Attractive electron-electron interaction induced by geometric phase in a Bloch band

We investigate electron pairing in the presence of the Berry curvature field that ubiquitously exists in ferromagnetic metals with spin-orbit coupling. We show that a sufficiently strong Berry curvature field on the Fermi surface can transform a repulsive interaction between electrons into an attractive one in the p-wave channel. We also reveal a topological possibility for turning an attractive s-wave interaction into one in the p-wave channel, even if the Berry curvature field only exists inside the Fermi surface (circle). We speculate that these novel mechanism might be relevant to the recently discovered ferromagnetic superconductors such as UGe$_{2}$ and URhGe.