Junctions of three quantum wires

Abstract

We study a junction of three quantum wires enclosing a magnetic flux. The wires aremodelled as single-channel spinless Tomonaga–Luttinger liquids. This is the simplestproblem of a quantum junction between Tomonaga–Luttinger liquids in which Fermistatistics enter in a non-trivial way. We study the problem using a mapping onto thedissipative Hofstadter model, describing a single particle moving on a plane in a magneticfield and a periodic potential coupled to a harmonic oscillator bath. Alternatively we studythe problem by identifying boundary conditions corresponding to the low energy fixedpoints. We obtain a rich phase diagram including a chiral fixed point in which theasymmetric current flow is highly sensitive to the sign of the flux and a phase in whichelectron pair tunnelling dominates. We also study the effects on the conductance tensor ofthe junction of contacting the three quantum wires to Fermi liquid reservoirs.