Localization in an external electric field

TL;DR

This paper investigates how an external electric field influences electron localization, revealing that at low temperatures the field can delocalize electrons, while at higher temperatures the effect is negligible, with the behavior governed by temperature scaling.

Contribution

It introduces a field-theoretic approach to analyze electric field effects on electron localization, highlighting the interplay of two time scales and their impact on conductivity.

Findings

Electric field causes delocalization at very low temperatures.

Conductivity depends logarithmically on the electric field at low temperatures.

At higher temperatures, electric field effects are negligible on localization corrections.

Abstract

The impact of an electric field on the electron localization problem is studied within the framework of a field-theoretic formulation. The investigation shows that the impact of the electric field on the localization corrections is governed by the interplay between two time scales, one set by the electric field, and the other by the phase relaxation rate. At very low temperatures the scaling of the conductivity is governed by the electric field. In this regime the conductivity depends logarithmically on the field, and an arbitrarily small electric field delocalizes the electron states. At higher temperatures the behavior of the conductivity is governed by the temperature scaling. In this regime the field has no impact on the observable leading localization corrections.