1972).
5. Wojek, B. et al. Spin-polarized (001) surface states of the topological crystalline insulator
Pb0.73Sn0.27Se. Phys. Rev. B 87, 115106 (2013).
6. Xu, S.-Y. et al. Unconventional transformation of spin Dirac phase across a topological
quantum phase transition. Nature Commun. 6, 6870 (2015).
7. Yeh, J. J. & Lindau, I. Atomic subshell photoionization cross sections and asymmetry
parameters: 1≤ Z ≤ 103, in Atomic Data and Nuclear Data Tables, 32, 1-155 (1985).
Reprinted supplement page 18 of paper [61] “Topological transition from TCI to TI via Bi doping”.
CHAPTER 4. REPRINTED PAPERS 210
4.9 Giant Rashba effect in (Pb,Sn)Te
The topological properties of lead-tin chalcogenide topological crystalline insulators can be
tuned by temperature and composition. We have shown that bulk Bi doping of epitaxial
(Pb,Sn)Te (111) films induce a giant Rashba splitting at the surface that the doping level can
tune. Tight binding calculations identify their origin as Fermi-level pinning by trap states at
the surface.
Communication
© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com (1 of 9)  1604185
Giant Rashba Splitting in Pb1–xSnxTe (111) Topological
Crystalline Insulator Films Controlled by Bi Doping
in the Bulk
Valentine V. Volobuev,* Partha S. Mandal, Marta Galicka, Ondrˇej Caha,
Jaime Sánchez-Barriga, Domenico Di Sante, Andrei Varykhalov, Amir Khiar,
Silvia Picozzi, Günther Bauer, Perla Kacman, Ryszard Buczko, Oliver Rader,
and Gunther Springholz*
Dr. V. V. Volobuev, Dr. A. Khiar, Prof. G. Bauer,
Prof. G. Springholz
Institute for Semiconductor and Solid State Physics
Johannes Kepler Universität
Altenberger Str. 69, 4040 Linz, Austria
E-mail: valentyn.volobuiev@jku.at;
gunther.springholz@jku.at
Dr. V. V. Volobuev
National Technical University “Kharkiv Polytechnic Institute”
Frunze Str. 21, 61002 Kharkiv, Ukraine
P. S. Mandal, Dr. J. Sánchez-Barriga, Dr. A. Varykhalov, Prof. O. Rader
Helmholtz-Zentrum Berlin für Materialien und Energie
Albert-Einstein Str. 15, 12489 Berlin, Germany
Dr. M. Galicka, Prof. P. Kacman, Prof. R. Buczko
Institute of Physics
Polish Academy of Sciences
Aleja Lotników 32/46, PL-02-668 Warszawa, Poland
Dr. O. Caha
Department of Condensed Matter Physics
Masaryk University
Kotlárˇská 2, 61137 Brno, Czech Republic
Dr. D. Di Sante, Dr. S. Picozzi
Consiglio Nazionale delle Ricerche CNR-SPIN
Via dei Vestini 31, 66100 Chieti, Italy
Dr. D. Di Sante
Institut für Physik und Astrophysik
Universität Würzburg
Am Hubland Campus Süd, Würzburg 97074, Germany
DOI: 10.1002/adma.201604185
to external perturbations.[10,15,16]
Therefore, the trivial to nontrivial
topological phase transition can be controlled by many
different means, such as by varying temperature,[1,6]
pressure,[2]
hybridization in ultrathin film geometries,[17–19] magnetic
interactions,[20]
or by breaking of mirror symmetries by
strain,[16,21–23]
electrostatic fields,[18]
or ferroelectric (FE) lattice
distortions.[24,25] This provides ample degrees of freedom for
topology control not available in conventional Z2 TIs. For this
reason, TCIs offer an ideal template for observation of exotic
phenomena such as partially flat band helical snake states and
interfacial superconductivity,[16] large-Chern-number quantum
anomalous Hall effect,[26] as well as for realization of novel
topology-based devices such as topological photodetectors,[23]
spin transistors,[18]
and spin torque devices.[27]
For most of such applications, thin film structures with
precisely controlled composition and Fermi level are required.
Up to now, most work has been performed on highly p-type
bulk crystals exploiting the natural (001) cleavage plane of
the IV–VI compounds,[3,4,6] whereas for other surface orientations
and practical devices epitaxial TCI film structures are
required.[18,28–32]
The (111) orientation is particularly interesting
due to the polar nature of its surface[12] as well as the
ease of lifting the fourfold valley degeneracy at the L-points
of the Brillouin zone (BZ)[33] by opening a gap at particular
Dirac points by strain[16]
and quantum confinement[17–19]
to
induce a transition from a TCI to a normal Z2-TI material.[25]
Epitaxial growth strongly relies on lattice and thermal expansion
matching between films and substrate material. Good
results have been obtained, e.g., for PbSnTe on Bi2Te3 buffer
layers,[31,34] but transport and photoemission investigations
are offset by the intrinsic topological character of Bi2Te3,[31,35]
as well as by PbSnTe/Bi2Te3 interdiffusion and intermixing.
Most challenging, however, is the intrinsic p-type character of
PbSnTe caused by the natural tendency of cation vacancy formation,
creating resonant acceptor levels in the valence band
(VB).[9] This tendency strongly increases with increasing Sn
content and thus, SnTe always exhibits very high bulk hole
concentrations of around 1020 cm−3. This not only masks the
topological surface state in transport and optical investigations
but also impedes observing the Dirac point by angle-resolved
photoemission (ARPES).
In the present work, we employ molecular beam epitaxy
(MBE) to grow high-quality Pb1-xSnxTe films in which
A novel class of topological insulators (TIs), called topological
crystalline insulators (TCIs), has been recently predicted[1,2]
and experimentally demonstrated for SnTe,[2,3]
Pb1-xSnxTe,[4,5]
and Pb1-xSnxSe.[6] In these IV–VI materials, an inversion of the
L6+ and L6– valence and conduction bands (CBs) occurs above
a certain critical Sn content (see Figure 1a).[7–9]
This induces
a trivial to nontrivial topological phase transition that, due to
the bulk-surface connectivity, gives rise to the formation of a
2D topological surface state (TSS) with linear dispersion of a
Dirac cone and helical spin texture due to spin-momentum
locking.[1,2,6,10–12] In TCIs, these TSSs are protected by crystal
mirror symmetries[1,2] rather than by time-reversal symmetry
as in conventional Z2 topological insulators.[13,14]
Thus, these
surface states are formed on particular surfaces such as (001),
(111), and (110), where the crystalline mirror symmetries are
preserved.[1,2,12] Moreover, the band inversion is highly sensitive
Adv. Mater. 2017, 29, 1604185
www.advancedsciencenews.com www.advmat.de
Reprinted page 1 of paper [88] “Rashba splitting in (Pb,Sn)Te controlled by Bi doping”.
Communication
© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheimwileyonlinelibrary.com1604185  (2 of 9)
“extrinsic” n-type doping is employed for compensation and
control of carrier concentration. We show that Bi doping allows
us to tune the Fermi level over a wide range from the valence to
the conduction band and thus to observe the trivial to nontrivial
topological phase transition under temperature and composition
variation. By careful tuning of the doping level and growth
conditions, low free carrier concentrations of about 1018 cm−3
and carrier mobilities as high as 104 cm2 V−1 s−1 are achieved,
providing excellent conditions for quantum transport and
optical studies of nontrivial topology effects.[32] Most strikingly,
we find that Bi doping induces a very large Rashba splitting
of the valence band that is absent for undoped material and
reaches values as high as 0.022 Å−1. This yields a giant Rashba
coupling constant of 3.8 eV Å−1 that is comparable to the record
values recently reported for the BiTe–halide compounds.[36–38]
By tight binding (TB) calculations we reveal that this Rashba
splitting is caused by pinning of the Fermi level by acceptorlike
trap states at the surface. The important outcome is that
the Rashba effect can be tailored and tuned by bulk Bi doping.
The coexistence and hybridization of TSS and Rashba-split surface
states is unexpected due to the inversion symmetry of the
rock salt structure and paves the way for novel topological spin–
orbitronic devices.[39]
Epitaxial growth of Pb1-xSnxTe was performed by molecular
beam epitaxy on BaF2 (111) substrates using stoichiometric
PbTe and SnTe beam flux sources.[40,41] The chemical composition
of the layers was varied over a wide range from xSn = 0 to 1
by control of the SnTe/PbTe beam flux ratio, which was measured
precisely using the quartz crystal microbalance method.[40]
n-type doping was realized using a Bi2Te3 compound source to
promote substitutional incorporation of bismuth into cation lattice
sites,[42] where Bi acts as a donor because of its additional
Adv. Mater. 2017, 29, 1604185
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Figure 1.  Basic properties of Pb1–xSnxTe (111) films. a) Band gap in dependence of Sn content xSn at T = 300, 150, and 4 K (solid/dashed lines) according
to refs. [7] and [8]. Symbols: ARPES data for room temperature (), 200 K (), 150 K (), and 100 K (). The band inversion and trivial to nontrivial
topological phase transition occur at xSn = 0.36 and = 0.6 for 4 and 300 K, respectively. b,c) RHEED patterns and AFM image of a Pb0.4xSn0.6Te film
grown by MBE on BaF2 (111) substates. d) The extracted surface profile shows only single monolayer steps with a height of 3.7 Å. e–g) X-ray diffraction
reciprocal space maps around the (513) Bragg reflection for three epilayers with xSn = 0, 0.46, and 1. As indicated, the layer peaks lie exactly on the line
connecting the peak positions of bulk PbTe (◊) and SnTe (), evidencing that all films are fully relaxed without residual lattice distortion. The expected
peak positions of fully strained epilayers are indicated by (Δ, ).
