Non-Relativistic Spin-Orbit Interaction in Triplet Superconductors: Edelstein Effect and Spin Pumping by Electric Fields

Abstract

Non-relativistic momentum-dependent spin splitting, as observed in collinear altermagnets and non-collinear $p$-wave magnets, provides exciting avenues for controlling spin dynamics. Here, we reveal a distinct form of non-relativistic ``spin-orbit coupling" in triplet superconductors by demonstrating that the triplet order parameter induces a wave-vector-dependent spin texture of Bogoliubov quasiparticles, thereby entangling their orbital and spin motions. Even in the absence of relativistic spin-orbit coupling, this intertwining of spin and orbital motion allows an electric field to generate spin polarization in a $p$-wave superconductor -- that is, an Edelstein effect. Building on this mechanism, we propose an efficient scheme for the nonlinear generation of a DC spin current via electric near fields, driven by AC spin polarization and electron velocity. This general principle offers a powerful route for generating and manipulating spin currents in unconventional superconductors.