Renormalization group study of transport through a superconducting junction of multiple one-dimensional quantum wires

TL;DR

This paper studies the complex transport behavior in multi-wire superconducting junctions, revealing rich fixed point structures and non-monotonic conductance due to electron interactions and proximity effects.

Contribution

It introduces a detailed renormalization group analysis of multi-wire superconducting junctions, uncovering new fixed points and non-Luttinger liquid behavior influenced by electron-electron interactions.

Findings

Fixed point structure is richer than in normal metal-superconductor junctions.

Non-monotonic conductance behavior as a function of temperature.

Transport depends on two independent interaction parameters.

Abstract

We investigate transport properties of a superconducting junction of many ($N \ge 2$) one-dimensional quantum wires. We include the effectofelectron-electron interaction within the one-dimensional quantum wire using a weak interaction renormalization group procedure. Due to the proximity effect, transport across the junction occurs via direct tunneling as well as via the crossed Andreev channel. We find that the fixed point structure of this system is far more rich than the fixed point structure of a normal metal$-$superconductor junction ($N = 1$), where we only have two fixed points - the fully insulating fixed point or the Andreev fixed point. Even a two wire (N=2)system with a superconducting junction i.e. a normalmetal$-$superconductor$-$normal metal structure, has non-trivialfixed points with intermediate transmissions and reflections. We also include electron-electron interaction induced back-scattering in the quantum wires in our study and hence obtain non-Luttinger liquid behaviour. It is interesting to note that {\textsl{(a)}} effects due to inclusion of electron-electron interaction induced back-scattering in the wire, and {\textsl{(b)}} competition between the charge transport via the electron and hole channels across the junction, give rise to a non-monotonic behavior of conductance as a functionof temperature. We also find that transport across the junction depends on two independent interaction parameters. The first one is due to the usual correlations coming from Friedel oscillations for spin-full electrons giving rise to the well-known interaction parameter (${{\alpha = (g_2-2g_1)/2 \pi \hbar v_F}}$). The second one arises due to the scattering induced by the proximity of the superconductor and is given by(${{\alpha^\prime = (g_2 + g_1)/2 \pi \hbar v_F}}$).