Superconducting Berry curvature dipole and dissipationless nonreciprocal responses

We reveal a superconducting Berry curvature dipole that arises from the cooperative effect of quantum geometry and the many-body collective motion of a superconductor. Critically, we find that superconducting Berry curvature dipole is sensitive to the phase of the superconducting gap parameter and encodes the the broken centrosymmetry of the pairing. This feature leads to a an unconventional Berry curvature dipole proximity wherein superconducting Berry curvature dipole (and its attendant nonreciprocal responses) can be proximitized even in a centrosymmetric. Strikingly, we superconducting Berry curvature dipole produces a range of non-dissipative and giant non-reciprocal responses such as second-order nonlinearity that outstrips that found in metals. This makes noncentrosymmetric superconductors an attractive platform for exploiting pronounced BCD nonlinearities as well as opens nonlinear response as an unconventional way of diagnosing the fine structure of the superconducting gap.