A soluble theory for the density of states of a spatially disordered system

From an exact theory presented in a previous paper (see Logan and Winn, 1988), the authors develop systematically an approximate single-site description for the density of states of a random tight-binding model characterised by quenched liquid-like disorder. The resultant theory is formally equivalent to the single super-chain approximation (SSCA) introduced by Wertheim (1973) in the context of classical dielectric theory. The authors show that the SSCA is equivalent to the effective-medium approximation (EMA) of Roth (1976), and further, for a simple choice of the pair distribution function, that the SSCA/EMA is formally equivalent to the mean spherical approximation of liquid-state theory. For a Yukawa transfer matrix element, an analytic solution of the SSCA/EMA is derived and its predictions discussed. A comparison is also made with the Matsubara-Toyozawa approximation (1961) to illustrate the effect of including the structural characteristics of the system. Finally, the authors discuss some straightforward extensions of the theory including incorporation of site-diagonal disorder, multiple-hopping processes, and the effects of orbital overlap.