Definition of Energy Bands in the Presence of an External Force Field

Abstract

It is shown that for an electron moving in a periodic potential perturbed by a weak electric field the "physical energy bands" differ from the energy bands in the absence of the perturbing field. By means of a wave-packet treatment it is shown that for very weak fields the modified bands are those suggested earlier by Wannier and by Adams and Argyres. In stronger fields, no such treatment can be given, and the functions defined by Wannier for that case do not represent "physical energy bands" in the same sense.