Localization of electron states in two dimensional disordered potential arrays

Abstract

A numerical method is employed to determine the nature of the eigenstates near the band extremities in two dimensional disordered arrays of potential wells. The states are found to be strongly localized within the band tails for both structurally and cellularly disordered systems. The range of localizing is found to be determined by the average size of a region which, at the current energy, is able to support a Bloch type state independent of its environment. The exponential modification of the wavefunction elsewhere in the lattice simply guarantees the localization. Comparison is made with the analogous behaviour of the wavefunctions near the band edges in disordered chains. The Anderson model for cellular disorder in a tight-bound band is also investigated. The observed localization of computed eigenstates enables a critical appraisal of existing localization criteria derived from a analysis of this model. It is found that the eigenstates are localized far beyond the Anderson and Ziman localization criteria.