Berry phase in magnetic superconductors

In magnetic systems, electronic bands often acquire nontrivial topological structure characterized by gauge flux distribution in momentum k space. It sometimes follows that the phase of the wave functions cannot be defined uniquely over the whole Brillouin zone. In this Letter, we develop a theory of superconductivity in the presence of this gauge flux both in two- and three-dimensional systems. It is found that the superconducting gap has "nodes" as a function of k where the Fermi surface is penetrated by a gauge string.