Quantum percolation in a two-dimensional finite binary alloy: Interplay between the strength of disorder and alloy composition

Abstract

We address the rather controversial issue of wave propagation in two-dimensional disordered systems. We have followed the time evolution of wave packets in a binary alloy in a two-dimensional finite square lattice where the on-site energies ${\ensuremath{\varepsilon}}_{a}$ and ${\ensuremath{\varepsilon}}_{b}$ are randomly distributed. The parameter that measures the degree of disorder is $\ensuremath{\eta}=|({\ensuremath{\varepsilon}}_{b}\ensuremath{-}{\ensuremath{\varepsilon}}_{a})/W|,$ where W is the hopping term. We were able to construct a phase diagram in the $(\ensuremath{\eta},x)$ plane characterizing the different kind of wave propagation, x being the concentration of type-a atoms.