Duality between normal and superconducting junctions of multiple quantum wires

TL;DR

This paper explores the duality between normal and superconducting junctions of quantum wires, revealing new fixed points and dualities, with implications for understanding electron transport in superconducting quantum systems.

Contribution

It generalizes previous models by including superconducting effects, establishing a duality between charge conserving and non-conserving junctions, and analyzing fixed points for two- and three-wire systems.

Findings

Identified charge non-conserving fixed points in superconducting junctions.

Established a duality between normal and superconducting junctions via scaling dimensions.

Found stable fixed points for three-wire superconducting junctions at g<1.

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 $g \leftrightarrow 1/g$ 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, $D_P$ 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.