Problem 1
A ferromagnetic material is known to undergo a structural phase transition and an electronic phase transition. You can use Raman spectroscopy to measure the sample at different temperatures. How can you see the phase transitions with Raman spectroscopy and how can you tell which phase transition is structural and which is electronic?

Problem 2
CsCl is an ionic crystal and an electrical insulator. Light waves couple to both the ions and the electrons in this material.

(a) Sketch the dielectric function for CsCl indicating the coupling to the ions and to the electrons.

(b) If CsCl is an insulator, why does the light couple to the electrons?

(c) Sketch the reflectance for the CsCl. Explain your sketch of the reflectance.

(d) Would there be polarons in CsCl? How could you measure them?

Problem 3

(a) Give an expression for the electrical current density using Boltzmann transport theory.

(b) How would you calculate the group velocity associated with and electron state $\vec{k}$? What happens to the group velocity near the Brillouin zone boundaries?

(c) Why do we need to define an electrochemical potential to explain the Seebeck effect in a metal?

Problem 4
(a) Density functional theory calculations often underestimate the size of the band gaps of semiconductors. What experiment could you use to check the calculation?

(b) What different effective masses are defined in a semiconductor?

(c) Sometimes an effective mass is defined for a metal. How is the effective mass related to the band structure?