Josephson current through semiconductor nanowire with spin-orbit interaction in magnetic field

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