Far-Infrared Absorption in Thin Superconducting Lead Films

Abstract

We describe measurements of the far-infrared conductivity ${\ensuremath{\sigma}}_{1}\ensuremath{-}i{\ensuremath{\sigma}}_{2}$ of thin superconducting lead films with resistances of about $\frac{200\ensuremath{\Omega}}{\mathrm{square}}$ in the normal state. The conductivity is inferred from measurements of the transmittance and reflectance of a thin film of lead which has been evaporatively deposited on a quartz crystal. We report results for the real part of the conductivity of lead over the frequency range 9 to 120 ${\mathrm{cm}}^{\ensuremath{-}1}$. From these we infer an energy gap for lead films at $T=0$ of 22.5\ifmmode\pm\else\textpm\fi{}0.5 ${\mathrm{cm}}^{\ensuremath{-}1}$, or $(4.5\ifmmode\pm\else\textpm\fi{}0.1)k{T}_{c}$, where $k$ is the Boltzmann constant and ${T}_{c}$ is the superconducting transition temperature. The measurements were made at 2.0, 4.3, and 5.5\ifmmode^\circ\else\textdegree\fi{}K, and the energy gap varies with temperature in the manner predicted by the Bardeen-Cooper-Schrieffer theory. The frequency dependence of the real part of the conductivity also is in good agreement with the theory. No evidence is found of the strong precursor absorption which had been previously reported in the energy gap in lead, but ${\ensuremath{\sigma}}_{2}$ is found to be anomalously low (by \ensuremath{\sim}25%) near and below the gap frequency. This is believed to result from the strong-coupling anomalies discussed by Nam. This anomalously low ${\ensuremath{\sigma}}_{2}$ would also account for the anomalously steep absorption edge observed in other experiments on lead.