Integral-equation approach to the electronic density of states in disordered materials

Abstract

A few years ago, Winn and Logan demonstrated that, within a single-site theory, the electronic density-of-states (DOS) for disordered materials may be determined from a complex-valued Ornstein-Zernike (OZ)-type integral equation, involving the pair distribution function, g( r), of the system and the transfer matrix element, V( r). Winn and Logan derived by graph theoretical methods an additional closure relation and succeeded to solve these equations analytically for a model system, where g( r) is a step function. A numerical method has been implemented which allows solution of this equation for arbitrary g( r) and V( r). The influence of these two quantities has been studied on the electronic DOS for hard-core systems: (i) concerning the influence of g( r), the contact value turns out to be the most important parameter; (ii) concerning the influence of V( r), the DOS is very sensitive both to range and shape of this function. Further, it is found — as asssumed by Winn and Logan — that a DOS which is determined via this OZ-type equation is automatically normalized.