Effect of the Energy Gap on the Penetration Depth of Superconductors

Abstract

The dependence on temperature of the penetration depth of superconducting tin crystals has been measured by a new low-frequency (100 kc/sec) method. The sample serves as the core of a solenoid whose inductance changes with the penetration depth. The inductance controls the frequency of an oscillator which can be measured precisely. It is found that there are departures from the law $\ensuremath{\lambda}={\ensuremath{\lambda}}_{0}{[1\ensuremath{-}{(\frac{T}{{T}_{c}})}^{4}]}^{\frac{1}{2}}$ derived from the Gorter-Casimir two-fluid theory. The departures are shown to arise from an energy gap in the spectrum of electron excitations and are qualitatively like those predicted by Lewis' extension of the two-fluid model to include a gap. Throughout the temperature range from 1.8\ifmmode^\circ\else\textdegree\fi{}K to 3.69\ifmmode^\circ\else\textdegree\fi{}K the measured penetration depths agree well with the theory of Bardeen, Cooper, and Schrieffer.