Interaction effects in multi-subband quantum wires

TL;DR

This paper studies how electron-electron interactions influence transport in disordered multi-subband quantum wires, revealing a power-law temperature dependence of conductivity with an exponent related to the number of subbands.

Contribution

It introduces two analytical methods to address divergence issues and derives a power-law behavior of conductivity in multi-channel quantum wires.

Findings

Conductivity follows a power-law temperature dependence.

The power-law exponent is approximately the inverse of the number of subbands.

Analytical solutions are obtained in the weak coupling limit.

Abstract

We investigate the effect of electron-electron interactions on the transport properties of disordered quasi one-dimensional quantum wires with two or more subbands occupied. We apply two alternative methods to solve the logarithmic divergent problem, namely the parquet graph theory and a renormalization group calculation. We solve the group equations analytically in the weak coupling limit and find a power-law for the temperature dependent conductivity of a multi-channel system. The exponent is roughly equal to the inverse of the number of the occupied subbands.