Study Guide for Exam 2

14 Measuring the Fermi surface

What is the de Haas van Alphen effect and how is it used to map out the Fermi surface?

What do the Fermi surfaces of the Alkali metals look like?
What do the Fermi surfaces of the Noble metals look like?
What happens to the Fermi surfaces of metals as the number of electrons per unit cell increases? Why?
What is a semimetal?

Write down the Boltzmann equation.
What is the Wiedemann-Franz law? Under what conditions is it expected to be valid?
What is Matthiessen’s rule? When is it valid or not valid?
For elastic scattering how is the transport scattering rate modified so as to make forward scattering not important?

What are the Hartree equations? What are they missing?
What is the trial wave function for the Hartree-Fock approximation?
What does it include that is not in the Hartree approximation?
What is screening?
What is the basis of Thomas-Fermi screening?
What is the typical screening length in a metal?
What are the assumptions of Lindhard screening?
How does Lindhard screening differ from Thomas-Fermi screening for a static potential?
Why does electron-electron scattering rate in metals become small at low temperatures? What is the temperature dependence of this rate?
What is a quasiparticle?
What is Fermi liquid theory?

What is the work function if we neglect surface charge rearrangement?
How does the work function change if we allow for surface charge rearrangement?
Sketch the charge density and the potential for the case when there is surface charge rearrangement.
Can the work function depend on the surface - not just the material? Why?
What is a contact potential?
How does one measure the work function using contact potentials?
What is a typical work function in a metal?

What is the form of the energy of a harmonic crystal in terms of the D(R-R’) matrix?
What is the law of Dulong and Petit?
What is F=ma for a simple one dimensional lattice modeled by masses and springs? What is the form of the solution?
What does omega vs k look like for this model? How does omega behave for small k?
For a three dimensional crystal what is omega_s(k)? How does it behave at small k?
What is an acoustic mode?
What is an optical mode?

What is the energy density of a harmonic crystal in terms omega_s(k)?
what is the specific heat of a harmonic crystal in terms of omega_s(k)?
What is the form of the low temperature and high temperature specific heat of a quantum harmonic crystal?
What is the Debye model for phonons?
What is a typical Debye energy and temperature?
What is the Einstein model for phonons?

What are the conservation laws for neutron scattering from phonons?
What are the zero phonon scattering processes and how are they related to x-ray scattering?
What does the scattering from one phonon processes look like? Why? How does one use it to determine omega_s(k)?
What does the scattering from two phonon processes look like? Why?
What are Brillouin and Raman scattering of visible light?
Compare the energy and wave vectors of visible light and phonons.

Name three failures of the harmonic crystal
What is the Grüneisen parameter? How is it related to the thermal expansion in insulators?
What is umklapp scattering and why is it important for the lattice thermal conductivity?
Sketch the temperature dependence of the thermal conductivity in insulators. Explain the high and low temperature limits of your graph.

What does the band structure of a semiconductor look like? How is it different from a metal and an insulator?
What determines the effective masses of the electrons and holes?
Where is the Fermi energy of a semiconductor in relation to the conduction and valence band edges?
What is the form of the temperature dependence of the density of electrons and holes in a semiconductor?
How is the product of the density of electrons and holes related to the intrinsic density in a semiconductor?
What is a donor?
What is an acceptor?
In a p-type semiconductor, how is the density of electrons and holes related to N_a and n_i?
In a n-type semiconductor, how is the density of electrons and holes related to N_d and n_i?