Bloch Oscillations of an Electron in a Crystal under the Action of an Electric Field

Abstract

Abstract The dynamical localization problem of an electron in a ID crystal under the action of a uniform de electric field E is solved. Starting with a determined state at t = 0, it is solved for the Wannier amplitudes (propagator) and shown that they oscillate in time with the Bloch frequency. Moreover, it is shown the behaviour of the optical absorption coefficient as a function of the photon frequency ω which shows jumps whenever the photon energies equal multiples of eEa .