Abstract
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 $\mathit{B},$ 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 $\mathit{B},$ which may be used as a probe for the spin-orbit interaction intensity. Under certain conditions, the system reveals the properties of $\ensuremath{\pi}$ junctions.
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