Week 4

Lecture 7, 12 February, 13.15-15.00, FL51

Electrons in periodic potential. Tight-binding approximation.

Reading

A&M: Chapter 10, 11, 14, 15.

Review questions

1. What is the basic idea behind the tight-binding method? What it can be used for?
2. Sketch how the energy levels change as atoms condense to form a crystal solid.
3. What is a Wannier function?
4. Compare tight-binding approximation and nearly free electron approximation. What are advantages of each method?

Lecture 8, 14 February, 10.00-12.00, FL51

Electrons in periodic potential. The Fermi surface.
Semi-classical dynamics of the Bloch electrons.

Reading

A&M: Chapter 9, 12, 13, 1.

Review questions

1. How many electrons can a band accomodate?
2. What is the density of states in a band? What are van-Hove singularities?
3. What are the differences in band structure between metals, semiconductors, and isolators? Is the density of electrons important?
4. Derive equation for velocity of Bloch electron.
5. Why would the conductivity of a perfect crystal be infinite? What is the source of the electrical resistance in metals?
6. What is the effective mass tensor?
7. Explain the concept of hole.

Home task

A&M: Problem 8.2.