Electron backscattering from dynamical impurities in a Luttinger liquid

TL;DR

This paper studies how zero point phonon motion influences electron backscattering in a Luttinger liquid with various impurities, revealing finite energy effects through renormalization group analysis.

Contribution

It introduces a finite Debye frequency into the RG equations for backscattering, accounting for phonon spectrum modifications due to impurities.

Findings

Finite Debye frequency affects RG flow of backscattering.

Local density of states is modified by phonon-related effects.

Finite energy effects are significant in impurity-induced backscattering.

Abstract

Electron backscattering in a Luttinger liquid with an impurity is investigated in the presence of zero point motion of the phonon lattice. The impurity can mean either a mass defect, an elastic defect or a pinning defect. The phonon spectrum is then affected by the presence of the defect, which enters in the renormalization group equations for backscattering. The RG equation becomes dependent on the energy cutoff for finite Debye frequency $\omega_D$ giving rise to finite energy effects. We compute the local density of states and show how the renormalization group flow is affected by a finite $\omega_D$.