Spin Hall effect in a superconductor/normal metal junction

We theoretically study a spin Hall effect of normal metal in a superconductor/normal metal (SN) junction based on perturbation theory. The skew scattering and side jump contributions are both taken into account to calculate the spin Hall conductivity (SHC) in the normal metal. We fin that both contributions are anomalously enhanced when the voltage (eV) between the superconductor and the normal metal approaches to the superconducting gap (Δ0). We also fin that the SHC at eV =Δ0 increases with decreasing the junction resistance (RT). These results clearly demonstrate that the SHC in SN junctions can be controlled by applying an external dc electric fiel and by varying RT, suggesting that SN junctions have potential applications for spintronic devices with large spin Hall effects.