Inverse Spin Hall Effect in Josephson Contacts

We demonstrate that Rashba spin orbit coupling together with Zeeman fields create an effective electromagnetic vector-potential in the normal part of an SNS Josephson junction in thermal equilibrium. Consequently, a phase difference between order parameters of the two superconducting terminals is induced, in analogy to the Meissner effect. The resulting phase-coherent equilibrium supercurrent is a counterpart of the non-equilibrium inverse spin Hall effect in normal metals. The calculations have been carried out in the diffusive regime on the basis of Usadel equations and assuming low transparency tunneling contacts. Apart from this effect, we also consider an in-plane homogeneous Zeeman field in the transverse direction.