Problem 1
Many observable properties of a metal can be estimated if the electron density is known.

(a) How is the electronic contribution to the specific heat related to the electron density?

(b) How is the electrical conductivity of a metal related to the electron density?

(c) What does a Hall effect measurement tell us about the electron density?

(d) How could you use an EELS measurement of bulk plasmons to help sketch the dielectric function of a metal? Sketch the dielectric function of a metal.

Problem 2
Silicon is doped with boron (an acceptor) at a concentration of $10^{15}$ cm^-3.

(a) How could you calculate the chemical potential?

(b) Sketch the concentration of holes as a function of temperature.

(c) How could you calculate the conductivity as a function of temperature? Make a sketch of the conductivity vs. T.

(d) How can you experimentally determine the bandgap from the plot in (c)?

Problem 3
Piezoresistance is the change in the electrical resistivity because of a mechanical stress.

(a) What rank tensor is piezoresistance? Can it be observed in crystals of all point groups?

(b) How could you calculate piezoresistance?

(c) NiTi alloys undergo structural phase transitions when stress is applied. How could this affect piezoresistance in these alloys?

Problem 4
To plot the frequency response of the magnetic susceptibility of a paramagnet, consider how a paramagnet would respond if an magnetic field were pulsed on and off. Plot the real and imaginary parts of the magnetic susceptibility of a paramagnet. Explain why the susceptibility has the form that you have drawn.

Make a similar plot of the frequency dependence of the magnetic susceptibility of a diamagnet.