Calculating condensed matter properties using the KKR-Green's function method—recent developments and applications

TLDR

The KKR method now represents electronic structure directly through its single‑particle Green’s function, offering a more efficient alternative to traditional wave‑function band‑structure approaches for periodic solids. This review surveys recent advances in the KKR‑GF method across embedding schemes, magnetic response, transport, DMFT, spectroscopies, and model‑parameter determination. It outlines the core multiple‑scattering framework of KKR‑GF and discusses techniques for solving the scattering problem and applying the method to atoms, clusters, surfaces, and bulk systems. Direct access to the Green’s function provides several appealing features and, combined with multiple‑scattering theory, grants the method wide applicability.

Abstract

The modern version of the KKR (Korringa–Kohn–Rostoker) method represents the electronic structure of a system directly and efficiently in terms of its single-particle Green's function (GF). This is in contrast to its original version and many other traditional wave-function-based all-electron band structure methods dealing with periodically ordered solids. Direct access to the GF results in several appealing features. In addition, a wide applicability of the method is achieved by employing multiple scattering theory. The basic ideas behind the resulting KKR-GF method are outlined and the different techniques to deal with the underlying multiple scattering problem are reviewed. Furthermore, various applications of the KKR-GF method are reviewed in some detail to demonstrate the remarkable flexibility of the approach. Special attention is devoted to the numerous developments of the KKR-GF method, that have been contributed in recent years by a number of work groups, in particular in the following fields: embedding schemes for atoms, clusters and surfaces, magnetic response functions and anisotropy, electronic and spin-dependent transport, dynamical mean field theory, various kinds of spectroscopies, as well as first-principles determination of model parameters.