Josephson $\pi$-state in superconductor-Luttinger liquid hybrid systems

TL;DR

This paper theoretically investigates the Josephson current in superconductor-Luttinger liquid systems, revealing how electron interactions influence critical currents and the formation of $\

Contribution

It introduces an analytical model for Josephson current in LL systems and shows how electron interactions suppress the $\

Findings

Critical currents are renormalized by electron-electron interactions.

Generation of $\

The $\

Abstract

Josephson current through a Luttinger liquid (LL) under a magnetic field is theoretically studied. We derive an analytical expression of Josephson current for clean interfaces, by using quasiclassical Green's function and functional bosonization procedure. We show that critical currents can be renormalized by electron-electron interactions at perfect transparency when LL is adiabatically connected with superconductors. We also find that a generation of $\pi$-state, due to spin-dependent energy shift in Andreev bound states (ABS), is prohibited even at zero temperature when the strength of repulsive interactions reaches some critical value. The suppression of $\pi$-state is caused by the low energy fluctuations propagating in LL, and making the Zeeman splitting in ABS blurred.