Josephson Current through Semiconductor Nanowire with Spin-Orbit Interaction in Magnetic Field

TL;DR

This paper provides a theoretical analysis of the Josephson effect in semiconductor nanowires with strong spin-orbit interaction under magnetic fields, revealing 0-$ ext{pi}$ transitions and anomalous supercurrents.

Contribution

It offers analytical expressions for Andreev bound states and supercurrent, demonstrating magnetic field tuning of 0-$ ext{pi}$ transitions and spin-orbit effects on supercurrent asymmetry.

Findings

Demonstrates 0-$ ext{pi}$ transition controlled by magnetic field.

Shows finite supercurrent at zero phase difference due to spin-orbit interaction.

Reveals direction-dependent critical current in multi-channel systems.

Abstract

We theoretically study the DC Josephson effect of a semiconductor nanowire (NW) with strong spin-orbit interaction when a magnetic field is applied parallel to the NW. We adopt a model of single scatterer in a quasi-one-dimensional system for the case of short junctions where the size of normal region is much smaller than the coherent length. In the case of single conduction channel in the model, we obtain analytical expressions for the energy levels of Andreev bound states, $E_n$, and supercurrent $I$, as a function of phase difference $\varphi$ between two superconductors. We show the 0-$\pi$ transition by tuning the magnetic field. In the case of more than one conduction channel, we find that $E_n (-\varphi) \ne E_n (\varphi)$ by the interplay between the spin-orbit interaction and Zeeman effect, which results in finite supercurrent at $\varphi =0$ (anomalous Josephson current) and direction-dependent critical current.