Cluster coherent potential approximation for electronic structure of disordered alloys

TL;DR

This paper extends the coherent potential approximation to include short-range order effects in disordered alloys by using a cluster approach, revealing new features in the density of states and insights into Anderson localization.

Contribution

It introduces a cluster-based extension of CPA that accounts for non-local disorder correlations and short-range order effects in alloy electronic structures.

Findings

Cluster-CPA recovers CPA for N_c=1 and ensures positive-definite DOS.

Short-range order influences the density of states and scattering features.

Anderson localization occurs before band splitting, with a transition from insulator to metal.

Abstract

We extend the single-site coherent potential approximation (CPA) to include the effects of non-local disorder correlations (alloy short-range order) on the electronic structure of random alloy systems. This is achieved by mapping the original Anderson disorder problem to that of a selfconsistently embedded cluster. This cluster problem is then solved using the equations of motion technique. The CPA is recovered for cluster size $N_{c}=1$, and the disorder averaged density-of-states (DOS) is always positive definite. Various new features, compared to those observed in CPA, and related to repeated scattering on pairs of sites, reflecting the effect of SRO are clearly visible in the DOS. It is explicitly shown that the cluster-CPA method always yields positive-definite DOS. Anderson localization effects have been investigated within this approach. In general, we find that Anderson localization sets in before band splitting occurs, and that increasing partial order drives a continuous transition from an Anderson insulator to an incoherent metal.