Interacting electrons in disordered wires: Anderson localization and low-temperature transport

TL;DR

This paper investigates how electron-electron interactions influence low-temperature transport in disordered wires, revealing a transition from finite conductivity to localization at a critical temperature due to many-particle effects.

Contribution

It introduces a detailed analysis of the transition in conductivity caused by Anderson localization in Fock space, highlighting the critical behavior near the transition temperature.

Findings

Conductivity remains finite above T_c due to electron-electron scattering.

A transition to zero conductivity occurs at T=T_c due to Anderson localization in Fock space.

Critical behavior follows a lnσ(T) ∝ -(T-T_c)^(-1/2) dependence.

Abstract

We study transport of interacting electrons in a low-dimensional disordered system at low temperature $T$. In view of localization by disorder, the conductivity $\sigma(T)$ may only be non-zero due to electron-electron scattering. For weak interactions, the weak-localization regime crosses over with lowering $T$ into a dephasing-induced "power-law hopping". As $T$ is further decreased, the Anderson localization in Fock space crucially affects $\sigma(T)$, inducing a transition at $T=T_c$, so that $\sigma(T<T_c)=0$. The critical behavior of $\sigma(T)$ above $T_c$ is $\ln\sigma(T)\propto - (T-T_c)^{-1/2}$. The mechanism of transport in the critical regime is many-particle transitions between distant states in Fock space.