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Spin-Hall current and spin polarization in an electrically biased SNS Josephson junction

Periodic in time spin-Hall current and spin polarization induced by a dc electric bias has been calculated in a superconductor-normal 2DEG-superconductor (SNS) Josephson junction. We assumed that the band energies of electrons in the normal system are splitted due to Rashba spin-orbit coupling. The transport parameters have been calculated within the diffusion approximation and using perturbation expansion over a small SN contact transparency. We found out that in contrast to the stationary Josephson effect, the spin-Hall current does not turn to zero. Besides a direct proximity effect caused by Cooper pair's transition into a triplet state, the spin current and polarization are also driven by a periodic electric field associated with the charge imbalance.