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

Abstract

We theoretically study the DC Josephson effect of a semiconductor nanowire\n(NW) with strong spin-orbit interaction when a magnetic field is applied\nparallel to the NW. We adopt a model of single scatterer in a\nquasi-one-dimensional system for the case of short junctions where the size of\nnormal region is much smaller than the coherent length. In the case of single\nconduction channel in the model, we obtain analytical expressions for the\nenergy levels of Andreev bound states, $E_n$, and supercurrent $I$, as a\nfunction of phase difference $\\varphi$ between two superconductors. We show the\n0-$\\pi$ transition by tuning the magnetic field. In the case of more than one\nconduction channel, we find that $E_n (-\\varphi) \\ne E_n (\\varphi)$ by the\ninterplay between the spin-orbit interaction and Zeeman effect, which results\nin finite supercurrent at $\\varphi =0$ (anomalous Josephson current) and\ndirection-dependent critical current.\n