Superconducting diode effect and nonreciprocal transition lines

Nonreciprocity in superconductors is attracting much interest owing to its fundamental importance as well the potential applicability engineering. In this paper, we generalize previous theories of intrinsic superconducting diode effect (SDE) and microscopically elucidate relationship with nonreciprocity transition lines under supercurrent. We derive a general formula for SDE by using phenomenological Ginzburg-Landau theory thereby show that determined relative angle between magnetic field an effective anti-symmetric spin-orbit coupling defined from coefficients. The obtained offers convenient criterion obtain finite SDE. also study nonreciprocal phase transitions $s$-wave $d$-wave mean-field theory. It established sign reversal accompanied crossover helical superconductivity feature irrespective system details. temperature-magnetic-field diagram supercurrent, clarify generally accompanies crossings positive negative current directions. Furthermore, phases supercurrent even become re-entrant moderate strength electric current, implying current-induced first-order transitions. Our findings establish control parameter powerful probe properties related finite-momentum Cooper pairs.