Dynamic fluctuations in the superconductivity of NbN films from microwave conductivity measurements
We have measured the frequency and temperature dependences of complex ac conductivity, σ(ω)=σ_1(ω)-iσ_2(ω), of NbN films in zero magnetic field between 0.1 to 10 GHz using a microwave broadband technique. In the vicinity of superconducting critical temperature, Tc, both σ_1(ω) and σ_2(ω) showed a rapid increase in the low frequency limit owing to the fluctuation effect of superconductivity. For the films thinner than 300 nm, frequency and temperature dependences of fluctuation conductivity, σ(ω,T), were successfully scaled onto one scaling function, which was consistent with the Aslamazov and Larkin model for two dimensional (2D) cases. For thicker films, σ(ω,T) data could not be scaled, but indicated that the dimensional crossover from three dimensions (3D) to 2D occurred as the temperature approached Tc from above. This provides a good reference of ac fluctuation conductivity for more exotic superconductors of current interest.