Self-consistent theory of localization. II. Localization near the band edges

Abstract

For pt. I see abstr. A43970 of 1973. The solution of the integral equation which arises in the self-consistent theory of localization has been explored for a Cauchy distribution of site energies, for a uniform distribution, and for a binary alloy, with particular attention to the behaviour of the localization edge in the case of weak disorder, when it is close to the unperturbed band edge. The solution could be calculated because an exact solution is found in the limit of zero disorder, and because the Fredholm expansion truncated after two terms gives a good approximation in many cases. For the rectangular distribution at the band edge the results are similar to those obtained by other workers, but for the Cauchy distribution and the binary alloy localization occurs less easily than other theories predict.