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.

Electronic density of states of fluid mixtures in the single superchain/effective medium approximation

“…, and following other authors [9][10][11] we have performed the diagonalization of the tight-binding Hamiltonian as defined in Eq. ͑4.3͒ of Ref.…”

On the conductivity of topologically disordered systems

“…where the only structural connector g 2 (1, 2) is the pair distribution function. The series is readily summed and insertion in equation (8) yields…”

“…During recent years a new interest has emerged in developing self-consistent tight-binding schemes for the densities of states (DOSs) of liquid metals [1][2][3][4][5][6][7][8]. Such theories are quite general and may be extended to any system characterized by quenched liquid-like disorder such as alloys and doped semiconductors.…”

“…In the low-density limit this method could be the starting point for a consistent evaluation of the conductivity in the context of some non-single-site theory, while in the high-density regime it could be employed for a systematic and consistent study of the conductivity in the framework of single-site theories. To our knowledge the best of these theories is the EMA which is believed [8,17] to be the most natural extension of the coherent-potential approximation for diagonal (e.g. substitutional) disorder to the case of topological disorder.…”

Frequency spectra of two-band fluids and fluid mixtures: Mean spherical approximation and beyond

“…The problem of frequency spectra ͑or electronic density of states͒ in disordered systems has been a topic of renewed interest in recent years. 1,2 The most successful approaches to date are based on the mapping of quantum degrees of freedom into complex quantities of a model classical fluid. Two different formulations were proposed by Xu and Stratt 3 and Logan and Winn 4 that led to closely related approximations, of which the simplest approach was based on the mean spherical approximation ͑MSA͒ which is linear.…”