Interaction-induced backscattering in short quantum wires

TL;DR

This paper investigates how interactions cause backscattering in short quantum wires, affecting conductance, by modeling hole dynamics with a Fokker-Planck equation and analyzing length-dependent corrections.

Contribution

It introduces a novel approach to describe interaction-induced backscattering in short wires using a Fokker-Planck framework, focusing on non-equilibrated regimes.

Findings

Backscattering rate depends on wire length and interaction strength.

Interaction-induced conductance correction exhibits specific length dependence.

Hole diffusion near the band bottom governs backscattering processes.

Abstract

We study interaction-induced backscattering in clean quantum wires with adiabatic contacts exposed to a voltage bias. Particle backscattering relaxes such systems to a fully equilibrated steady state only on length scales exponentially large in the ratio of bandwidth of excitations and temperature. Here we focus on shorter wires in which full equilibration is not accomplished. Signatures of relaxation then are due to backscattering of hole excitations close to the band bottom which perform a diffusive motion in momentum space while scattering from excitations at the Fermi level. This is reminiscent to the first passage problem of a Brownian particle and, regardless of the interaction strength, can be described by an inhomogeneous Fokker-Planck equation. From general solutions of the latter we calculate the hole backscattering rate for different wire lengths and discuss the resulting length dependence of interaction-induced correction to the conductance of a clean single channel quantum wire.