Junction of several weakly interacting quantum wires: a renormalization group study

TL;DR

This paper investigates how weak interactions in multiple quantum wires affect conductance at a junction using renormalization group analysis, identifying stable fixed points and potential experimental observations.

Contribution

It derives RG equations for the S-matrix at a junction of multiple weakly interacting quantum wires and analyzes their fixed points and conductance behavior.

Findings

Identification of stable and unstable fixed points of the S-matrix.

Analysis of conductance variation with temperature and parameters.

Discussion of experimental observability in quantum wire setups.

Abstract

We study the conductance of three or more semi-infinite wires which meet at a junction. The electrons in the wires are taken to interact weakly with each other through a short-range density-density interaction, and they encounter a general scattering matrix at the junction. We derive the renormalization group equations satisfied by the S-matrix, and we identify its fixed points and their stabilities. The conductance between any pair of wires is then studied as a function of physical parameters such as temperature. We discuss the possibility of observing the effects of junctions in present day experiments, such as the four-terminal conductance of a quantum wire and crossed quantum wires.