Weighted two particle Green's functions in the CPA

TL;DR

This paper extends the CPA to compute weighted two-particle Green's functions in disordered alloys, enabling detailed analysis of linear response and optical properties in such systems.

Contribution

It introduces a method to evaluate weighted two-particle Green's functions within CPA for binary alloys, building on Velický's approach.

Findings

Analytic expressions for weighted two-particle Green's functions

Application to optical absorption in disordered alloys

Behavior analysis in strong disorder limit

Abstract

We extend the two particle theory of disordered systems within the coherent potential approximation CPA to obtain weighted contributions to averaged two particle resolvents which arise from separate alloy components. Starting from first principles in a model of diagonal disorder and the single site approximation for a binary substitutional alloy $A_cB_{1-c}$ we extend the approach of a fundamental paper by Velick{\'y} to evaluate various weighted forms of a general class of two particle Green's functions. Applications in a wide range of linear response theory are discussed in detail as well as the behavior of the weighted functions in a strong disorder limit. To exemplify our analytic calculations the optical absorption in a disordered model- alloy is studied numerically.