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

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-reflection is realized by means of two different 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 φ and oscillates with 4π 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 4π period not only with φ but also with orientational angle of the in-plane magnetic field θ resulting in a magneto-Josephson effect. In the presence of Rashba spin-orbit coupling (SOC) and normal-to-plane magnetic field h, a forbidden gap is shown to open in the dependence of Andreev bound state energies on the phases φ and θ at several values of SOC strength and magnetic field, where Josephson current seems to vanish. We present a detailed theoretical analysis of both DC and AC Josephson effects in such a system showing contributions from these channels and discuss experiments which can test our theory.