Josephson current between two $p$-wave superconducting nanowires in the presence of Rashba spin-orbit interaction and Zeeman magnetic fields

TL;DR

This paper theoretically analyzes the Josephson current between two p-wave superconducting nanowires influenced by Rashba spin-orbit interaction and magnetic fields, revealing complex oscillatory behaviors and multiple tunneling channels.

Contribution

It introduces a comprehensive theoretical model for Josephson effects in p-wave nanowires with spin-orbit and magnetic interactions, identifying three distinct tunneling channels and their impact.

Findings

Josephson current oscillates with phase difference and magnetic field orientation.

Three tunneling channels contribute to the Josephson current.

Magneto-Josephson effect arises from magnetic field orientation dependence.

Abstract

Josephson current between two one-dimensional nanowires with proximity induced $p$-wave superconducting pairing is calculated in the presence of Rashba spin-orbit interaction, in-plane and normal magnetic fields. We show that Andreev retro-tunneling is realized by means of three channels. The main contribution to the Josephson current gives a scattering in a conventional particle-hole channel, when an electron-like quasiparticle reflects to a hole-like quasiparticle with opposite spin yielding a current which depends only on the order parameters' phase differences $\varphi$ and oscillates with $4\pi$ period. Second anomalous particle-hole channel, corresponding to the Andreev reflection of an incident electron-like quasiparticle to an hole-like quasiparticle with the same spin orientation, survives only in the presence of the in-plane magnetic field. The contribution of this channel to the Josephson current oscillates with $4\pi$ period not only with $\varphi$ but also with orientational angle of the in-plane magnetic field $\theta$ resulting in a magneto-Josephson effect. Third anomalous particle-particle channel, which represents a reflection of an electron-like (hole-like) quasiparticle to a electron-like (hole-like) quasiparticle with opposite spin-orientation, oscillates only with the in-plane magnetic field orientation angle $\theta$. We present a detailed theoretical analysis of both DC and AC Josephson effects in such a system showing contributions from all these channels and discuss experiments which can test our theory.