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valence electron compared to Pb or Sn.[42,43] The solubility of
Bi2Te3 in SnTe and PbTe amounts to several percent according
to the quasi binary phase diagrams.[44]
For compensation of the
native p-type carrier concentration, however, only small Bi concentrations
well below 1% and Bi flux rates of 10−4
– 10−3
monolayer
(ML) per second are required, compared to overall film
growth rates of 1 ML s−1
(= 3.7 Å s−1
).
2D growth of Pb1-xSnxTe (111) films is observed for all compositions
beyond a thickness of 100 nm as demonstrated by
the reflection high-energy electron diffraction (RHEED) patterns
and atomic force microscopy (AFM) image depicted in
Figure 1b,c for xSn = 0.4. The high film quality is evidenced
by sharp diffraction spots arranged on the Laue circle and the
intense Kikuchi lines arising from scattering at subsurface lattice
planes. No surface reconstruction is observed. The surface is
atomically flat exhibiting about 200 nm wide terraces separated
by single monolayer steps of 3.7 Å height (cf. Figure 1d). At the
given substrate temperature of 350 °C, growth proceeds in a
step-flow mode with the surface steps pinned by threading dislocations
as described in detail in refs. [45] and [46]. Structural
characterization by high-resolution X-ray reciprocal space mapping
(see Figure 1e–g) demonstrates that the layers with 1–2 µm
thickness are fully relaxed. Accordingly, their Bragg peaks lie
exactly along the line connecting the bulk PbTe (aPbTe = 6.462 Å)
and SnTe (aSnTe = 6.323 Å) reciprocal lattice points, as indicated
by the dashed and solid lines, respectively. Thus, the epilayers
are undistorted with equal in- and out-of-plane lattice constants.
Systematic evaluation of the lattice parameter as a function of
composition shows that it precisely follows Vegard’s law.[47]
In
particular, for all samples the Sn content derived by X-ray diffraction
perfectly agrees with the nominal growth values. Moreover,
no traces of any secondary phases were detected.
The Bi doping action and transport properties were evaluated
by Hall effect measurements, as summarized in
Figure 2. Undoped PbTe layers are n-type in the low 1017
cm−3
range under stoichiometric MBE growth conditions.[40,42]
On the
contrary, the carrier type of Pb1-xSnxTe switches from n to p-type
at xsn > 15% and thereafter the hole concentration rises exponentially
with increasing Sn content, reaching hole densities as
high as 2 × 1020
cm−3
for pure SnTe (see Figure 2a). This demonstrates
an exceedingly low cation vacancy formation energy EV of
SnTe compared to PbTe.[48]
For undoped Pb1-xSnxTe TCI films
requiring xSn larger than 40%, the Fermi level is therefore always
deep in the valence band.[3–5,33]
We model the dependence of the
cation vacancy formation energy on composition using EV(xSn)
= EV,SnTe + ΔEV (1 – xSn), where ΔEV is the vacancy energy difference
between PbTe and SnTe. Assuming an Arrhenius-like
behavior for the equilibrium vacancy concentration, the native
free carrier concentration in Pb1-xSnxTe is predicted as
n x n n e E x kT
n,p Sn n,PbTe p,SnTe
1 /V Sn
( )= − + ( )−∆ −

(1)
where nn,PbTe and np,SnTe are the intrinsic carrier concentrations
of the parent binary materials for the given growth conditions.
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1E17
1E18
1E19
1E20
1E17 1E18 1E19 1E20
1E19
1E18
0 20 40 60 80 100
1E16
1E17
1E18
1E19
1E20
γ = 0.3
n0 = 1017
cm-3
300K
Carrier
concentration
PbTe:Bi
nHall(cm-3
)
n-type
γ = 1
xSn=46%
γ = 1 0.5 0.3
PbSnTe:Bi
p-typep0 = 1019
cm-3
γ = 1
PbSnTe:Bi
Bi Concentration nBi (cm-3
)
pHall(cm-3
)
1E-4 1E-3 0.01 0.1 1
(b)
Bi concentration nBi (%)
xSn=46%
Sn content xSn (%)
Pb1-xSnxTe
undoped
n-type
p-type
nHall(cm-3
)
(a)
1E18 1E19 1E20
0.2
0.4
0.6
0.8
1.0
1.2
(p)
(n)
γ = 1
PbTe:Bi (n)
PbSnTe:Bi
(c)
Dopingefficiency
Bi Concentration nBi (cm-3
)
Figure 2.  Effect of Bi doping of TCI films. a) Intrinsic carrier concentration of undoped Pb1-xSnxTe epilayers as a function of Sn content, revealing the
high p-type character with increasing Sn content due to Sn vacancy formation. The solid line represents the fit of the experimental data assuming that
the formation energy of vacancies decreases linearly with xSn. b) Hall concentrations nHall obtained for PbTe:Bi () and Pb0.54Sn46Te:Bi (: p-type; :
n-type) as a function of Bi-dopant concentration. Solid lines: Expected nHall for different doping efficencies γ = 1 for PbTe (black line) and γ = 1, 0.5, and
0.3 for PbSnTe as indicated, based on the background carrier concentration measured for the undoped reference layers. c) Bi doping efficiency derived
for PbTe () and Pb0.54Sn46Te (: p-type; : n-type) versus Bi concentration.
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As demonstrated by the solid line in Figure 2a, this model perfectly
describes our experimental findings and from the fit of
our data, a difference in the cation vacancy formation energy
between PbTe and SnTe of ΔEv = 360 meV is derived.
Effective control of the carrier type and tuning of the carrier
concentration by Bi doping is demonstrated in Figure 2b, where
the Hall concentrations of Bi-doped PbTe () and Pb0.54Sn0.46Te
(,) epilayers are plotted versus Bi concentration. For PbTe,
the electron concentration rises perfectly linearly with Bi
dopant concentration (solid line), evidencing a single ionized
donor state and a unity doping efficiency γ = (n − n0)/nBi for
Bi concentrations as high as 1020
cm−3
. This provides a precise
calibration of the Bi flux for growth. For Pb0.54Sn0.46Te,
Bi doping partially compensates the native hole concentration
until for nBi > 2 × 1019
cm−3
the material switches from p to
n-type with electron concentrations up to the mid-1019
cm−3
range (cf. Figure 2b). Thus, the carrier density can be tuned
over a wide range. By precise control of the Bi flux, low carrier
densities within the 1017
cm−3
range can be obtained, resulting
in Hall mobilities as high as μH = 13 000 cm2 V−1 s−1 at 77 K,
comparable to or even exceeding the highest values reported for
long-term annealed bulk PbSnTe single crystals with similar Sn
content.[49] Inspection of Figure 2b reveals, however, that for
highly doped Pb0.54Sn0.46Te films the actual electron concentration
is significantly below the expected values for γ = 1 (dashed
line) and that the maximum electron concentration saturates in
the mid-1019 cm−3 range even at high Bi concentrations. This
means that the doping efficiency decreases with increasing Sn
content to γ < 0.4 for xSn = 46% (Figure 2c), whereas for pure
PbTe it is unity for all investigated Bi concentrations. This suggests
that Bi develops an amphoteric character in the ternary
materials and starts to occupy Te lattice sites as well, on which it
acts like an acceptor. Thus, compensation of the native hole concentration
becomes increasingly difficult at higher Sn contents.
The effect of Bi doping on the topological surface state and
population of the electronic bands was studied in detail by
ARPES as a function of temperature and composition in the
17–90 eV photon energy range. As shown by Figure 3, for n-doped
Pb0.54Sn0.46Te:Bi films both conduction and valence bands are
clearly visible in ARPES, whereas for undoped films only the
lower branch of the valence band is seen because the Fermi level
is well below the VB edge (see Figure 4a). For a Bi doping of nBi =
4 × 1019 cm−3 (= 0.3% Bi), the Fermi level EF at room temperature
is already by +100 meV above the CB edge and lowering the
temperature induces a further upward shift to +160 meV at 110 K
(cf. Figure 3a–c). At this temperature a well-resolved 2D TSS with
linear dispersion appears, indicating the transition from the trivial
to the nontrivial TCI state. Also, an increase in the Fermi velocity,
i.e., slope of the E(k) dispersion, occurs due to the decrease of the
effective masses accompanying the closing of the gap.[8,9] This in
turn leads to a decrease in the electronic density of states, which
means that at lower temperatures the Fermi energy must shift
upward to accommodate the nearly constant carrier concentration
found by the Hall effect measurements.
The 2D nature of the observed surface state was verified
by photon-energy-dependent ARPES investigations shown in
Figure 3e–h. In spite of different admixtures of dispersive bulk
and nondispersive surface signals at different photon energies,
the absence of any photon energy dispersion corroborates that
the observed bands are indeed surface states with 2D character.
For the n-doped Pb0.54Sn0.46Te films, linear extrapolation of the
TSS from the CB yields a Dirac point position at 10–20 meV
below the VB maximum at 110 K. This is revealed clearly by
Figure 3j,k, where the ARPES intensity is depicted on a logarithmic
scale. Also shown for comparison are the ARPES data
of a film with xSn = 26%, in which the gap remains fully open
with Eg ≈ 120 meV even at low temperatures, i.e., for low Sn
contents Pb1-xSnxTe remains topologically trivial. Thus, the
trivial to nontrivial topological phase transition is demonstrated
for (111) epitaxial films both as a function of temperature and
Sn content. It is noted that the topological phase transition was
previously suggested to occur already at xsn ≈ 0.25 for cleaved
(001) bulk Pb1-xSnxTe crystals.[5]
However, this conclusion
was based only on extrapolation of the dispersion of the VB
of highly p-type material without directly observing the Dirac
point and conduction band.
