Electron Density of States in Random Systems

Abstract

The well-known result of Halperin and Lax for the tail of the density of an electron moving in a Gaussian random potential is reviewed. We then show that complete universality exists for the density of states near band edges for weak disorder in less than two dimensions and modified universality exists in more than two dimensions. Deep in the tail, non-universal behavior emerges as the localized states become sensitive to potential fluctuations on individual sites. This non-universal exponential behavior is responsible for the observed Urbach tails.