Interfacial spin Hall current in a Josephson junction with Rashba spin–orbit coupling

We theoretically investigate the spin transport properties of the Cooper pairs in a conventional Josephson junction with Rashba spin--orbit coupling considered in one of the superconducting leads. It is found that an angle-resolved spin supercurrent flows through the junction and a nonzero interfacial spin Hall current driven by the superconducting phase difference also appears at the interface. The physical origin of this is that the Rashba spin--orbit coupling can induce a triplet order parameter in the s-wave superconductor. The interfacial spin Hall current dependences on the system parameters are also discussed.