Soluble theories for the density of states of a spatially disordered two-level tight-binding model

Abstract

An analysis is given for the configurationally averaged Green functions of a random multi-level tight-binding model characterised by quenched liquid-like disorder, using graph-theoretical methods. An exact self-consistency equation for the average diagonal Green function matrix, G(z), is derived, from which follow the partial densities of states (DOS). From the exact description, various approximate theories for G(z) may be developed systematically. The authors examine in particular three tractable theories for the case of a two-band system: the Hubbard approximation, the Matsubara-Toyozawa approximation and the single super-chain approximation (SSCA) which is equivalent to the effective medium approximation (EMA) of Roth (1974, 1976). With Yukawa transfer matrix elements the SSCA/EMA is solved analytically by exploiting direct analogies with the theory of classical binary liquid mixtures. For all three theories the material parameter dependence of the DOS is examined systematically and comparatively, with particular regard to band overlap effects which may lead to a metal-insulator transition.