Statistics of local density of states in the Falicov-Kimball model with local disorder

TL;DR

This paper investigates how local disorder and electron interactions influence the local density of states in a two-dimensional Falicov-Kimball model, revealing insights into metal-insulator transitions and Anderson localization.

Contribution

It introduces a statistical dynamical mean-field approach to analyze the local density of states distribution in disordered interacting systems, highlighting the role of the most probable value.

Findings

Most probable local density of states indicates extended states.

Discontinuity in the most probable value signals localization transition.

A phase diagram delineates metal, extended, and localized phases.

Abstract

Statistics of the local density of states in the two-dimensional Falicov-Kimball model with local disorder is studied by employing the statistical dynamical mean-field theory. Within the theory the local density of states and its distributions are calculated through stochastic self-consistent equations. The most probable value of the local density of states is used to monitor the metal-insulator transition driven by correlation and disorder. Nonvanishing of the most probable value of the local density of states at the Fermi energy indicates the existence of extended states in the two-dimensional disordered interacting system. It is also found that the most probable value of the local density of states exhibits a discontinuity when the system crosses from extended states to the Anderson localization. A phase diagram is also presented.