The conductivity near a mobility edge

Abstract

An argument is given based on the Kubo-Greenwood formula to show that the zero-temperature conductivity of a three-dimensional degenerate electron gas in the absence of a magnetic field will always tend to zero as e ²/ħξ when the Fermi energy approaches a mobility edge. Here ξ varies with energy just above the Anderson transition in the same way as the localization length just below it. This is in agreement with scaling theory and recent experimental results on Si: P and a-Si-Nb. On the other hand, many experimental results show that when the Fermi energy E _F lies below the mobility edge E _c, the behaviour of the conductivity is described by

where [sgrave]_min ∼ 0.03e ²/ha and a is the distance between potential wells. An attempt to explain this result is given. Also for metal-insulator (MI) transitions in a strong magnetic field, [sgrave]_min is observed to exist in measurements on InP down to 30 mK. It is proposed that the pre-exponential factor in a field H should be 0.03e ²/hL_H , with L = L_H = (ch/He)^1/2 if L_H > a and L = a for L_H <a.

In Si: P it appears from the results of Thomas and co-workers (Thomas 1983) that the MI transition takes place in the conduction band, not in an impurity band. It is argued that this can only be so in a many-valley conduction band. In most other systems we suggest that it takes place in an impurity band.