Remarkably, all n-doped films show a very large Rashba
splitting of the valence band in the kII direction. To map out
its correlation with the doping level, ARPES was performed for
a series of Pb0.54Sn0.46Te layers with systematically increasing
doping level. The results are presented in Figure 4 for Bi concentrations
varying from 0% to 1%. Whereas for the undoped
film the Fermi level is deep inside the VB, it strongly moves
upward with increasing Bi content so that for nBi > 0.2% the
full VB dispersion and CB appear. In fact, a total shift of EF
by as much as +280 meV is achieved by 1% Bi doping, evidencing
the effective control of the Fermi level. Most importantly,
we find that the Rashba splitting systematically increases
with the Bi concentration. Thus, the Rashba effect is induced
by the “bulk doping” of the material, which is in complete
contrast to the Rashba effect in Z2-TIs such as Bi2Se3, which
is usually induced by alkaline[50,51]
or transition metal deposi-
tion[52]
or adsorption of water on the surface,[53,54]
but not upon
bulk doping.[52,55–58] Moreover, it is to be noted that in these
Z2-TIs the Rashba bands are completely separated in energy
from the TSS, whereas in our TCI case the Dirac and Kramers
point overlap (see Figure 3j). This suggests that a hybridization
between the TSS and the Rashba bands may occur.
For quantitative evaluation, the Rashba bands were modeled
using the effective mass approximation where the energy–
momentum dispersion is given by
/2 * ˆ ˆ /2 *2 2
R
2 2
RE k k m k z k m kα σ α( )( ) = + × = ±±

(2)
where m* is the effective carrier mass in the kII direction, σ
is the Pauli spin matrix, and αR is the Rashba constant due
to spin–orbit coupling and structural asymmetry at the surface.
The Rashba effect causes the formation of two separate
spin-polarized bands k+ and k– that are split by 2ΔkR in the kII
direction, as indicated schematically by the dashed lines in
Figure 4d. This leads to a nested band structure with helical
spin texture, forming concentric rings in the kxy plane as corroborated
by the constant energy ARPES maps depicted in
Figure 4e–h. This is a key hallmark of the Rashba effect. From
the data, we derive the momentum splitting ΔkR and Rashba
energy ER (= energy difference between the band maxima and
the Kramers point) for each sample, which yields the Rashba
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coupling constant αR = 2ER/ΔkR as a function of the doping
level. The results are summarized in Table 1, demonstrating a
clear correlation between the Rashba parameters and Bi concentration.
In particular, the Rashba constant assumes exceedingly
large values of αR = 3.8 eV Å−1 for 1% Bi doping, which is
comparable to the recently reported record values of the giant
Rashba systems such as BiTeX (X = I, Br, and Cl) and α-GeTe
where αR is of the order of 2–4 eV Å−1.[36–38,59–62]
The giant Rashba splitting is unexpected for materials possessing
inversion symmetry as applies for the IV–VI compounds
with cubic rock salt crystal structure. As recently suggested, FE
lattice distortions can lead to a giant bulk Rashba splitting[59]
in α-GeTe[61,62] and SnTe.[25] In our Pb1–xSnxTe films, however,
we do not observe such distortions by X-ray diffraction down
to 80 K, and even pure SnTe becomes ferroelectric only at low
temperatures. Moreover, we do not observe any abrupt change
of the Rashba effect with temperature (cf. Figure 3) as would
be expected to occur at such an FE phase transition. Thus, we
rule out bulk inversion symmetry breaking and the Dresselhaus
mechanism as an origin for the observed Rashba effect.
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Figure 3.  Topological phase transition characterized by ARPES. a–d) Temperature-dependent E(k) maps of a Pb0.54Sn0.46Te (111) epilayer with 0.25%
Bi measured around Γ of the surface BZ using a photon energy of 18 eV. The topological transition occurs at about 110 K. Below 80 K photoemission
becomes unstable due to photoninduced adsorption of residual gases and charging of the surface.[11] e–h) Photon energy dependence measured at
110 K. i–k) ARPES spectra of Pb1–xSnxTe epilayers with low (xSn = 26%) and high (46%) Sn content, demonstrating the trivial to nontrivial phase transition
as a function of composition with an open gap for the former and with a closed gap for the latter at 110 K. The intensity is shown on a logarithmic
scale to reveal the TSS in the CB.
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Instead, we invoke a symmetry breaking at the surface. In fact,
the mere existence of the surface can produce spin-polarized
surface states, as has been shown in the case of Pb0.73Sn0.27Se in
the normal insulator phase.[47] A surface band bending can tune
these states to the band gap region, and/or produce new states
localized at the surface and enhance the spin splitting. The pertaining
Rashba effect will be thus confined to the surface, in
agreement with the observed 2D nature of the Rashba bands
revealed by the photon-energy dependence of Figure 3. We suggest
that the surface band bending for PbSnTe (111) is caused
by a pinning of the Fermi level by localized trap states at the
surface due to dangling bonds. This results in the presence
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Table 1. Rashba parameters of Pb0.54Sn0.46Te (111) as a function of Bi
concentration nBi measured by ARPES at 110 K (Figure 4), including
Fermi energy EF (relative to the top of the valence band), Rashba energy
ER, momentum splitting kR, and Rashba coupling constant αR = 2ER/kR
of the Rashba bands.
nBi
[%]
EF
[meV]
ER
[meV]
kR
[Å−1]
αR
[eV Å−1]
0 −80 – – –
0.3 +140 13 0.011 2.4
0.7 +170 30 0.017 3.5
0.9 +190 38 0.022 3.8
Figure 4.  Effect of bulk Bi doping on the Rashba effect. a–d) ARPES spectra of Pb0.54Sn0.46Te (111) with bulk Bi concentrations varying nBi = 0 to 1%, demonstrating
effective tuning of the Fermi level and the strong increase of the Rashba splitting with Bi concentration. The ARPES maps were recorded around
the Γ-point at 100 K with a photon energy of 18 eV. The derivation of the Rashba constants αR from the measured ΔkR and ER is shown schematically in (d)
andtheresultsarelistedinTable1.e–h)Constant-energycontoursatdifferentbindingenergiesforthesamplewithnBi =0.7%showingtheconcentricrings
of the Rashba bands and increasing hexagonal warping at lower energy. i) Core-level spectra excited with hν = 90 eV showing the Bi 4d3/2 peak for increasing
dopinglevel.TheupperinsetillustratesthesurfacebandbendinginducedbylocalizedelectrontrapsNT
−
atthesurfacethatbecomepopulatedwithincreasing
bulk doping, whereas without Bi doping (lower inset) the traps are not occupied and no band bending occurs. j–l) Tight binding supercell calculation of the
Rashba effect in Pb0.54Sn0.46Te (111) induced by j) an upward or k,l) a downward band bending toward the surface due to a negative and a positive surface
potential V0, respectively. The screening length was set to λ = 25Å and T = 200 K. The Rashba constants derived from calculations kR, (), ER (), and
αR = 2ER/kR () are plotted in (m) as a function of surface potential.
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of a fixed surface charge σS that induces a depletion layer
below the surface. For degenerately doped semiconductors
this is described by the Thomas Fermi screening model with a
screening potential of
V z V zexp( / )0 λ( ) = −

(3)
where V0 is the potential at the surface at z = 0 and
e m n/ (3 )2/3
0 s
2 * 1/3
λ π ε ε= is the Thomas Fermi screening
length,[63] which is of the order of few nanometers for highly
doped semiconductors. The surface potential V0 is related to the
surface charge by V0 = −σSλ/ε0εs through the Poisson’s equation
and the overall charge neutrality condition. For acceptorlike
trap states, the trapped surface charge σS is negative so that
the bands bend upward at the surface and V0 assumes a positive
value. Likewise, for donor-like surface states σS is positive,
inducing a downward band bending corresponding to negative
V0 values.
The influence of the surface band bending on the surface
spectral density of states was evaluated by tight binding calculations
in which different surface potentials according to
Equation (3) were superimposed on the atomic potentials
of Pb0.54Sn0.46Te obtained in refs. [6] and [12]. We assume an
anion (Te) termination of the (111) surface as density functional
theory (DFT) calculations[48]
suggest that this surface
exhibits a lower surface energy than the cation termination.
The results are presented in Figure 4 for λ = 2.5 and V0 varying
from −0.5, +0.3, and +0.1 eV from (j) to (l), respectively,
where the solid lines correspond to the 2D surface states and
the shaded regions to the bulk bands. Evidently, surface band
bending induces a strong Rashba splitting in either the CB
or VB depending on the “sign” of V0. Positive V0 (i.e., upward
band bending) leads to a Rashba splitting in the VB due to the
confinement of the hole wave functions near the surface. Conversely,
for negative V0 the Rashba-split states appear in the CB.
Comparison with our experiments reveals that only the upward
band bending, i.e., V0 > 0, is consistent with the ARPES data,
which demonstrates the presence of a negative surface charge
σS on the anion-terminated surface.
From our TB calculations, we derive the dependence of
Rashba parameters as a function of surface potential as presented
in Figure 4m. Evidently, the momentum splitting ΔkR
and Rashba constant scale linearly, and ER quadratically with the
surface potential V0, i.e., with increasing electric field strength
E ≈ dV/dz at the surface. Comparison with the experimental
values indicates a surface potential V0 of around +0.1 to +0.3 eV
for our samples, which for the given screening length and dielectric
constant yields a surface charge of the order of 1/10 electron
per surface atom. However, the observed increase of the
Rashba splitting with increasing Bi doping dictates that this
surface charge is not constant but varies with the bulk Fermi
level. Thus, it cannot be simply due to the polar nature of the
(111) surface as previously suggested,[64] but rather by localized
surface trap states that are successively filled by electrons
as the bulk Fermi level increases. For p-doped samples these
trap states are unoccupied, corresponding to a flat band condition
(cf. inset of Figure 4i) without a Rashba effect—as seen in
our experiments. Comparing calculated and measured Rashba
parameters, we find a good agreement for V0 = +0.2 eV, where
αR is of the order of 3 eV Å−1 in both theory and experiment.
