Electron transport in disordered Luttinger liquid

TL;DR

This paper investigates how electron interactions and disorder affect transport in one-dimensional quantum wires, showing weak localization applies to strongly correlated systems and developing two combined fermionic-bosonic methods.

Contribution

It introduces two novel approaches combining fermionic and bosonic physics to analyze disordered Luttinger liquids, advancing understanding of mesoscopic effects in strongly correlated electrons.

Findings

Weak localization is applicable to strongly correlated 1D systems.

Dephasing rate depends on electron-electron interaction and disorder.

Framework enables systematic study of mesoscopic effects in such systems.

Abstract

We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger liquid model. We demonstrate that the notion of weak localization is applicable to the strongly correlated one-dimensional electron system. Two alternative approaches to the problem are developed, both combining fermionic and bosonic treatment of the underlying physics. 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. Our approach provides a framework for a systematic study of mesoscopic effects in strongly correlated electron systems.