F7301 Elementary excitation in solids

Faculty of Science
Autumn 2008
Extent and Intensity
2/0/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
prof. Mgr. Dominik Munzar, Dr. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: prof. Mgr. Dominik Munzar, Dr.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Description of excited states of solids could be expected to be more complicated than that of the ground state. This is certainly true for highly excited states, that are very different from the ground state. Most of the relevant properties of solids (e.g., thermal, electrical, optical properties), however, can be understood in terms of low-energy excited states that are close to the ground state. Surprisingly, these states have a fairly simple structure: they can be viewed as consisting of a few building blocks that are called elementary excitations. The concept of elementary excitations will be introduced and the most important examples (quasielectrons, quasiholes, phonons, plasmons etc.) presented. At the end of the course, students should be able (a) to understand the concepts of elementary excitations, quasiparticles, collective excitations, Hartree-Fock quasielectrons, phonons etc. (b) to be familiar with the basic applications of the concepts, including the experimental background, and (c) to solve simple related problems, e.g., compute the electronic band structures of semiconductors and simple transition metals using the semiempirical tight-binding method or to compute the phonon dispersion relations using common semiempirical models.
Syllabus
  • 1. Introduction. (a) Excited states in solids. (b) The concept of elementary excitations, quasiparticles and collective excitations, examples. 2. Quasiparticles in Fermi liquids - three aproaches. (a) Hartree-Fock theory. (b) Landau's theory of Fermi liquids. (c) Method of Green's functions. 3. One-electron description of electronic states in crystalline solids. (a) Bloch theorem in a broader context, classification of electronic states based on group theory. (b) Band structure and density of states. (c) Examples of band structures. (d) Methods of measuring the band structure. 4. Methods for calculating the band structure. (a) A survey of the methods, classification of the methods according to the choice of the effective potential and according to the method of solving the Schroedinger equation. (b) Empirical tight-binding method, a unified approach to the electronic structure of atoms, molecules, and solids. (c) Augmented plane waves and pseudopotentials. 5. One-electron theory in the presence of perturbing fields. (a) Effective Hamiltonian and semiclassical approximation. (b) Impurity states in semiconductors. (c) Dynamics of electrons in an external electric field. (d) Dynamics of electrons in a magnetic field. (e) Methods of measuring the Fermi surface. 6. Theory of lattice vibrations. (a) Equations of motion for a lattice in the harmonic approximation. (b) Dispersion relation, density of states, polarization vectors. (c) Quantum properties, phonons. (d) Methods of measuring the phonon dispersion relation. (e) Methods for calculating the dispersion relation. 7. Electron-phonon interaction. (a) Interaction Hamiltonian. (b) Scattering of electrons by phonons. (c) Influence of the electron-phonon interaction on the dispersion relations.
Literature
  • ANDERSON, P. W. Concepts in solids : lectures on the theory of solids. Singapore: World Scientific, 1997, xiii, 188. ISBN 9810232314. info
  • ASHCROFT, Neil W. and N. David MERMIN. Solid state physics. South Melbourne: Brooks/Cole, 1976, xxi, 826 s. ISBN 0-03-083993-9. info
  • MATTUCK, Richard D. A guide to Feynman diagrams in the many-body problem. 2nd ed. New York: Dover Publications, 1992, xv, 429 s. ISBN 0-486-67047-3. info
  • CELÝ, Jan. Kvazičástice v pevných látkách. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1977, 283 s. info
Assessment methods
Lectures. Oral exam. Solution of a certain amount of problems by a student, before the exam, is required.
Language of instruction
English
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018.
  • Enrolment Statistics (Autumn 2008, recent)
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