  We theoretically study the generation of spin current due to a surface
acoustic wave (SAW) in a superconductor. We model an s-wave superconductor as
the mean-field Hamiltonian and calculate spin current generated via
spin-vorticity coupling based on kinetic theory. The results suggest that the
spin current can be driven in a single superconductor layer, and our estimation
suggests that the detectable magnitude of the spin current can be generated in
aluminum. Our proposal may contribute to the advancement of spin transport in
superconductors from application and fundamental physics aspects.
