The electronic density of states in liquids: computer simulation versus integral-equation approach

Abstract

A recently developed method due to Winn and Logan (and in a similar formulation by Xu and Stratt) allows the determination of the electronic density of states (DOS) of disordered systems by solving a generalized, complex-valued Ornstein-Zernike-type equation. The only input required is the pair distribution function (characterizing the structure of the disordered system) and the transfer matrix element. A closure relation, necessary for the solution has been proposed by the authors: it is derived-assuming some approximations-from an originally exact relation. Up to now this method has only been applied to model systems, where an exact analytical solution of the equations was possible. For this study the authors have solved the integral equation along with the closure relation numerically. For the pair interaction of the particles they have considered both hard-core and continuous potentials; various transfer-matrix elements have been used. The results for the DOS have been compared to molecular-dynamics results, where the electronic DOS has been determined by direct diagonalization of the tight-binding Hamiltonian: they find the agreement between the numerical results and the simulation data to be good. Differences may be attributed to the approximations made in the derivation of the closure relation.