Non-reciprocity in low-symmetry superconductors*

On the time-reversal and spatial symmetry grounds, the noncentrosymmetric superconductors can exhibit the supercurrents, superconducting diode and non-reciprocity effects of an intrinsic origin. The currents in an equilibrium vanish in a simply connected superconductors or normal metals. Even when the external current flows, the Lifshits invariants linear in the Cooper pair momentum cannot result in non-reciprocity in uniform superconductors. We derive the nonreciprocity effects due to intrinsic spin-orbit and Zeemann coupling microscopically at low temperatures and near the critical temperature and demonstrate their origin in superconductors with low symmetry. The linear Rashba and Dressselhaus interactions in the electorn spectrum result in the odd-power terms of higher order in the Cooper pair momentum in the Cooperon/Fluctuations propagator in the presence of the magnetic Zeemann coupling.The odd-power terms result in nonreciprocity in the critical current and kinetical inductance. The cubic in momentum Dresselhaus terms in the electron spectum also contribute to nonreciprocity. The presence of Dresselhaus- and Rashba-induced contributions to non-reciprocity result in strong anisotropy of nonreciprocal signals, particularly in proximitized noncentrosymmetric materials.