Study of electronic states with off-diagonal disorder in two dimensions

The nature of electronic states in a two-dimensional tight-binding model with off-diagonal disorder is examined by iterative methods applied to very long strips of finite width M. We find that for $E=0$ the localization length depends linearly on M for all disorders W. This indicates a R^-γ(W) behavior of the wave function, and provides a singular deviation from the belief based on scaling theory that all states are exponentially localized in two dimensions. However, for all E≠0, states are exponentially localized and scaling behavior is obeyed.