Fluctuation nonlinear responses below the superconducting transition

Determine how the photogalvanic effect, second-harmonic generation, and photovoltaic Hall currents of fluctuating Cooper pairs transform across the superconducting transition below $T_c$, including which divergences are cut off by the established condensate and what replaces dephasing regularization of the Maki–Thompson channel.

Background

The paper develops a time-dependent Ginzburg–Landau theory for nonlinear optical and transport responses of two-dimensional noncentrosymmetric superconductors above TcT_c. It treats Aslamazov–Larkin and Maki–Thompson fluctuation channels, thermodynamic and kinetic Lifshitz invariants, photogalvanic and second-harmonic responses, and the photovoltaic Hall effect.

The analysis is restricted to the fluctuation regime above the transition. Below TcT_c, a well-established condensate coexists with fluctuations, requiring a theory that connects the fluctuation channels to condensate and collective-mode responses, including nonreciprocal superfluid weight, Higgs and phase modes, and finite-momentum electrodynamics. The unresolved problem also includes identifying the behavior of the response divergences and the mechanism that replaces dephasing regularization of the Maki–Thompson contribution.

References

A question we regard as both natural and, to our knowledge, not rigorously answered is the fate of these responses below $T_c$: once a well-established condensate coexists with the fluctuations, the AL and MT channels must evolve into condensate and collective-mode responses, nonreciprocal superfluid weight, Higgs and phase-mode contributions, and their finite-momentum electrodynamics, and how the PGE, SHG, and photovoltaic Hall currents computed here transform across the transition, which divergences are cut by the condensate, and what replaces the dephasing regularization of the MT channel, remain open problems that we leave for future work.

— Photogalvanic transport of nonreciprocal Cooper-pair fluctuations  (2608.20166 - Miranda et al., 20 Aug 2026) in Summary and outlook, Section 7 (immediately before the paragraph beginning “The finite-momentum generalization”)