Problem: Bloch Oscillations

    Electrons are moving in a semiconductor superlattice, represented by a weak periodic potential of lattice spacing a. The lowest band is filled by electrons of density n. An electric field E applied along the x direction. The electron scattering is negligible, the temperature is low, and the quasiclassical approximation is valid. An oscillatory electron response, called Bloch oscillations, is expected.

(a) Calculate the fundamental frequency of the oscillation for a=50 Å\ and V/cm. Compare the result to the typical relaxation time of the electrons.

(b) Explain, in a few words, how does the oscillation in the electric polarization develop. Sketch the electric polarization vs. time for various band fillings.