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

1989; IOP Publishing; Volume: 1; Issue: 9 Linguagem: Inglês

10.1088/0953-8984/1/9/018

1361-648X

Martyn Winn, David E. Logan,

Spectroscopy and Quantum Chemical Studies

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.