Transport in Double-Crossed Luttinger Liquids

TL;DR

This paper investigates electron transport in two coupled Luttinger liquids, revealing how interaction strength and external conditions influence conductance and resonance phenomena in one-dimensional quantum wires.

Contribution

It provides a detailed analysis of transport behavior in double-crossed Luttinger liquids, including effects of interactions, asymmetry, and external biases, extending understanding of coupled quantum wire systems.

Findings

Weak interactions do not affect transport due to renormalization to zero.

Strong interactions lead to significant inter-wire coupling effects.

Resonance transmission is achievable with symmetric barriers and no bias, but system becomes insulating otherwise.

Abstract

We study transport through two Luttinger liquids (one-dimensional electrons interacting through a Coulomb repulsion in a metal) coupled together at {\it two} points. External voltage biases are incorporated through boundary conditions. We include density-density couplings as well as single-particle hops at the contacts. For weak repulsive interactions, transport through the wires remains undisturbed by the inter-wire couplings, which renormalise to zero. For strong repulsive interactions, the inter-wire couplings become strong. For symmetric barriers and no external voltage bias, a single gate voltage is sufficient to tune for resonance transmission in both wires. However, for asymmetric couplings or for finite external biases, the system is insulating.