Superconducting fluctuations in a thin NbN film probed by the Hall effect

We present a comprehensive study of how superconducting fluctuations in the normal state contribute to the conductivity tensor in a thin (119 $\AA$) film of NbN. It is shown how these fluctuations drive a sign change in the Hall coefficient $R_\mathrm{H}$ for low magnetic fields near the superconducting transition. The scaling behaviours as a function of distance to the transition $\epsilon=\ln(T/T_\mathrm{c})$ of the longitudinal ($\sigma_\mathrm{xx}$) and transverse ($\sigma_\mathrm{xy}$) conductivity is found to be consistent with Gaussian fluctuation theory. Moreover, excellent quantitative agreement between theory and experiment is obtained without any adjustable parameters. Our experimental results thus provide a case study of the conductivity tensor originating from short-lived Cooper pairs.