Critical current in semiconductor nanowire Josephson junctions in the presence of magnetic field

We study theoretically the critical current in semiconductor nanowire Josephson junction with strong spin-orbit interaction. The critical current oscillates with an external magnetic field. We reveal that the oscillation of critical current depends on the orientation of magnetic field in the presence of spin-orbit interaction. We perform a numerical simulation using a tight-binding model. The Andreev levels are calculated as a function of phase difference ψ between two superconductors. The DC Josephson current is evaluated from the Andreev levels in the case of short junctions. The spin-orbit interaction induces the effective magnetic field. When the external field is parallel with the effective one, the critical current oscillates accompanying the 0-π like transition at the cusp of critical current. The distance of cusps increases gradually with increasing of the angle between the external and effective fields. The magnetic anisotropy of critical current is attributed to the spin precession due to the spin-orbit interaction.