The electronic structure of weak, random, two- and three-dimensional potentials

Abstract

The electronic structure of weak, random, two- and three-dimensional potentials is calculated by transforming the Hamiltonian to a chain model. The eigenvalues and eigenvectors are calculated for the chain model. In two dimensions all states are localized either exponentially at the band edges or more weakly at the band centre. In three dimensions the states at the band edges are also exponentially localized, but are extended at the band centre. The proportion of states localized, the size of localized states, the position of mobility edges and the density of extended states near the mobility edge are all calculated.