Nonequilibrium transport for crossed Luttinger liquids

TL;DR

This paper analyzes electron transport in two coupled Luttinger liquids, revealing how strong interactions lead to nonlinear conductance, with a focus on electrostatic coupling and boundary condition modeling.

Contribution

It provides a full solution to the transport problem in coupled Luttinger liquids using boundary conditions, highlighting the effects of interaction strength on conductance.

Findings

Weak interactions do not significantly affect transport.

Strong interactions produce nonlinear conductance laws.

Electrostatic coupling dominates the interaction mechanism.

Abstract

Transport through two one-dimensional interacting metals (Luttinger liquids) coupled together at a single point is analyzed. The dominant coupling mechanism is shown to be of electrostatic nature. Describing the voltage sources by boundary conditions then allows for the full solution of the transport problem. For weak Coulomb interactions, transport is unperturbed by the coupling. In contrast, for strong interactions, unusual nonlinear conductance laws characteristic for the correlated system can be observed.