The upward surface band bending also nicely explains the weak
intensity of the CB band states in the ARPES measurements
because it pushes the CB wave functions into the bulk away
from the surface for which reason their spectral weight at the
surface is strongly reduced. Also note that for a given αR value,
ΔkR and ER of the TB calculations are somewhat smaller than
the experimental values. Since both are proportional to the inplane
effective mass m*, this is attributed to the fact that m* is
underestimated by a factor of 1.8 in the TB binding calculations
as compared to the experiments. The effect of temperature
and screening length variation is discussed in the Supporting
Information.
To show that the Rashba effect is neither due to Bi accumulation
at the surface nor due to specific properties of the Bi, additional
experiments were performed. This is because it is well
known that Bi on metal surfaces such as Ag(111) can induce a
large Rashba splitting due to its large spin–orbit coupling.[65,66]
To
rule out such an effect, we have deposited 0.5–1 monolayer of Bi
on top of undoped Pb0.54Sn0.46Te (111) at a temperature of 200 K.
The resulting ARPES data, shown in Supporting Information,
Figure S1,[67]
reveal that this does not cause any Rashba splitting
of the PbSnTe bands, i.e., simple Bi accumulation on the surface
by surface segregation cannot explain the observed Rashba effect.
This is further underlined by the core level spectra of our films in
Figure 4i that reveal that the surface concentration of Bi is very
small in all samples, i.e., that no Bi accumulation actually occurs.
To further demonstrate that the Rashba effect also does not rely
on any specific property of the Bi dopant, we have prepared
Pb0.54Sn0.46Te films where Bi was replaced by Sb as group V n-type
dopant. As shown in Supporting Information, Figure S1,[67] for
such films a similar giant Rashba effect is observed. In fact, for a
nominal Sb concentration of 3% we obtain an even larger Rashba
splitting of ΔkR = 0.036 Å−1
and ER = 56 meV as compared to the
1% Bi-doped sample. This clearly corroborates that the Rashba
effect is solely controlled by the bulk Fermi level and thus it will
occur for any other n-type dopant in this system.
In summary, we have shown that Bi and Sb-doped topological
crystalline insulator Pb1-xSnxTe (111) films represent a
giant Rashba system that features Rashba coupling constant as
high as the record values reported in the literature. Contrary to
most other systems, the strength of the Rashba effect is effectively
controlled by the bulk doping. Our detailed analysis using
tight binding calculations reveals that it originates from a large
upward band bending at the surface due to electron surface traps
whose occupancy is controlled by the bulk Fermi level. Since the
Fermi level can also be tuned by electrostatic gates, this opens
up a pathway for spintronic field effect device applications.
Doping also allows compensating the intrinsic p-type character
of TCI materials, resulting in high carrier mobilities that enable
optical and topological quantum transport investigations otherwise
screened by the bulk contribution. The magnitude of spin
splitting is already sufficient for room temperature operation
of spin-galvanic spintronic devices,[39,68–70] but beyond that the
observed trend implies that the spin splitting can be even further
enhanced by increased Bi or Sb doping levels. Thus, our findings
open up new avenues for exploring exotic electrical and optical
phenomena in topological systems, as well as novel spintronic
devices driven by the Rashba effect.
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Methods
Sample Preparation: Bi-doped Pb1-xSnxTe thin films were grown
in a Varian Gen II MBE system on cleaved (111) BaF2 substrates
at 350 °C at a pressure below 10−9 mbar. The film growth was
in situ monitored by RHEED. PbTe, SnTe, and Bi2Te3 were
evaporated from compound effusion cells. In some cases, a
Pb0.44Sn0.56Te stoichiometric source was used. The PbTe/SnTe/
Bi ratio was controlled and calibrated by a quartz crystal microbalance
moved into the substrate position. The thickness of the
films was in the range of 1—2 µm.
Sample Characterization: The surface of grown films was
examined by AFM in contact mode. X-ray diffraction measurements
and reciprocal space maps were performed using
a double crystal Seifert 3003 diffractometer equipped with a
channel cut Ge (200) monochromator. The composition was
determined using the Vegard’s law as well as energy dispersive
X-ray microanalysis and photoelectron spectroscopy.
Transport Characterization: Hall measurements were carried
out in Van der Pauw geometry with external magnetic fields
up to 0.9 Tesla. Measurements were performed and room and
liquid nitrogen temperature. Selected samples were also measured
in high magnetic fields up to 7 T at 1.7 K. The obtained
high field and low field carrier concentrations are consistent
with each other within 20%.
ARPES Measurements: Angle-resolved photoemission was
measured at UE112_PGM-2a-1^
2 beamline at the Bessy II synchrotron
(Berlin, Germany) with photon energies ranging from
15 to 90 eV and horizontally polarized light using a six-axes
automated cryo-manipulator and a Scienta R8000 hemispherical
analyzer with typical energy resolution better than 5 meV.
For these investigations, the as-grown samples were transferred
from the MBE to the synchrotron using a battery-operated ion
getter pumped UHV suitcase (Ferrovac VSN40S) sustaining a
base pressure better than 2 × 10−10
mbar. The ARPES experiments
were carried out at pressures below 2 × 10−10 mbar.
Theoretical Calculations: The surface spectral density of states
in the studied Pb0.54Sn0.46Te films was obtained using the tightbinding
approach within the virtual crystal approximation. The
parameters for the constituent compounds, PbTe and SnTe,
were taken from ref. [71], where they were obtained within a
nearest-neighbor 18-orbital sp3
d5
model with spin–orbit interactions
included. To obtain a correct dependence of the band
gap with temperature, an appropriate scaling of the hopping
integrals with temperature had, however, to be found. The Bi
incorporation was simulated by applying a surface potential
described by Equation (3) within the Thomas Fermi screening
model. The surface spectral functions were calculated using
recursive Green’s function method described in ref. [72].
Supporting Information
Supporting Information is available from the Wiley Online Library or
from the author.
Acknowledgements
The authors acknowledge Helmholtz-Zentrum Berlin for provision of
synchrotron radiation beam time at the UE112-PGM-2a beamline of
BESSY II, and thank Prof. E. I. Rogacheva, National Technical University
“KhPI” Kharkiv, Ukraine, and Dr. A. Szczerbakow, Institute of Physics
of the Polish Academy of Sciences in Warszawa for providing the MBE
source material. Tight binding calculations were partially carried out
in the Academic Computer Center in Gdansk, Poland. This work was
supported by the Austrian Science Funds (Grant SFB 025-IRON), the
EU CALIPSO Program (Grant No. 312284), the Polish National Science
Center (Grant Nos. 2013/11/B/ST3/03934 and 2014/15/B/ST3/03833),
the Deutsche Forschingsgemeinschaft (Grant No. SPP 1666) and the
Impuls-und Vernetzungsfonds der Helmholtz-Gemeinschaft (Grant No.
HRJRG-408).
Note: The author list and article number in ref. 56 were corrected on
January 12, 2017, after initial publication online.
Received: August 4, 2016
Revised: September 29, 2016
Published online: November 17, 2016
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Reprinted page 9 of paper [88] “Rashba splitting in (Pb,Sn)Te controlled by Bi doping”.
Copyright WILEY-VCH Verlag GmbH & Co. KGaA, 69469 Weinheim, Germany, 2016.
Supporting Information
for Adv. Mater., DOI: 10.1002/adma.201604185
Giant Rashba Splitting in Pb1–xSnxTe (111) Topological
Crystalline Insulator Films Controlled by Bi Doping in the
Bulk
Valentine V. Volobuev,* Partha S. Mandal, Marta Galicka,
Ondřej Caha, Jaime Sánchez-Barriga, Domenico Di Sante,
Andrei Varykhalov, Amir Khiar, Silvia Picozzi, Günther
Bauer, Perla Kacman, Ryszard Buczko, Oliver Rader, and
Gunther Springholz*
Reprinted supplement page 1 of paper [88] “Rashba splitting in (Pb,Sn)Te controlled by Bi doping”.
1
Copyright WILEY-VCH Verlag GmbH & Co. KGaA, 69469 Weinheim, Germany, 2013.
Giant Rashba Splitting in Pb1-xSnxTe (111) Topological Crystalline Insulator
Films Controlled by Bi-Doping in the Bulk
V. V. Volobuev1,2
*, P.S. Mandal3
, M. Galicka5
, O. Caha4
, J. Sanchez-Barriga3
, D. Di Sante6,7
,
A. Varykhalov3
, A. Khiar1
, S. Picozzi6
, G. Bauer1
, P. Kacman5
, R. Buczko5
, O. Rader3
, and G. Springholz1
*
1
Dr. V. V. Volobuev, Dr. A. Khiar, Prof. G. Bauer, Prof. G. Springholz, Institute for Semiconductor
Physics, Johannes Kepler University, Altenberger Str. 69, 4040 Linz, Austria
2
Dr. V. V. Volobuev, National Technical University "Kharkiv Polytechnic Institute", Frunze Str.
21, 61002 Kharkiv, Ukraine
3
P.S. Mandal, Dr. J. Sanchez-Barriga, Dr. A. Varykhalov, Prof. O. Rader, Helmholtz-Zentrum Berlin,
Elektronenspeichering BESSY II, Albert-Einstein Str. 15, 12489 Berlin, Germany
4
Dr. O. Caha, Masaryk University, Kotlářská 2, 61137 Brno, Czech Republic
5
Dr. M. Galicka, Prof. P. Kacman, Prof. R. Buczko, Institute of Physics, Polish Academy of Sciences,
Aleja Lotników 32/46, PL-02-668 Warszawa, Poland
6
Dr. D. Di Sante, Dr. S. Picozzi, Consiglio Nazionale delle Ricerche CNR-SPIN, Via dei Vestini 31,
66100 Chieti, Italy
7
Dr. D. Di Sante, Institut für Physik und Astrophysik, Universität Würzburg, Am Hubland Campus Süd,
Würzburg 97074, Germany
*) e-mail: valentyn.volobuiev@jku.at, gunther.springholz@jku.at
Synopsis: This supplemental information provides (i) results on additional investigations on
the effect on the surface electronic band structure caused by bulk Sb-doping of PbSnTe epilayers
and of deposition of Bi on the top of the surface, (ii) tight binding calculations concerning
the influence of the width of the depletion layer, i.e., Thomas Fermi screening length,
as well as of temperature on the Rashba splitting of PbSnTe, including information of the
spin polarization and (iii) magnetic field dependent Hall effect data.
