Problem 1
(a) Because of the mathematical difficulties of solving the Schrödinger equation including the electron-electron interactions, we often consider systems of non-interacting electrons. Landau's theory of a Fermi liquid shows that we should really consider non-interacting quasipartcles instead of non-interacting electrons. Describe these non-interacting quasiparticles. What properties do they have?

(b) Electron screening is a way to include the electron-electron interactions. How can screening lead to a metal-insulator transition?

(c) Describe a Peierls transition. What properties does a material need to exhibit a Peierls transition?

Problem 2

(a) What is the impulse response function for a diffusive metal? Sketch the impulse response function.

(b) How is the impulse response function related to the dielectric function of a diffusive metal. Sketch the dielectric function for positive and negative frequencies.

(c) How can you measure the dielectric function at dc and at optical frequencies?

(d) What are plasmons? What determines the plama frequency?

(d) How can you measure plasmons?

Problem 3
The piezo-thermal conductivity describes how stress induces changes in the thermal conductivity. The stress changes the arrangement of the atoms in the crystal.

(a) The thermal conductivity has two contributions that are typically calculated separately. What are these two contributions?

(b) How can the stress lead to a change in the thermal conductivity? How could this be calculated starting from the arrangement of atoms in the crystal?

Problem 4
A material is known to have zero density of states at the Fermi energy.

(a) What does this tell you about the electrical, thermal, and optical properties of this material?

(b) Which of the following quasiparticles would you expect to observe in this material? (phonons, bipolarons, excitons, polaritons, plasmons) Why?