Spin-Galvanic Response to Nonequilibrium Spin Injection in Superconductors with Spin-Orbit Coupling

We show that nonequilibrium spin injection into a superconductor can generate an anomalous supercurrent or induce a phase gradient, even for spin voltages below the superconducting gap. Our mechanism does not require breaking time-reversal symmetry in the effective superconducting Hamiltonian, but instead relies on nonequilibrium spin injection. We further demonstrate that superconductivity enhances spin injection due to the large quasiparticle density of states near the gap edge, an effect that persists well below the gap. This contrasts with earlier works predicting the absence of spin injection at zero temperature and small spin voltages. Our results provide a natural explanation for long-standing experimental observations of spin injection in superconductors and predict novel effects arising from spin-charge coupling, including the electrical control of anomalous phase gradients in superconducting systems with spin-orbit coupling. These effects are broadly testable in a variety of materials and hybrid superconducting structures.