Supercurrent-induced charge-spin conversion in spin-split superconductors

We study spin-polarized quasiparticle transport in a mesoscopic superconductor with a spin-splitting field in the presence of coflowing supercurrent. In such a system, the nonequilibrium state is characterized by charge, spin, energy, and spin-energy modes. Here we show that in the presence of both spin splitting and supercurrent, all these modes are mutually coupled. As a result, the supercurrent can convert charge imbalance, which in the presence of spin splitting decays on a relatively short scale, to a long-range spin accumulation decaying only via inelastic scattering. This effect enables coherent charge-spin conversion controllable by a magnetic flux, and it can be detected by studying different symmetry components of the nonlocal conductance signal.