Direct and inverse superspin Hall effect in two-dimensional systems: Electrical detection of spin supercurrents

A useful experimental signature of the ordinary spin Hall effect is the spin accumulation it produces at the sample edges. The superspin Hall current [Phys. Rev. B 96, 094512 (2017)] is a transverse equilibrium spin current which is induced by a charge supercurrent. We study the superspin Hall current numerically, and find that it does not give rise to a similar edge magnetization. We also predict and numerically confirm the existence of the inverse superspin Hall effect, which produces a transverse charge supercurrent in response to an equilibrium spin current. We verify the existence of the inverse superspin Hall effect both for a spin-polarized charge supercurrent and an exchange spin current, and propose that a $\phi_0$ junction produced by the inverse superspin Hall effect can be used to directly and electrically measure the spin polarization of a charge supercurrent. This provides a possible way to solve the long-standing problem of how to directly detect the spin-polarization of supercurrents carried by triplet Cooper pairs.