Duality between normal and superconducting junctions of multiple quantum wires
Abstract
We study junctions of single-channel spinless Luttinger liquids using bosonisation. We generalize earlier studies by allowing the junction to be superconducting and find new charge non-conserving low energy fixed points. We establish the existence of g 1/g duality (where g is the Luttinger Liquid parameter) between the charge conserving (normal) junction and the charge non-conserving (superconducting) junction by evaluating and comparing the scaling dimensions of various operators around the fixed points in normal and superconducting sectors of the theory. For the most general two-wire junction, we show that there are two conformally invariant one-parameter families of fixed points which are also connected by a duality transformation. We also show that the stable fixed point for the two-wire superconducting junction corresponds to the situation where the crossed Andreev reflection is perfect between the wires. For the three-wire junction, we study, in particular, the superconducting analogs of the chiral, DP and the disconnected fixed points obtained earlier in the literature in the context of charge conserving three-wire junctions. We show that these fixed points can be stabilized for g < 1 (repulsive electrons) within the superconducting sector of the theory which makes them experimentally relevant.