Conductivity and mobility edges for two-dimensional disordered systems

Abstract

The energy levels of an electron in a disordered two-dimensional lattice are evaluated numerically for the honeycomb, square and triangular lattices with between 36 and 196 sites. The density of states and their localization properties are deduced from the results and the dependence of the positions of the mobility edges on disorder is studied. An analysis of the conductivity confirms the claim that the minimum metallic conductivity should have a universal value in two dimensions and that value was found to be (0.12+or-0.03)e2/h. A comparison of the predictions for the conductivity with the weak scattering limit is given.