Junctions of three quantum wires

Details Junctions of three quantum wires Junctions of three quantum wires

2005-09-27

arxiv.org/abs/cond-mat/0509675v1

J.Stat.Mech.0602:P02008,2006

Physics

Condensed Matter

Strongly Correlated Electrons

Full paper of Phys.Rev.Lett. 91 (2003) 206403 (arXiv:cond-mat/0305121)

Scientific paper

10.1088/1742-5468/2006/02/P02008

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.

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