Condensed Matter II
Problem set #2
Spring 2023
1 Density of states 1D-3D
• Give the generic expression for the density of states in the 1D, 2D and 3D cases,
given the dispersion relation E(k) in a material.
• Consider parabolic (E1(k) ∝ k2) and linear (E2(k) ∝ k) dispersion relations, and
compute the actual density of states in each of the six cases, assuming that the bands
admit a minimum at point k = 0.
2 Fermi surface in 2D
We consider a 2D system in which each atom occupies a site on a regular triangular
lattice of lattice constant a. The electrons are treated in the free electron framework, and
each atom carries two electrons.
• Determine the parameters of the reciprocal lattice.
• Represent the Fermi surface in the reduced zone.
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