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Pairing Fluctuation AC Conductivity of Disordered Thin Films

We study temperature $T$ and frequency $ω$ dependence of the in-plane fluctuation conductivity of a disordered superconducting film above the critical temperature. Our calculation is based on the nonlinear sigma model within the Keldysh technique. The fluctuation contributions of different physical origin are found and analyzed in a wide frequency range. In the low-frequency range, $ω\ll T$, we reproduce the known leading terms and find additional subleading ones in the Aslamazov-Larkin and the Maki-Thompson contributions to the ac conductivity. We also calculate the density of states ac correction. In the dc case these contributions logarithmically depend on the Ginzburg-Landau rate and are considerably smaller that the leading ones. However, in the ac case an external finite-frequency electromagnetic field strongly suppresses the known Alsamazov-Larkin and Maki-Thompson ac contributions, while the corresponding new terms and the density of states contribution are weakly suppressed and therefore become relevant at finite frequencies.