Possibility of two types of localized states in a two-dimensional disordered lattice

Abstract

We report results of our numerical calculations, based on the equation of motion method, of dc electrical conductivity, and of density of states for up to 40×40 two-dimensional square lattices modeling a tight-binding Hamiltonian for a binary (AB) compound, disordered by randomly distributed B vacancies up to 10%. Our results indicate strongly localized states away from band centers separated from the relatively weakly localized states towards midband. This is in qualitative agreement with the idea of a "mobility edge" separating exponentially localized states from the power-law localized states as suggested by the two-parameter scaling theory of Kaveh in two dimensions. An alternative explanation, consistent with one-parameter scaling theory, is that the observed numerical effects may arise as a consequence of the variation of the localization length over the band.