Transport and scattering in inhomogeneous quantum wires

TL;DR

This paper investigates how inhomogeneities affect electron transport in quantum wires, showing conditions under which perfect conduction can occur despite abrupt changes, and providing tools to analyze backscattering effects.

Contribution

It identifies a velocity matching condition that enables perfect conduction in inhomogeneous quantum wires and derives the Green's function for such systems.

Findings

Existence of a perfectly conducting fixed point despite inhomogeneities

Analytical expression for the position-dependent Green's function

Method to estimate backscattering strength from density oscillations

Abstract

We consider scattering and transport in interacting quantum wires that are connected to leads. Such a setup can be represented by a minimal model of interacting fermions with inhomogeneities in the form of sudden changes in interaction strength and/or velocity. The inhomogeneities generally cause relevant backscattering, so it is a priori unclear if a perfectly ballistic quantum wire can exist in the low temperature limit. We are able to identify such a perfectly conducting fixed point even for large abrupt changes, which in the considered model corresponds to a velocity matching condition. The general position dependent Green's function is calculated in the presence of a sudden change, which is confirmed numerically with high accuracy. The exact form of the interference pattern in the form of density oscillations around inhomogeneities can be used to estimate the effective strength of local backscattering sources.