Numerical Calculation of the Electrical Conductivity of the Anderson Model in Two Dimension

Abstract

The sample averaged DC conductivity of the Anderson model in two dimension is numerically calculated by directly applying the Kubo-Greenwood formula to samples of size 40×40 (=1,600 lattice sites). The calculated conductivity is in good agreement with the one obtained by the coherent potential approximation (CPA) for W/V ≲3 where W is the width of the distribution of the site energy and V the transfer energy. However, it deviates downwards from the CPA conductivity as W/V is increased further. The present numerical investigation indicates that the Mott-Hindley conductivity formula in the random phase model is rather a crude formula.