Systematic Quantum Cluster Typical Medium Method For the Study of Localization in Strongly Disordered Electronic Systems

TL;DR

This paper reviews the development and application of the typical medium dynamical cluster approximation, a quantum cluster method that captures electronic localization in strongly disordered systems, bridging theoretical models and realistic materials.

Contribution

It introduces the typical medium dynamical cluster approximation, a novel method that enables first-principles study of localization in strongly disordered electronic systems.

Findings

Successfully applied to single and multi-band Anderson models

Extended to systems with local and off-diagonal disorder

Used in conjunction with density functional theory for realistic materials

Abstract

Great progress has been made in the last several years towards understanding the properties of disordered electronic systems. In part, this is made possible by recent advances in quantum effective medium methods which enable the study of disorder and electron-electronic interactions on equal footing. They include dynamical mean field theory and the coherent potential approximation, and their cluster extension, the dynamical cluster approximation. Despite their successes, these methods do not enable the first-principles study of the strongly disordered regime, including the effects of electronic localization. The main focus of this review is the recently developed typical medium dynamical cluster approximation for disordered electronic systems. This method has been constructed to capture disorder-induced localization, and is based on a mapping of a lattice onto a quantum cluster embedded in an effective typical medium, which is determined self-consistently. Here we provide an overview of various recent applications of the typical medium dynamical cluster approximation to a variety of models and systems, including single and multi-band Anderson model, and models with local and off-diagonal disorder. We then present the application of the method to realistic systems in the framework of the density functional theory.