Interactions and Disorder in Multi-Channel Quantum Wires

TL;DR

This paper investigates how increasing the number of channels in quantum wires causes a transition from Luttinger-liquid to Fermi-liquid behavior, affecting conductance temperature dependence, with theoretical and experimental implications.

Contribution

It provides an exact expression for the scaling exponent in N coupled Luttinger chains and explores the crossover behavior in multi-channel quantum wires.

Findings

Scaling exponent decreases as 1/N with more channels.

Crossover from Luttinger-liquid to Fermi-liquid behavior observed.

Qualitative agreement with experimental data for N=2 case.

Abstract

Recent experiments have revealed that the temperature dependence of the conductance of quasi-ballistic quantum wires bears clear features of the Luttinger-liquid state. In this paper, the conductance of an N-channel quantum wire is calculated within the model of N coupled Luttinger liquids and under the assumption of weak disorder. It is shown that as the number of channels increases, a crossover from the Luttinger-liquid to the Fermi-liquid behavior occurs. This crossover manifests itself in the 1/N decrease of the scaling exponent of the temperature dependence. An exact expression for the scaling exponent for the case of N coupled Luttinger chains is obtained, and the large N limit is studied for the case of a quantum wire. The case of N=2 for electrons with spin is analyzed in detail, and a qualitative agreement with the experiment is achieved.