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

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.