Transport through asymmetric two-lead junctions of Luttinger liquid wires

TL;DR

This paper analyzes the conductance of two spinless Luttinger liquid wires with different interactions connected through a short junction, deriving RG equations and stability regions for conductance fixed points.

Contribution

It formulates the problem in current algebra language and derives a universal RG equation for conductance in asymmetric Luttinger liquid junctions.

Findings

Derived RG equations for conductance depending on interaction strengths

Identified stability regions for conductance fixed points G=0 and G=1

Provided analytical solutions for conductance behavior based on interactions

Abstract

We calculate the conductance of a system of two spinless Luttinger liquid wires with different interaction strengths g_1, g_2, connected through a short junction, within the scattering state formalism. Following earlier work we formulate the problem in current algebra language, and calculate the scale dependent contribution to the conductance in perturbation theory keeping the leading universal contributions to all orders in the interaction strength. From that we derive a renormalization group (RG) equation for the conductance. The analytical solution of the RG-equation is discussed in dependence on g_1, g_2. The regions of stability of the two fixed points corresponding to conductance G=0 and G=1, respectively, are determined.