Resonance in a Tomonaga-Luttinger liquid

TL;DR

This paper investigates resonance phenomena in a Tomonaga-Luttinger liquid with backscattering, revealing how electron interactions influence conductance and resonance behavior, with implications for quantum Hall experiments.

Contribution

It provides a perturbative analysis of conductance near resonance in a Luttinger liquid, highlighting the dominance of single-electron backscattering for certain interaction strengths.

Findings

Backscattering of one electron dominates for K ≥ 1/3.

Resonance point varies with temperature.

Results relate to shot-noise experiments in FQHE.

Abstract

We study a homogeneous Tomonaga-Luttinger liquid with backscattering potential. A perturbative computation of the conductance at and near resonance is given. We find that the backscattering of one electron dominates that of two electrons for an interaction parameter $K\geq 1/3$ and that the resonance point depends on temperature. Our results may be relevant for recent experiments on shot-noise in FQHE, where the charge 1/3 and not $2*1/3$ is measured on resonance.