Total and component densities of states in the coherent potential approximation and various averaget-matrix approximations

Abstract

We discuss and compare numerically on the basis of a one-dimensional model, several single-site methods for calculating total and component densities of states in alloys desribable by muffin-tin Hamiltonians. We focus on the coherent potential approximation (CPA) and the average $t$-matrix approximation (ATA) and contrast methods which are based on a knowledge of the ensemble-averaged Green's function with those which are derived from the Lloyd formula for the density of states. We find that the expressions for the total and component densities of states derived from the average Green's function yield physically acceptable results for both CPA and ATA. On this basis we identify a best ATA theory. The expressions based on the Lloyd formula which have been used by various authors for calculating component densities of states in the CPA and total and component densities of states in the ATA yield results which are not only incorrect but are often negative.