Effect of superconducting fluctuations on nonreciprocal dichroism and gyrotropy

We study the spatially dispersive conductivity of a two-dimensional noncentrosymmetric superconductor, demonstrating that it acquires a nonreciprocal, odd-in-wavevector component from fluctuation-induced Cooper pairs above the critical temperature $T_c$. Utilizing time-dependent Ginzburg-Landau theory generalized to include particle-hole asymmetry and the cubic Lifshitz invariant of trigonal superconductors, we compute the Aslamazov-Larkin contribution to the gyrotropic conductivity in closed form, including its complete frequency dependence. The dissipative part describes nonreciprocal directional dichroism: it is odd in frequency and displays a nonmonotonic dependence, peaking at frequencies comparable to the decay rate of fluctuating Cooper pairs. Its Kramers-Kronig dual component describes gyrotropic birefringence, which remains finite in the static limit and is strongly enhanced as the temperature approaches $T_c$. Both effects require simultaneously broken inversion and time-reversal symmetries, are dependent on particle-hole asymmetry in close analogy to the fluctuation Hall effect, and trace to the same asymmetric Cooper-pair dispersion responsible for the superconducting diode effect and the giant magnetochiral anisotropy observed near $T_c$. This critical enhancement dominates over the smooth normal-state gyrotropy, which we evaluate for the same band model as a baseline. Finally, we frame our analysis within the context of gated transition metal dichalcogenides like MoS$_2$, discussing the implications for probing superconducting dynamics through nitrogen-vacancy-center quantum noise spectroscopy.