Cooper-pairing interaction at the edge of an electron energy gap due to antiferromagnetism

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Abstract
There is no effect of static antiferromagnetism (AF) on the phonon-mediated Cooper-pairing interaction represented by a structureless interaction in the gap equation when the spins of the AF are centered at ion sites. This result includes effects of all magnetic and nonmagnetic umklapp processes with correct phases and would apply in a simple way as well for any electron-electron interaction arising from phase-mode (phononlike) magnetic vibrations of a spin-density wave. In some cases other than these the s-wave pairing interaction for electron states near the edge of an energy gap due to AF may be reduced in strength by the static AF.