Reprinted supplement page 2 of paper [88] “Rashba splitting in (Pb,Sn)Te controlled by Bi doping”.
2
1. Sb-Doping and the Effect of Bi Surface deposition
Additional control experiments were performed in order to demonstrate that the observed
Rashba effect of PbSnTe is neither due to Bi accumulation at the surface nor due to specific
properties of the Bi dopant. In the first set of experiments, we have deposited stepwise Bi on
top of the Pb0.54Sn0.46Te (111) surface at a temperature of 200K up to a coverage of 1 monolayer.
The resulting ARPES data recorded after 1 ML deposition is shown in Figure S1c in
comparison to the initial ARPES data recorded before Bi deposition. The result reveal that Bi
on the surface alone does not cause any Rashba splitting of the PbSnTe bands. This unequivocally
shows that the Rasbha effect we observed for our Pb0.54Sn0.46Te films doped by Bi in
the bulk cannot be caused by Bi surface segregation. This is further corroborated the comparison
of the core level spectra of the bulk Bi-doped and the surface deposited Bi PbSnTe
samples shown in Figure S1d and in the article Figure 4i, respectively. Whereas after 1ML
surface deposition the characteristic Bi 5d3/2 core level peak is higher than the Sn 4d and Pb
5d core level peaks, for the bulk Bi-doped films with Bi concentration up to 1% the Bi core
level peaks are very small and barely visible over the background. This evidences that no
significant Bi accumulation occurs for the bulk-doped films.
Figure S1: Effect of Sb-doping and Bi surface deposition. (a) ARPES map of a Pb0.54Sn0.46Te
(111) film with 3% Sb-doping in the bulk. A similar huge Rashba effect occurs as observed for
the Bi-doped samples. (b,c) ARPES maps of an undoped Pb0.54Sn0.46Te (111) layer before,
respectively, after 1 monolayer Bi deposition on the surface at 200K. No Rashba effect is
observed in this case. The maps were recorded around the -point at 100 K with a photon
energy of h = 18 eV. (d) Core level spectra recorded before and after 1 ML Bi deposition
using h = 90 eV.
Reprinted supplement page 3 of paper [88] “Rashba splitting in (Pb,Sn)Te controlled by Bi doping”.
3
To demonstrate that the Rashba effect does not rely on a specific property of the n-type
dopant, we have also grown Pb0.54Sn0.46Te films where Bi was replaced by Sb as group V ntype
dopant. As shown by Figure S1a, for the Sb-doped film a similar huge Rashba effect is
observed. In fact, for a nominal Sb concentration of 3% of this film, we obtain an even larger
Rashba splitting of kR = 0.036 Å−1
and ER = 56 meV than for the Pb0.54Sn0.46Te doped with
1% of Bi. This corroborates that the Rashba effect is solely controlled by the bulk Fermi level
and therefore occurs for any n-type dopant of the system.
2. Tight Binding Calculations
To find appropriate parameters for the Thomas Fermi screening potential, we have performed
series of calculations, in which both the potential amplitude as well as the potential
screening length have been changed (Equation 3 of main Article). For each pair of parameters
the recursive, decimation method for finding the spectral density function for surface
atoms [1] has been used. The method requires a finite range of the applied potential and
therefore, the potential has been cut off at the range equal to λ and shifted in order to avoid
a potential step. It has been checked that further increase of the range influences the obtained
densities negligibly. The results have been compared with experiment. The most accurate
agreement was achieved for λ=25 Å. To illustrate the dependence of the spectral
density on the screening length λ we show in Figure S2 the results obtained for four different
λ values and fixed V0 = +0.3 eV. It can be seen that with increasing width λ of the depletion
layer underneath the surface the position of the Kramers point shifts upwards and the number
of localized bands increases. At λ = 50 Å the Kramers point of the surface state is shifted
into the bulk CB and a second subband appears in the VB. At λ = 100 Å even a third subband
appears. Since we do not see such additional subbands in the ARPES measurements, we
conclude that the Thomas Fermi screening length must be well below 50 Å in our samples.
Figure S2: Tight binding calculation af the surface spectral density of states of Pb0.54Sn0.46Te (111) as a
function of screening length λ varying from 10 to 100Å, while the surface potential of V0 = +0.3 eV
and T=200K was kept constant. he solid lines correspond to the surface states and the shaded regions
to the bulk bands.
Reprinted supplement page 4 of paper [88] “Rashba splitting in (Pb,Sn)Te controlled by Bi doping”.
4
Temperature dependence and spin polarization. In Figure S3 we present the temperature
dependence of the TB calculations for the anion terminated (111) surface of Pb0.54Sn0.46Te
with applied surface potential V0 = +0.2 eV and λ = 25 Å. Comparing Figure S3 with Figure 3ad
in the main article one can see that in both cases the gap closes at 110K. Below 110K the
band gap opens and the electronic band structure is inverted. Together with reopening of
the band gap also a gap in the Kramers point opens. The band above the Kramers point becomes
now the lower part of the Dirac cone and the band below the Kramers point forms
the upper band of the new Rashba pair. The lower part of Figure S3 shows the in-plane spin
polarization of the bands where the green and red colors indicate opposite spin directions.
Upon band inversion the spin chirality of the Rashba pair is opposite to the one in normal
case. The Dirac cone is highly deformed by Thomas Fermi potential, which shifts the Dirac
point to the position, where it appears to hybridize with the conduction band.
Figure S3: Tight binding surface spectral density (top) and in-plane spin polarization (bottom) of the
spectral density of states in (111) Pb0.54Sn0.46Te as a function of temperature with surface potential
V0 = +0.2 eV and λ = 25 Å. The solid lines correspond to the surface states and the shaded regions to
the bulk bands and the red and green color to opposite in-plane spin polarization direction.
Reprinted supplement page 5 of paper [88] “Rashba splitting in (Pb,Sn)Te controlled by Bi doping”.
5
3. Magnetic Field Dependent Hall Measurements
Hall measurements were carried out in Van der Pauw geometry within variable external
magnetic fields up to 0.9 Tesla. Measurements were performed and room temperature and
liquid nitrogen. To verify that the obtained Hall concentrations and carrier mobilities do not
depend on the applied magnetic field strength even for nearly compensated samples, we
show in Fig. S4 the magnetic field dependence of the longitudinal and Hall resistance xx and
xy of such a film with xSn = 46% and a Bi-doping level of 3.4 x 1019
cm-3
. From the linear fit of
the Hall resistance a carrier concentration (n-type) of n = 1.43 x 1018
cm-3
at room temperature
and of 1.02 x 1018
cm-3
at 77K is obtained. The corresponding carrier mobilities are µ =
600, respectively, 11000 cm2
/Vsec for this sample. Selected samples were also measured in
high magnetic fields up to 7 T at 1.7K. The obtained high field carrier concentrations are consistent
within 20% of the low field data.
0.0 0.2 0.4 0.6 0.8 1.0
0
1x10-6
2x10-6
3x10-6
4x10-6
5x10-6
6x10-6
0.0 0.2 0.4 0.6 0.8 1.0
0
1x10-6
2x10-6
3x10-6
4x10-677 K
xy
xx
xyandxx(m)
Magnetic field B (Tesla)
PbSnTe, xSn = 46%
nH,77K = 1.02 x 1019
cm-3
µ77K = 11000 cm2
/Vsec
300 K
xy
xx/10
xyandxx/10(m)
Magnetic field B (Tesla)
PbSnTe, xSn = 46%
nH,77K = 1.43 x 1019
cm-3
µ77K = 600 cm2
/Vsec
Figure S4: Magnetic field dependent longitudinal and Hall resistances xx and xy of a 1.9 µm thick
Pb0.54Sn0.46Te epilayer with Bi-doping level of 3.4 x 1019
cm-3
measured at 77 and 300 K. From the
linear fit of the Hall resistance xy an n-type carrier concentration of n = 1.43 x 1018
cm-3
at room
temperature and 1.02 x 1018
cm-3
at 77K were obtained, with corresponding carrier mobilities of µ =
600 and 11000cm2
/Vsec, respectively.
References:
[1] M. P. Lopez Sancho, J. M. Lopez Sancho and J. Rubio, J. Phys. F 1985, 15, 851.
Reprinted supplement page 6 of paper [88] “Rashba splitting in (Pb,Sn)Te controlled by Bi doping”.
Chapter 5
Conclusion and outlook
The topological insulators were intensively studied during the last one and a half decades since
their prediction. We have focused on the experimental studies of chalcogenide topological
insulators of Bi2Te3 and Bi2Se3 types. We have also studied manganese magnetically doped
naturally grown heterostructures. We have experimentally supported theoretical predictions
of a magnetic band gap opening in the Dirac point of the topological surface states. The
magnetic order temperature below 20 K for bismuth telluride was later improved to almost
50 K in manganese antimony telluride.
We have also studied the properties of topological crystalline insulator films (Pb,Sn)Se and
(Pb,Sn)Te. These materials can be n-doped by electrons with bismuth. The bulk doping of
the materials can lead to a rhombohedral distortion of the crystal lattice and the appearance
of the piezoelectric field. The electric field on the surface regions of the TCI film can lift up the
degeneracy of one of four Dirac points and transform material from a topological crystalline
insulator to a Z2 topological insulator.
Further research directions in the field will focus on preparing better-controlled systems.
Instead of naturally grown random heterostructures, artificial heterostructures with periodically
ordered magnetic and topological insulator layers promise possibilities of higher temperature
ferromagnetic order. One of the possible outputs is to prepare a quantum anomalous
Hall effect device working at a higher temperature than the achieved couple of Kelvin. However,
since such a device needs suppressed charge carrier density in the bulk of the material,
I wonder if such a device can work at room temperature in the foreseeable future or with
current topological insulators.
