A Singlet-pairing superconductor is always also a super-spin-current-conductor

Abstract

It is shown that, in a conductor carrying a moderate spin current, singlet pairing can still take place almost as effectively as without a spin current. The system will still be fully gapped for all spin-up and -down single-particle excitations, with no depaired electrons. All thermodynamic properties will be practically the same as without the spin current. All universality relations and laws of corresponding states found in the theory of Bardeen, Cooper, and Schrieffer should remain valid. Thus a singlet-pairing superconductor can always carry a persistent and dissipation-less spin-current. A heuristic argument to support this conclusion is also given, as well as two possible experimental tests of this prediction.