Conductivity coherence factors in the conventional superconductors Nb and Pb

We have performed microwave measurements at 60 GHz of the surface impedance (${\mathit{Z}}_{\mathit{s}}$=${\mathit{R}}_{\mathit{s}}$-${\mathit{iX}}_{\mathit{s}}$) on superconducting Nb and Pb. The temperature dependence of the complex conductivity (σ^=${\mathrm{\sigma }}_1$+i${\mathrm{\sigma }}_2$) is inferred from the data down to T/${\mathit{T}}_{\mathit{c}}$∼0.25 for both materials. The imaginary part, ${\mathrm{\sigma }}_2$(T), gives the temperature dependence of the superconducting gap and the real part, ${\mathrm{\sigma }}_1$(T), exhibits the predicted conductivity coherence peak below ${\mathit{T}}_{\mathit{c}}$. The findings are compared with the expressions calculated by Mattis and Bardeen to describe the electrodynamics of weak-coupling BCS superconductors. Furthermore, we calculate the complex conductivity within the framework of the standard Eliashberg electron-phonon theory of superconductivity. The experimental results obtained on Nb are in good agreement with the BCS weak-coupling theory while the data on Pb are analyzed in the anomalous (Pippard) limit and show deviations from BCS laws, accounted for only by the Eliashberg strong-coupling description of the electrodynamics of the superconducting state.