Tunneling in One-Dimensional non-Luttinger Electron Liquid

TL;DR

This paper investigates the conductance behavior of a weakly interacting one-dimensional electron system with a scatterer, revealing non-Luttinger-liquid effects and magnetic field-induced conductance peaks.

Contribution

It introduces a renormalization group method to analyze backscattering effects in weakly interacting electrons, extending beyond standard bosonization techniques.

Findings

Backscattering causes non-Luttinger-liquid conductance behavior.

Magnetic field induces a peak in differential conductance at the Zeeman energy.

Method applies at arbitrary scattering potential strength.

Abstract

The conductance of a weakly interacting electron gas in the presense of a single scatterer is found at arbitrary strength of the scattering potential. At weak interaction, a simple renormalization group approach can be used instead of the standard bosonization procedure. Our technique allows to take into account the {\em backscattering\/} of electrons that leads to a non-Luttinger-liquid behavior of the low-temperature conductance. In the presence of magnetic field, the backscattering may give rise to a peak in differential conductance at bias equal to the Zeeman energy.