Journal
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
Volume -, Issue -, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1742-5468/2006/02/P02008
Keywords
bosonization; conformal field theory (experiment); Luttinger liquids (theory); quantum wires (theory)
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We study a junction of three quantum wires enclosing a magnetic flux. The wires are modelled 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 tunnelling 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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