Spin Hall effect in a Josephson contact

Abstract

The spin Hall effect on the Josephson tunneling through a two-dimensional normal contact with a spin-orbit split conduction band has been studied in the diffusive regime and at the zero electric bias. Linearized Usadel equations for triplet components of the pairing function in the presence of intrinsic spin-orbit interaction have been derived. These equations have been employed for analysis of the spin Hall effect induced by the super-current. We predict that a nondissipative out-of-plane spin Hall polarization accumulates at lateral edges and an in-plane polarization is induced throughout the entire normal region. At the same time, in contrast to the spin Hall effect in normal systems, the spin current is absent in the considered case of the stationary Josephson effect.