Numerical study of conductivity for the Anderson model in two and three dimensions

Abstract

The equation-of-motion method is applied to the calculation of the conductivity for the Anderson model in two and three dimensions. The Kubo-Greenwood formula is evaluated by averaging suitable combinations of time-dependent states and extrapolating to the limit of infinite time. In agreement with earlier work we have found the critical value of the disorder parameter for a transition from localized to extended states to be $\frac{W}{V}=6\mathrm{}$ for the square lattice and $\frac{W}{V}=15\mathrm{}$ for the simple cubic lattice. No conclusion about the critical behavior of the conductivity near the Anderson transition was drawn because of rather large scatter in the data. The reasons for this scatter are discussed. It is concluded that statistically satisfactory information about the critical behavior of the conductivity can only be obtained from a numerical calculation for systems containing more than ${10}^5$ sites in any dimension.