Problem 1

(a) The specific heat of a metal is measured at low temperatures to have the form, $c_v = \gamma T$, where $T$ is the absolute temperature. How could this information be used to determine the plasma frequency of the metal?

(b) How could the plasma frequency be measured?

(c) De Haas - van Alphen oscillations are measured for a metal. How could you tell from these measurements if the states at the Fermi surface are electron-like or hole-like?

(d) Use the form of the dielectric function to explain why losses increase with frequency in the microwave regime.

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?

(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 3
By shining light on a semiconductor, excitons are created.

(a) Describe what an exciton is.

(b) By adjusting the intensity of the light, the density of excitons can be controlled. At high exciton densities, the semiconductor goes through a Mott transition. Explain what this means.

(c) By changing the light intensity at the frequency that creates excitons, it would be possible to adjust the plasma frequency. Explain why the plasma frequency would change. What properties of the material would be modulated by changing the plasma frequency?

Problem 4
(a) Explain how the exchange energy leads to ferromagnetism.

(b) What is mean field theory? How is mean field theory used to calculate the Curie-Weiss law?

(c) How was Landau's theory of phase transitions used to calculate the Curie-Weiss law?