CONDUCTION NEAR A MOBILITY EDGE

Abstract
The existence or otherwise of a minimum metallic conductivity σ_min is examined. It is found that the formulae given previously for this quantity are correct in the limit of high temperatures. At low temperatures, following the considerations of Mott and Stein and Krey, we find that its existence depends on the index s in the behaviour of the localization length 1/α, where α ~ (E_C - E)^S. If s ≥ 2/3, σ_min exists ; if not, a behaves like σ_min (E - E_C)^t where t ≈ 2/3 - s and σ_min is the value obtained previously. If s is 0.6, as some calculations suggest, t is 0.067 and a very rapid rise with E is predicted. This is in fair agreement with the observations of Rosenbaum et al³ on Si:P. The situation in two dimensions is reviewed, and some of the results of the scaling theory of Abrahams et al⁴ in 3d are criticised.