Metal-Insulator-Transition in a Weakly interacting Disordered Electron System

TL;DR

This study investigates how electron interactions influence the metal-insulator transition in disordered systems, revealing that interactions can stabilize metallic phases and affect localization properties.

Contribution

It introduces a second-order perturbation approach within the typical medium dynamical cluster approximation to analyze non-local correlations in the Anderson-Hubbard model.

Findings

Critical disorder strength increases with interaction U.

Interactions stabilize the metallic phase.

A pseudogap appears near the transition.

Abstract

The interplay of interactions and disorder is studied using the Anderson-Hubbard model within the typical medium dynamical cluster approximation. Treating the interacting, non-local cluster self-energy ($\Sigma_c[{\cal \tilde{G}}](i,j\neq i)$) up to second order in the perturbation expansion of interactions, $U^2$, with a systematic incorporation of non-local spatial correlations and diagonal disorder, we explore the initial effects of electron interactions ($U$) in three dimensions. We find that the critical disorder strength ($W_c^U$), required to localize all states, increases with increasing $U$; implying that the metallic phase is stabilized by interactions. Using our results, we predict a soft pseudogap at the intermediate $W$ close to $W_c^U$ and demonstrate that the mobility edge ($\omega_\epsilon$) is preserved as long as the chemical potential, $\mu$, is at or beyond the mobility edge energy.