Junctions of three quantum wires

TL;DR

This paper investigates the complex behavior of a three-wire quantum junction with magnetic flux, revealing a rich phase diagram with chiral and pairing-dominated phases using advanced theoretical models.

Contribution

It introduces a novel analysis of a three-wire quantum junction with magnetic flux, employing a mapping to the dissipative Hofstadter model and boundary condition methods.

Findings

Identification of a chiral fixed point with flux-sensitive asymmetric current flow

Discovery of a phase dominated by electron pair tunneling

Analysis of conductance tensor modifications due to Fermi liquid reservoirs

Abstract

We study a junction of three quantum wires enclosing a magnetic flux. The wires are modeled as single-channel spinless Tomonaga-Luttinger liquids. This is the simplest problem of a quantum junction between Tomonaga-Luttinger liquids in which Fermi statistics enter in a non-trivial way. We study the problem using a mapping onto the dissipative Hofstadter model, describing a single particle moving on a plane in a magnetic field and a periodic potential coupled to a harmonic oscillator bath. Alternatively we study the problem by identifying boundary conditions corresponding to the low energy fixed points. We obtain a rich phase diagram including a chiral fixed point in which the asymmetric current flow is highly sensitive to the sign of the flux and a phase in which electron pair tunneling dominates. We also study the effects on the conductance tensor of the junction of contacting the three quantum wires to Fermi liquid reservoirs.