Frequency Dependence of the Surface Resistance of Superconducting Tin in the Millimeter Wavelength Region

Abstract

The ratio of the superconducting to normal surface resistance of polycrystalline tin has been measured at seven frequencies between 17 kMc/sec and 77 kMc/sec and at temperatures from 1.5\ifmmode^\circ\else\textdegree\fi{}K to 3.0\ifmmode^\circ\else\textdegree\fi{}K. These data plus those of other investigators have been compared with the predictions of two theories: the first a calculation made by Serber (unpublished) based on the London two-fluid model of superconductivity and the Reuter-Sondheimer theory of the anomalous skin effect, and the second a calculation based on the Bardeen-Cooper-Schrieffer theory as developed by Bardeen and Mattis.Agreement between experimental and theoretical results is only fair in the case of the two-fluid theory. The best values of the relevant parameters, Fermi velocity $v$ and mean free path $l$, were found to be, respectively, (1.25\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}${10}^{7}$ cm/sec and ${10}^{\ensuremath{-}3}$\ensuremath{\rightarrow}${10}^{\ensuremath{-}1}$ cm. A value of $v$ of approximately ${10}^{8}$ cm/sec would be expected for tin. The surface resistance ratio from the Bardeen-Cooper-Schrieffer theory has been calculated only for the extreme anomalous limit and the calculation therefore should not apply too accurately for tin. However, a curve of the right general shape is obtained and further calculations more appropriate to tin should improve the agreement between theory and experiment.