Problem 1

(a) Draw the real and imaginary parts of the dielectric function for a semiconductor with a bandgap of 1 eV. Label the frequency axis in eV.

(b) Draw the real and imaginary parts of the dielectric function for silver. Label the frequency axis in eV.

(c) How can the dielectric function be measured near optical frequencies? How can it be measured at low frequencies?

Problem 2
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? How are they calculated?

(b) How can the stress lead to a change in the thermal conductivity? How could this be calculated?

Problem 3
(a) List as many experimental methods as you can think of to determine the electron density of a metal.

(b) How can you calculate the electron density of a metal theoretically?

(c) Often divalent metals (with two valence electrons) have a lower conductivity than monovalent metals (with one valence electron). Why is this?

(d) Semimetals have a low electron density. Compare some properties of semimetals to typical metals.

Problem 4
Ferromagnetism can be described by mean field theory and by Landau's theory of second order phase transitions.

(a) What properties of ferromagnetism can be predicted by mean field theory?

(b) What properties of ferromagnetism can be predicted by Landau's theory of second order phase transitions?

(c) What rank tensor is the magnetic susceptibility?

(d) Does the Kramers-Kronig relation imply that the magnetic susceptibility has an imaginary part?

(c) Explain what a hard magnet is and what materials are hard magnets.