Combined effect of Zeeman splitting and spin-orbit interaction on the Josephson current in a superconductor-two-dimensional electron gas-superconductor structure

We analyze spin effects in the current-carrying state of a superconductor-two-dimensional-electron gas-superconductor (S-2DEG-S) device with spin-polarized nuclei in the 2DEG region. The hyperfine interaction of 2D electrons with nuclear spins, described by the effective magnetic field B, produces Zeeman splitting of Andreev levels without orbital effects, which leads to an interference pattern of supercurrent oscillations over B. The spin-orbit effects in 2DEG cause a strongly anisotropic dependence of the Josephson current on the direction of B, which may be used as a probe for the spin-orbit interaction intensity. Under certain conditions, the system reveals the properties of pi junctions.