Transverse Electromagnetic Standing Waves: A New Length Scale in Superconducting Thin Films

Abstract

The resonance condition for transverse standing waves in superconducting thin films is derived and shown to relate the film's thickness (d) to its material parameters. Surface reactance (Xs) data are shown to be important in interpreting the surface resistance (Rs) data: their relative magnitude bears on the detectability of these standing wave resonances. The periodicity of these resonant thicknesses of otherwise identical films (Δ d) is a new length scale in superconductors and is given by \(\Delta d = {{ - \pi \left| {\tilde \lambda } \right|^2 } \mathord{\left/ {\vphantom {{ - \pi \left| {\tilde \lambda } \right|^2 } {\Im \left( {\tilde \lambda } \right)}}} \right. \kern-\nulldelimiterspace} {\Im \left( {\tilde \lambda } \right)}}\), where \({\tilde \lambda }\) is the complex electromagnetic penetration depth of the superconducting thin film. Many signatures of these standing waves, including an oscillatory transition temperature (Tc) vs. d and an anticorrelation between Tc and the normal state resistance—as a function of the film thickness—collaborate with data reported in the literature. It is important to delineate the contribution of this length scale in superconducting thin-film data that has been known for more than 30 years as, inter alia, the quantum-size effect, the Wyatt–Dayem effect, nonequilibrium superconductivity, and the Carlson–Goldman mode. This is the first report to suggest these standing waves are a possible origin to these phenomena. To further test if noted experimental data are consistent with the standing waves discussed herein, Xs experiments to compliment Rs experiments are proposed.