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We theoretically investigate the consequences of proximity-inducedconventional superconductivity in metals that break time-reversal and inversionsymmetries through their energy dispersion. We discover behaviors impossible inan isolated superconductor such as an equilibrium supercurrent that apparentlyviolates a no-go theorem and, at suitable topological defects, non-conservationof electric charge reminiscent of the chiral anomaly. The equilibriumsupercurrent is expected to be trainable by a helical electromagnetic field inthe normal state. Remarkably, if the band asymmetry exceeds the criticalcurrent of the parent superconductor in appropriate units, we predict a perfectsuperconducting diode effect with diode coefficient unity. We propose toroidalmetals such as UNi$_{4}$B and metals with directional scalar spin chiral orderas potential platforms.

Proximity-induced equilibrium supercurrent and perfect superconducting diode effect due to band asymmetry