Week 4

Lecture 21, 22 April, 10.00-12.00, FL51

Electron-phonon interaction.

Reading.

Review questions.

1. How do lattice vibrations affect the electrons? Derive correction to the Hamiltonian of the Bloch electron due to lattice vibrations.
2. Discuss a matrix element of electron-phonon interaction, focus on the conservation of crystal momentum and dependence on number of phonons.
3. Is the electron-phonon relaxation time temperature dependent? Present arguments and estimate temperature dependence of the electron-phonon relaxation time at high temperature, at low temperature. What is the criterion for distinguishing these regions?
4. Why does resistance of metals depend on temperature?

Home task.

Consider electron in 1D potential U(x)=2U[1-cos(2\pi x/a)].
Assume that the potential U is large and calculate the dispersion relation E(k) for first energy band using tight-binding approximation. (Hint: In the vicinity of the potential minimum, the potential can be approximated with parabolic form (oscillator!) U(x)= m(wx)^2/2. Consider the lowest level of the oscillator that broadens into a band).