Theory of Disordered Systems III. Single‐Site Theory of Transport in Systems with Randomly Distributed Scatterers

Abstract

Jn case of systems with randomly distributed scatterers the self-consistent, single-site approximation of Schwartz and Ehrenreich [l] leads to a simple expression for the kernel of the Rethe-Salpeter equation in terms of the local self-energies. Thus, a consistent singlesite theory of linear response of such systems is given. It is applied to the disordered KronigPenney model which permits exact solutions of the Schwartz-Ehrenreich and the corresponding Bethe-Salpeter equation. Numerical results of the density of states and the mobility of the electrons are given. The existence of a mobility edge is established. I m Falle von Systemen mit willkiirlich verteilten Streuern fiihrt die selbstkonsistciite Einzentren-Approximation von Schwartz und Ehrenreich [l] zu einem einfachen Ausdruck fur den Kern derBethe-Salpeter-Gleichung in den loknlen Sclbstenergien. Uadurch ist eine konsistente Einzentren-Theorie der linearen Responsion solcher Systeme gegeben. Sie wird auf das ungeordnete KronigPenney-Model1 angewendet, das exakt,e Losungen dcr Schwartz-Ehrenreich-und der entsprochenden Bethe-Salpeter-Gleichung erlaubt. Kumerische Resultate der Zustandsdichte und der Beweglichkeit der Elektronen werden angegeben. Die Existenz einer BeTveglichkeitskante wird nachgewiesen.

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