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We describe the far from equilibrium non-local transport in a diffusivesuperconducting wire with a Zeeman splitting, taking into account the differentspin relaxation mechanisms. We demonstrate that due to the Zeeman splitting aninjection of a current in a superconducting wire creates a spin accumulationthat can only relax via thermalization. In addition the Zeeman splitting alsocauses a suppression of the spin-orbit and spin-flip scattering rates. Thesetwo effects lead to long-range spin and charge accumulations detectable in thenon-local signal. Our model explains the main qualitative features of recentexperimental results in terms of realistic parameters and predicts a strongdependence of the non-local signal on the orbital depairing effect from aninduced magnetic field.

Long-range spin and charge accumulation in mesoscopic superconductors with Zeeman splitting