Dephasing and weak localization in disordered Luttinger liquid

TL;DR

This paper investigates how electron interactions and disorder affect transport in one-dimensional quantum wires, showing that weak localization persists and is governed by dephasing due to electron-electron interactions.

Contribution

It demonstrates the applicability of weak localization concepts to strongly correlated Luttinger liquids and calculates the dephasing rate considering interactions and disorder.

Findings

Weak localization applies to disordered Luttinger liquids.

Dephasing rate depends on electron-electron interactions and disorder.

Conductivity remains finite at finite temperature due to inelastic scattering.

Abstract

We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger liquid model. The conductivity at finite temperature is nonzero only because of inelastic electron-electron scattering. We demonstrate that the notion of weak localization is applicable to the strongly correlated one-dimensional electron system. We calculate the relevant dephasing rate, which for spinless electrons is governed by the interplay of electron-electron interaction and disorder, thus vanishing in the clean limit.