The field of artificial heterostructures also can include normal insulator-topological insulator
structures. Such structures can host topological states at each interface, enhancing
their density for future applications. The telluride-based topological insulators and topological
crystalline insulators can be combined with ferroelectric layers of GeTe-type ferroelectric.
The inherent electric field can also change the topological properties of the material.
The topological insulators will be further studied for their possible applications in spintronics
or quantum computing.
226
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Chapter 6
List of publications
1. O. Caha, V. Kˇr´apek, V. Hol´y, S. Moss, J. Li, A. Norman, A. Mascarenhas, J. Reno,
J. Stangl, and M. Meduˇna, X-ray diffraction on laterally modulated (InAs)(n)/(AlAs)(m)
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2. O. Caha, P. Mikul´ık, J. Nov´ak, V. Hol´y, S. Moss, A. Norman, A. Mascarenhas, J. Reno,
and B. Krause, Spontaneous lateral modulation in short-period superlattices investigated
by grazing-incidence X-ray diffraction, Phys. Rev. B 72, 035313 (2005).
3. J. Li, D. Stokes, O. Caha, S. L. Ammu, J. Bai, K. E. Bassler, and S. C. Moss, Morphological
instability in InAs/GaSb superlattices due to interfacial bonds, Phys. Rev. Lett.
95, 096104 (2005).
4. O. Caha, V. Hol´y, and K. E. Bassler, Nonlinear evolution of Surface morphology in
InAs/AlAs superlattices via Surface diffusion, Phys. Rev. Lett. 96, 136102 (2006).
5. O. Caha, V. Hol´y, and K. E. Bassler, Growth evolution of superlattice morphology, Acta
Crystallograpica A-Foundation and Advances 63, S254 (2007).
6. J. Kubena, A. Kubena, O. Caha, and P. Mikulik, Development of oxide precipitates in
silicon: calculation of the distribution function of the classical theory of nucleation by a
nodal-points approximation, J. Phys.-Condensed Matter 19, 496202 (2007).
7. J. Kubena, A. Kubena, O. Caha, and M. Meduna, Analysis of vacancy and interstitial
nucleation kinetics in Si wafers during rapid thermal annealing, J. Phys.-Condensed
Matter 21, 105402 (2009).
8. M. Meduna, O. Caha, M. Keplinger, J. Stangl, G. Bauer, G. Mussler, and D. Gruetzmacher,
Interdiffusion in Ge rich SiGe/Ge multilayers studied by in situ diffraction,
Physica Status Solidi A-Applications and Materials Science 206, 1775 (2009).
9. M. Meduna, O. Caha, J. Kubena, A. Kubena, and J. Bursik, Homogenization of CZ
Si wafers by Tabula Rasa annealing, Physica B-Condensed Matter 404, 4637 (2009),
25th International Conference on Defects in Semiconductors, St Petersburg, Russia,
JUL 20-24, 2009.
10. O. Caha and M. Meduna, X-ray diffraction on precipitates in Czochralski-grown silicon,
Physica B-Condensed Matter 404, 4626 (2009), 25th International Conference on
Defects in Semiconductors, St Petersburg, Russia, JUL 20-24, 2009.
232
CHAPTER 6. LIST OF PUBLICATIONS 233
11. A. Hospodkova, E. Hulicius, J. Pangrac, J. Oswald, J. Vyskocil, K. Kuldova, T. Simecek,
P. Hazdra, and O. Caha, InGaAs and GaAsSb strain reducing layers covering
InAs/GaAs quantum dots, J. Crystal Growth 312, 1383 (2010), 17th Amer
Conference on Crystal Growth and Epitaxy/14th United States Biennial Workshop
on Organometallic Vapor Phase Epitaxy/6th Inter Workshop on Modeling in Crystal
Growth, Lake Geneva, WI, Aug 09-14, 2009.
12. J. H. Li, D. W. Stokes, J. C. Wickett, O. Caha, K. E. Bassler, and S. C. Moss, Effect
of strain on the growth of InAs/GaSb superlattices: An x-ray diffraction study, J. Appl.
Phys. 107, 123504 (2010).
13. V. Hol´y, X. Marti, L. Horak, O. Caha, V. Novak, M. Cukr, and T. U. Schuelli, Density
of Mn interstitials in (Ga,Mn)As epitaxial layers determined by anomalous x-ray
diffraction, Appl. Phys. Lett. 97, 181913 (2010).
14. V. Cech, S. Lichovnikova, R. Trivedi, V. Perina, J. Zemek, P. Mikulik, and O. Caha,
Plasma polymer films of tetravinylsilane modified by UV irradiation, Surface & Coatings
Technology 205, S177 (2010), 7th Asian-European International Conference on Plasma
Surface Engineering, Busan, South Korea, Sep 20-25, 2009.
15. M. Meduˇna, O. Caha, J. R˚uˇziˇcka, S. Bernatov´a, M. Svoboda, and J. Burˇs´ık, Oxygen
precipitation studied by x-ray diffraction techniques, in Gettering and Defect Engineering
in Semiconductor Technology XIV, edited by Jantsch, W and Schaffler, F, , Solid
State Phenomena Vol. 178-179, p. 325, 2011, 14th International Biannual Meeting on
Gettering and Defect Engineering in Semiconductor (GADEST2011), Loipersdorf Spa
& Conf Ctr, Loipersdorf, Austria, Sep 25-30, 2011.
16. J. Kubena, A. Kubena, O. Caha, and M. Meduna, Homogeneous and heterogeneous
nucleation of oxygen in Si-CZ, in Gettering and Defect Engineering in Semiconductor
Technology XIV, edited by Jantsch, W and Schaffler, F, , Solid State Phenomena Vol.
178-179, p. 495, 2011, 14th International Biannual Meeting on Gettering and Defect Engineering
in Semiconductor (GADEST2011), Loipersdorf Spa & Conf Ctr, Loipersdorf,
Austria, Sep 25-30, 2011.
17. A. Hospodkova, J. Pangrac, J. Vyskocil, J. Oswald, A. Vetushka, O. Caha, P. Hazdra,
K. Kuldova, and E. Hulicius, InAs/GaAs quantum dot capping in kinetically limited
MOVPE growth regime, J. Cystal Growth 317, 39 (2011).
18. S. Piano, X. Marti, A. W. Rushforth, K. W. Edmonds, R. P. Campion, M. Wang,
O. Caha, T. U. Schuelli, V. Hol´y, and B. L. Gallagher, Surface morphology and magnetic
anisotropy in (Ga,Mn)As, Appl. Phys. Lett. 98, 152503 (2011).
19. D. Franta, I. Ohlidal, D. Necas, F. Vizda, O. Caha, M. Hason, and P. Pokorny, Optical
characterization of HfO2 thin films, Thin Solid Films 519, 6085 (2011).
20. O. Caha, S. Bernatova, M. Meduna, M. Svoboda, and J. Bursik, Study of oxide precipitates
in silicon using X-ray diffraction techniques, Physica Status Solidi A-Applications
and Materials Science 208, 2587 (2011).
CHAPTER 6. LIST OF PUBLICATIONS 234
21. L. Zabransky, V. Bursikova, J. Bursik, P. Vasina, P. Soucek, O. Caha, M. Jilek, and
V. Perina, Study of the Indentation Response of Nanocomposite n-TiC/a-C:H Coatings,
Chemicke Listy 106, S1508 (2012).
22. E. Mikmekova, M. Urbanek, T. Fort, R. Di Mundo, and O. Caha, Effect of Hydrogen
on the Properties of Amorphous Carbon Nitride Films, in Manufacturing Science and
Technology, PTS 1-8, edited by Fan, W, , Advanced Materials Research Vol. 383-390,
p. 3298, 2012, International Conference on Manufacturing Science and Technology
(ICMST 2011), Singapore, Singapore, SEP 16-18, 2011.
23. M. Meduna, O. Caha, M. Svoboda, and J. Bursik, X-ray Laue and Bragg diffraction
on oxygen precipitates in annealed CZ-Si wafers., Acta Crystallograpica A-Foundation
and Advances 68, S260 (2012).
24. M. Schmidbauer, A. Ugur, C. Wollstein, F. Hatami, F. Katmis, O. Caha, and W. T. Masselink,
Nucleation of lateral compositional modulation in InGaP epitaxial films grown
on (001) GaAs, J. Appl. Phys. 111, 024306 (2012).
25. E. Piskorska-Hommel, V. Hol´y, O. Caha, A. Wolska, A. Gust, C. Kruse, H. Kroencke,
J. Falta, and D. Hommel, Complementary information on CdSe/ZnSe quantum dot
local structure from extended X-ray absorption fine structure and diffraction anomalous
fine structure measurements, J. Alloys and Compounds 523, 155 (2012).
26. M. Meduna, O. Caha, and J. Bursik, Studies of influence of high temperature preannealing
on oxygen precipitation in CZ Si wafers, J. Crystal Growth 348, 53 (2012).
27. M. Meduˇna, J. R˚uˇziˇcka, O. Caha, J. Burˇs´ık, and M. Svoboda, Precipitation in silicon
wafers after high temperature preanneal studied by X-ray diffraction methods, Physica
B-Condensed Matter 407, 3002 (2012), 26th International Conference on Defects in
Semiconductors (ICDS), Nelson, New Zealand, JUL 18-22, 2011.
28. P. Soucek, T. Schmidtova, L. Zabransky, V. Bursikova, P. Vasina, O. Caha, M. Jilek,
A. El Mel, P.-Y. Tessier, J. Schaefer, J. Bursik, V. Perina, and R. Miksova, Evaluation
of composition, mechanical properties and structure of nc-TiC/a-C:H coatings prepared
by balanced magnetron sputtering, Surface & Coatings Technology 211, 111 (2012),
Symposium K on Protective Coatings and Thin Films held at the European-MaterialsResearch-Society
Spring Meeting (E-MRS), Nice, France, May 09-13, 2011.
