Transport in a one-dimensional wire connected to leads and proximity effects

TL;DR

This paper studies electron transport in a finite one-dimensional interacting wire connected to leads, revealing perfect transmission, contact-induced reflections, and proximity effects, with implications for understanding experimental quantum wire behavior.

Contribution

It provides a rigorous analysis of conductance and reflection phenomena in interacting quantum wires with varying contact properties, linking theory to recent experiments.

Findings

Conductance remains unrenormalized by interactions in the wire.

Abrupt changes in interaction parameters cause partial charge reflections.

Proximity effects influence correlation functions extending into leads.

Abstract

We investigate transport through a finite interacting wire connected to noninteracting leads. The conductance of the pure wire is not renormalized by the interactions for any spatial variation of the interaction parameters $u,K$, and not even for Coulomb interactions restricted to the wire. We rigorously relate the conductance to the transmission, that turns out to be perfect. If $K$ varies abruptly at the contacts, an electron incident on the wire is reflected into a series of partial spatially separated charges which sum up to unity. For attractive interactions, the reflection at the contact is similar to Andreev reflection on a gapless superconductor. This process affects the density-density or pairing correlation functions: they are enhanced on the bulk of the wire as in an infinite Luttinger liquid, then extend to the external noninteracting leads in a way reminiscent of the proximity effect. The effect of impurities is governed by the wire parameter but is affected by the leads close to the contacts. Our results give a possible explanation to recent experiments on quantum wires by Tarucha et al.