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Critical current oscillation by magnetic field in semiconductor nanowire Josephson junction

We study theoretically the critical current in semiconductor nanowire Josephson junction with strong spin-orbit interaction. The critical current oscillates by 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 for the nanowire by using a tight-binding model. The Andreev levels are calculated as a function of phase difference $φ$ 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. The period of oscillation is longer as the angle between the external and effective fields is larger.