29. E. Mikmekova, J. Polcak, J. Sobota, I. Muellerova, V. Perina, and O. Caha, Humidity
resistant hydrogenated carbon nitride films, Appl. Surface Science 275, 7 (2013), 7th
NANOSMAT, Prague, Czech Republic, Sep 18-21, 2012.
30. O. Caha, A. Dubroka, J. Huml´ıˇcek, V. Hol´y, H. Steiner, M. Ul-Hassan, J. S´anchezBarriga,
O. Rader, T. N. Stanislavchuk, A. A. Sirenko, G. Bauer, and G. Springholz,
Growth, Structure, and Electronic Properties of Epitaxial Bismuth Telluride Topological
Insulator Films on BaF2 (111) Substrates, Crystal Growth & Design 13, 3365 (2013).
31. O. Caha, P. Kosteln´ık, J. ˇSik, Y. D. Kim, and J. Huml´ıˇcek, Lattice constants and optical
response of pseudomorph Si-rich SiGe:B, Appl. Phys. Lett. 103, 202107 (2013).
CHAPTER 6. LIST OF PUBLICATIONS 235
32. P. Soucek, T. Schmidtova, V. Bursikova, P. Vasina, Y. T. Pei, J. T. M. De Hos, O. Caha,
V. Perina, R. Miksova, and P. Malinsky, Tribological properties of nc-TiC/a-C:H coatings
prepared by magnetron sputtering at low and high ion bombardment of the growing
film, Surface & Coatings Technology 241, 64 (2014), 56th Annual Technical Conference
of the Society-of-Vacuum-Coaters, Providence, France, Apr 20-25, 2013.
33. L. Zabransky, V. Bursikova, P. Soucek, P. Vasina, T. Gardelka, P. St’ahel, O. Caha,
V. Perina, and J. Bursik, Study of the thermal dependence of mechanical properties,
chemical composition and structure of nanocomposite TiC/a-C:H coatings, Surface &
Coatings Technology 242, 62 (2014).
34. J. Huml´ıˇcek, D. Hemzal, A. Dubroka, O. Caha, H. Steiner, G. Bauer, and G. Springholz,
Raman and interband optical spectra of epitaxial layers of the topological insulators
Bi2Te3 and Bi2Se3 on BaF2 substrates, Physica Scripta T162, 014007 (2014), 4th
International School and Conference on Photonics, Belgrade, Serbia, Aug 26-30, 2013.
35. L. Zabransky, V. Bursikova, P. Soucek, P. Vasina, T. Gardelka, P. St’ahel, O. Caha,
V. Perina, and J. Bursik, Study of the thermal dependence of mechanical properties,
chemical composition and structure of nanocomposite TiC/a-C:H coatings (Reprinted
from Surface & Coatings Technology, vol 242, pg 62-67, 2014), Surface & Coatings Technology
255, 158 (2014), Spring Meeting of the European-Materials-Research-Society
(EMRS), Univ Poitiers, Strasbourg, France, May 27-31, 2013.
36. P. Souˇcek, T. Schmidtov´a, L. Zabransky, V. Bursikova, P. Vasina, O. Caha, J. Bursik,
V. Perina, R. Miksova, Y. T. Pei, and J. T. M. De Hosson, On the control of
deposition process for enhanced mechanical properties of nc-TiC/a-C:H coatings with
DC magnetron sputtering at low or high ion flux, Surface & Coatings Technology 255,
8 (2014), Spring Meeting of the European-Materials-Research-Society (EMRS), Univ
Poitiers, Strasbourg, France, May 27-31, 2013.
37. H. Steiner, V. Volobuev, O. Caha, G. Bauer, G. Springholz, and V. Hol´y, Structure and
composition of bismuth telluride topological insulators grown by molecular beam epitaxy,
J. Appl. Crystallography 47, 1889 (2014).
38. J. R˚uˇziˇcka, O. Caha, V. Hol´y, H. Steiner, V. Volobuiev, A. Ney, G. Bauer, T. Duchoˇn,
K. Veltrusk´a, I. Khalakhan, V. Matol´ın, E. F. Schwier, H. Iwasawa, K. Shimada, and
G. Springholz, Structural and electronic properties of manganese-doped Bi2Te3 epitaxial
layers, New J. Phys. 17, 013028 (2015).
39. L. Zabransky, V. Bursikova, J. Daniel, P. Soucek, P. Vasina, J. Dugacek, P. St’ahel,
O. Caha, J. Bursik, and V. Perina, Comparative analysis of thermal stability of two
different nc-TiC/a-C:H coatings, Surface & Coatings Technology 267, 32 (2015).
40. J. S´anchez-Barriga, A. Varykhalov, G. Springholz, H. Steiner, R. Kirchschlager, G. Bauer,
O. Caha, E. Schierle, E. Weschke, A. A. Uenal, S. Valencia, M. Dunst, J. Braun,
H. Ebert, J. Minar, E. Golias, L. V. Yashina, A. Ney, V. Hol´y, and O. Rader, Nonmagnetic
band gap at the Dirac point of the magnetic topological insulator (Bi1-xMnx)(2)Se-
3, Nature Communications 7, 10559 (2016).
CHAPTER 6. LIST OF PUBLICATIONS 236
41. I. Gablech, V. Svatos, O. Caha, M. Hrabovsky, J. Prasek, J. Hubalek, and T. Sikola,
Preparation of (001) preferentially oriented titanium thin films by ion-beam sputtering
deposition on thermal silicon dioxide, J. Materials Science 51, 3329 (2016).
42. A. Akrap, M. Hakl, S. Tchoumakov, I. Crassee, J. Kuba, M. O. Goerbig, C. C. Homes,
O. Caha, J. Novak, F. Teppe, W. Desrat, S. Koohpayeh, L. Wu, N. P. Armitage,
A. Nateprov, E. Arushanov, Q. D. Gibson, R. J. Cava, D. van der Marel, B. A. Piot,
C. Faugeras, G. Martinez, M. Potemski, and M. Orlita, Magneto-Optical Signature of
Massless Kane Electrons in Cd3As2, Phys. Rev. Lett. 117, 136401 (2016).
43. M. Hakl, S. Tchoumakov, I. Crassee, A. Akrap, B. A. Piot, C. Faugeras, G. Martinez,
O. Caha, J. Novak, A. Nateprov, E. Arushanov, W.-L. Lee, M. O. Goerbig, F. Teppe,
M. Potemski, and M. Orlita, Cyclotron resonance of Kane electrons observed in Cd3As2,
in 2017 42ND International Conference on Infrared, Millimeter, and Terahetrz Waves
(IRMMW-THZ), International Conference on Infrared Millimeter and Terahertz Waves,
345 E 47TH ST, NEW YORK, NY 10017 USA, 2017, IEEE.
44. V. V. Volobuev, P. S. Mandal, M. Galicka, O. Caha, J. S´anchez-Barriga, D. Di Sante,
A. Varykhalov, A. Khiar, S. Picozzi, G. Bauer, P. Kacman, R. Buczko, O. Rader, and
G. Springholz, Giant Rashba Splitting in Pb1-xSnxTe (111) Topological Crystalline
Insulator Films Controlled by Bi Doping in the Bulk, Advanced Materials 29, 1604185
(2017).
45. V. ˇZelezn´y, O. Caha, A. Soukiassian, D. G. Schlom, and X. X. Xi, Temperaturedependent
far-infrared reflectance of an epitaxial (BaTiO3)(8)/(SrTiO3)(4) superlattice,
Phys. Rev. B 95, 214110 (2017).
46. G. Martinez, B. A. Piot, M. Hakl, M. Potemski, Y. S. Hor, A. Materna, S. G. Strzelecka,
A. Hruban, O. Caha, J. Nov´ak, A. Dubroka, C. Draˇsar, and M. Orlita, Determination
of the energy band gap of Bi2Se3, Scientific Reports 7, 6891 (2017).
47. I. Gablech, O. Caha, V. Svatos, J. Pekarek, P. Neuzil, and T. Sikola, Stress-free deposition
of [001] preferentially oriented titanium thin film by Kaufman ion-beam source,
Thin Solid Films 638, 57 (2017).
48. P. S. Mandal, G. Springholz, V. V. Volobuev, O. Caha, A. Varykhalov, E. Golias,
G. Bauer, O. Rader, and J. S´anchez-Barriga, Topological quantum phase transition
from mirror to time reversal symmetry protected topological insulator, Nature Communications
8, 968 (2017).
49. C. Wang, O. Caha, F. Munz, P. Kostelnik, T. Novak, and J. Huml´ıˇcek, Mid-infrared
ellipsometry, Raman and X-ray diffraction studies of AlxGa1-xN/AlN/Si structures,
Appl. Surface Science 421, 859 (2017).
50. A. Dubroka, O. Caha, M. Hronˇcek, P. Friˇs, M. Orlita, V. Hol´y, H. Steiner, G. Bauer,
G. Springholz, and J. Huml´ıˇcek, Interband absorption edge in the topological insulators
Bi-2(Te1-xSex)(3), Phys. Rev. B 96, 235202 (2017).
51. I. Gablech, O. Caha, V. Svatos, J. Prasek, J. Pekarek, P. Neuzil, and T. Sikola, Preparation
of [001] Oriented Titanium Thin Film for MEMS Applications by Kaufman Ion-
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Beam Source, in 9th International Conference on Nanomaterials - Research and Application
(NANOCON 2017), p. 117, 2018, 9th International Conference on Nanomaterials
- Research and Application (NANOCON), Brno, Czech Republic, Oct 18-20, 2017.
52. P. Fris, D. Munzar, O. Caha, and A. Dubroka, Direct observation of double exchange
in ferromagnetic La0.7Sr0.3CoO3 by broadband ellipsometry, Phys. Rev. B 97, 045137
(2018).
