Self-Consistent Theory of Metal Insulator Transitions in Disordered Systems

TL;DR

This paper extends the self-consistent theory of electron localization to include electron interactions, analyzing different schemes that predict either continuous or minimal conductivity metal-insulator transitions, with detailed calculations of diffusion and density of states.

Contribution

It introduces and compares various self-consistency schemes for interacting electrons, providing new insights into the nature of metal-insulator transitions in disordered systems.

Findings

Identification of conditions for continuous versus minimal conductivity transitions

Calculation of frequency-dependent diffusion coefficients in both phases

Observation of pseudogap growth during transition

Abstract

Self-consistent theory of electron localization in disordered systems is generalized for the case of interacting electrons. We propose and critically compare a number of possible self-consistency schemes which take into account the lowest perturbation theory contributions over the interaction. Depending on self-consistency scheme we can obtain either the continuous metal-insulator transition or that with the minimal metallic conductivity. Within the continuous transition approach we calculate the frequency dependence of generalized diffusion coefficient both for metallic and insulating phases. We also consider interaction renormalization of the single-electron density of states which demonstrates the growth of the effective pseudogap as system goes from metal to insulator.