Problem 1

A material is known to have a high electron density of states at the Fermi energy.

(a) What does this tell you about the electrical properties?

(b) What does it tell you about the thermal conductivity and the specific heat?

(c) Sketch the dielectric function as a function of frequency for this material. What consequence does the high density of states at the Fermi energy have for the dielectric function?

Problem 2
In a Seebeck effect experiment, a temperature gradient is applied across the sample and the voltage is measured. No current flows through the sample during the measurement. Describe how you could use the Boltzmann equation to calculate the Seebeck coefficent.

(a) Give an expression for the electrical current density in terms of $f$ and the density of states $D(\vec{k})$.

(b) Write down the Boltzmann equation that must be solved to find $f$. (Hint: Take the total derivative of $f$.)

(c) What rank tensor is the Seebeck coefficient? How do you calculate the off-diagonal components?

Problem 3
Describe the quantum Hall effect.

Problem 4
Describe electron screening. How can it be responsible for a metal-insulator transition?