53. P. Lepcio, F. Ondre´aˇs, K. Z´arybnick´a, M. Zbonˇc´ak, O. Caha, and J. Janˇc´aˇr, Bulk
polymer nanocomposites with preparation protocol governed nanostructure: the origin
and properties of aggregates and polymer bound clusters, Soft Matter 14, 2094 (2018).
54. I. Crassee, E. Martino, C. C. Homes, O. Caha, J. Novak, P. Tueckmantel, M. Hakl,
A. Nateprov, E. Arushanov, Q. D. Gibson, R. J. Cava, S. M. Koohpayeh, K. E. Arpino,
T. M. McQueen, M. Orlita, and A. Akrap, Nonuniform carrier density in Cd3As2
evidenced by optical spectroscopy, Phys. Rev. B 97, 125204 (2018).
55. M. Hakl, S. Tchoumakov, I. Crassee, A. Akrap, B. A. Piot, C. Faugeras, G. Martinez,
A. Nateprov, E. Arushanov, F. Teppe, R. Sankar, W.-l. Lee, J. Debray, O. Caha, J. Novak,
M. O. Goerbig, M. Potemski, and M. Orlita, Energy scale of Dirac electrons in
Cd3As2, Phys. Rev. B 97, 115206 (2018).
56. G. Springholz, S. Wimmer, H. Groiss, M. Albu, F. Hofer, O. Caha, D. Kriegner,
J. Stangl, G. Bauer, and V. Hol´y, Structural disorder of natural BimSen superlattices
grown by molecular beam epitaxy, Phys. Rev. Materials 2, 054202 (2018).
57. O. Sik, L. Skvarenina, O. Caha, P. M. Bullet, P. Skarvada, E. B. Bullet, and L. Grmela,
Determining the sub-Surface damage of CdTe single crystals after lapping, J. Materials
Science–Materials in Electronics 29, 9652 (2018).
58. R. Krumpolec, T. Homola, D. C. Cameron, J. Huml´ıˇcek, O. Caha, K. Kuldova, R. Zazpe,
J. Prikryl, and J. M. Macak, Structural and Optical Properties of Luminescent
Copper(I) Chloride Thin Films Deposited by Sequentially Pulsed Chemical Vapour Deposition,
Coatings 8, 369 (2018).
59. I. Gablech, V. Svatos, O. Caha, A. Dubroka, J. Pekarek, J. Klempa, P. Neuzil, M. Schneider,
and T. Sikola, Preparation of high-quality stress-free (001) aluminum nitride thin
film using a dual Kaufman ion-beam source setup, Thin Solid Films 670, 105 (2019).
60. C. V. Falub, S. V. Pietambaram, O. Yildirim, M. Meduna, O. Caha, R. Hida, X. Zhao,
J. Ambrosini, H. Rohrmann, and H. J. Hug, Enhanced permeability dielectric FeCo/Al2O3
multilayer thin films with tailored properties deposited by magnetron sputtering on silicon,
AIP Advances 9, 035243 (2019).
61. J. Rozboˇril, K. Broch, R. Resel, O. Caha, F. M¨unz, P. Mikul´ık, J. E. Anthony, H. Sirringhaus,
and J. Nov´ak, Annealing Behavior with Thickness Hindered Nucleation in
Small-Molecule Organic Semiconductor Thin Films, Crystal Growth & Design 19, 3777
(2019).
62. E. D. L. Rienks, S. Wimmer, J. S´anchez-Barriga, O. Caha, P. S. Mandal, J. R˚uˇziˇcka,
A. Ney, H. Steiner, V. V. Volobuev, H. Groiss, M. Albu, G. Kothleitner, J. Michaliˇcka,
CHAPTER 6. LIST OF PUBLICATIONS 238
S. A. Khan, J. Minar, H. Ebert, G. Bauer, F. Freyse, A. Varykhalov, O. Rader, and
G. Springholz, Large magnetic gap at the Dirac point in Bi2Te3/MnBi2Te4 heterostructures,
Nature 576, 423 (2019).
63. J. Krempasky, M. Fanciulli, L. Nicola, J. Minar, H. Volfova, O. Caha, V. V. Volobuev,
J. Sanchez-Barriga, M. Gmitra, K. Yaji, K. Kuroda, S. Shin, F. Komori, G. Springholz,
and J. H. Dil, Fully spin-polarized bulk states in ferroelectric GeTe, Phys. Rev. Research
2 (2020).
64. J. Seyd, I. Pilottek, N. Y. Schmidt, O. Caha, M. Urbanek, and M. Albrecht, Mn3Gebased
tetragonal Heusler alloy thin films with addition of Ni, Pt, and Pd, J. Phys.Condensed
Matter 32, 145801 (2020).
65. J. A. Arregi, O. Caha, and V. Uhlir, Evolution of strain across the magnetostructural
phase transition in epitaxial FeRh films on different substrates, Phys. Rev. B 101,
174413 (2020).
66. J. Fikacek, P. Prochazka, V. Stetsovych, S. Prusa, M. Vondracek, L. Kormos, T. Skala,
P. Vlaic, O. Caha, K. Carva, J. Cechal, G. Springholz, and J. Honolka, Step-edge assisted
large scale FeSe monolayer growth on epitaxial Bi(2)Se(3)thin films, New Journal of
Physics 22 (2020).
67. I. Mohelsky, A. Dubroka, J. Wyzula, A. Slobodeniuk, G. Martinez, Y. Krupko, B. A. Piot,
O. Caha, G. Bauer, G. Springholz, M. Orlita, and J. Humlicek, Landau level spectroscopy
of Bi2Te3, Phys. Rev. B 102 (2020).
68. J. Dvorak, O. Caha, and D. Hemzal, Tuning of SPR for Colocalized Characterization of
Biomolecules Using Nanoparticle-Containing Multilayers, Plasmonics 16, 1203 (2021).
69. R. Rechcinski, M. Galicka, M. Simma, V. V. Volobuev, O. Caha, J. Sanchez-Barriga,
P. S. Mandal, E. Golias, A. Varykhalov, O. Rader, G. Bauer, P. Kacman, R. Buczko, and
G. Springholz, Structure Inversion Asymmetry and Rashba Effect in Quantum Confined
Topological Crystalline Insulator Heterostructures, Advanced Functional Materials 31
(2021).
70. J. Krempasky, L. Nicolai, M. Gmitra, H. Chen, M. Fanciulli, E. B. Guedes, M. Caputo,
M. Radovic, V. V. Volobuev, O. Caha, G. Springholz, J. Minar, and J. H. Dil, TriplePoint
Fermions in Ferroelectric GeTe, Phys. Rev. Lett. 126 (2021).
71. A. Kazakov, W. Brzezicki, T. Hyart, B. Turowski, J. Polaczynski, Z. Adamus, M. Aleszkiewicz,
T. Wojciechowski, J. Z. Domagala, O. Caha, A. Varykhalov, G. Springholz, T. Wojtowicz,
V. V. Volobuev, and T. Dietl, Signatures of dephasing by mirror-symmetry
breaking in weak-antilocalization magnetoresistance across the topological transition in
Pb1-xSnxSe, Phys. Rev. B 103 (2021).
72. P. Mikulik, O. Caha, and M. Meduna, Laboratory and synchrotron rocking curve imaging
for crystal lattice misorientation mapping, Acta Crystallographica A-Foundation and
Advances 77, C837 (2021).
73. M. Meduna, O. Caha, E. Choumas, F. Bressan, and H. von Kanel, X-ray rocking curve
imaging on large arrays of extremely tall SiGe microcrystals epitaxial on Si, J. Appl.
Crystallography 54, 1071 (2021).
CHAPTER 6. LIST OF PUBLICATIONS 239
74. S. Wimmer, J. Sanchez-Barriga, P. Kueppers, A. Ney, E. Schierle, F. Freyse, O. Caha,
J. Michalicka, M. Liebmann, D. Primetzhofer, M. Hoffman, A. Ernst, M. M. Otrokov,
G. Bihlmayer, E. Weschke, B. Lake, E. V. Chulkov, M. Morgenstern, G. Bauer, G. Springholz,
and O. Rader, Mn-Rich MnSb2Te4: A Topological Insulator with Magnetic Gap Closing
at High Curie Temperatures of 45-50 K, Advanced Materials 33 (2021).
75. M. Horky, J. A. Arregi, S. K. K. Patel, M. Stano, R. Medapalli, O. Caha, L. Vojacek,
M. Horak, V. Uhlir, and E. E. Fullerton, Controlling the Metamagnetic Phase Transition
in FeRh/MnRh Superlattices and Thin-Film Fe50-xMnxRh50 Alloys, ACS Applied
Materials & Interfaces .
76. E. Gablech, Z. Fohlerova, K. Svec, F. Zales, O. Benada, O. Kofronova, J. Pekarkova,
O. Caha, I. Gablech, J. Gabriel, and J. Drbohlavova, Selenium nanoparticles with
boron salt-based compound act synergistically against the brown-rot Serpula lacrymans,
International Biodeterioration & Biodegradation 169 (2022).
77. M. Zahradnik, M. Kiaba, S. Espinoza, M. Rebarz, J. Andreasson, O. Caha, F. Abadizaman,
D. Munzar, and A. Dubroka, Photoinduced insulator-to-metal transition and
coherent acoustic phonon propagation in LaCoO3 thin films explored by femtosecond
pump-probe ellipsometry, Phys. Rev. B 105 (2022).
78. M. Kiaba, O. Caha, F. Abadizaman, and A. Dubroka, Stabilization of the oxygen
concentration in La0.3Sr0.7CoO3 delta thin films by 3 nm thin LaAlO3 capping layer,
Thin Solid Films 759 (2022).
79. N. Y. Schmidt, S. Abdulazhanov, J. Michalicka, J. Hintermayr, O. Man, O. Caha,
M. Urbanek, and M. Albrecht, Effect of Gd addition on the structural and magnetic
properties of L1(0)-FePt alloy thin films, J. Appl. Phys. 132 (2022).