Impurity Scattering in Luttinger Liquid with Electron-Phonon Coupling

TL;DR

This paper investigates how electron-phonon interactions affect electron transport in a Luttinger liquid with impurities, revealing complex phase behavior and multiple stable and unstable fixed points through RG analysis.

Contribution

It introduces a detailed RG framework for Luttinger liquids with electron-phonon coupling, uncovering new phase transitions and fixed points.

Findings

RG flows depend on coupling strengths and velocity ratios

Phase diagram includes up to three fixed points

Identification of stable metallic and insulating phases

Abstract

We study the influence of electron-phonon coupling on electron transport through a Luttinger liquid with an embedded weak scatterer or weak link. We derive the renormalization group (RG) equations which indicate that the directions of RG flows can change upon varying either the relative strength of the electron-electron and electron-phonon coupling or the ratio of Fermi to sound velocities. This results in the rich phase diagram with up to three fixed points: an unstable one with a finite value of conductance and two stable ones, corresponding to an ideal metal or insulator.