Equilibrium supercurrent in proximity-induced superconductors due to band asymmetry

We theoretically investigate the consequences of proximity-induced conventional superconductivity in metals that break time-reversal and inversion symmetries through their energy dispersion but may not harbor Berry phases in their bands. We discover behaviors impossible in an isolated superconductor, such as an equilibrium supercurrent that apparently violates Bloch's theorem and, at suitable topological defects, non-conservation of electric charge reminiscent of the chiral anomaly. We distinguish two cases, type-A and type-B, based on whether band asymmetry and equilibrium supercurrent onset at different temperatures or the same temperature, and sketch their Landau phase diagrams. For both types, the equilibrium supercurrent can be trained by a helical electromagnetic field.