The density of states of a spatially disordered tight-binding model

Abstract

The authors give an exact analysis of the configurationally averaged Green functions for a random tight-binding model characterised by quenched liquid-like disorder, using a graph-theoretical method originally applied by Wertheim to a problem in classical dielectric theory. The structural characteristics of the system are incorporated fully. They derive a formally exact self-consistency equation for the averaged diagonal Green function G(z), from which follows the density of states. A systematic derivation and critical discussion of various approximate theories for G(z) is given. They also show that extension to include site-diagonal disorder is straightforward for single-site theories. Finally, an illustrative calculation of the density of states is carried out for the low-density domain.