Microwave surface impedance of proximity-coupled Nb/Al bilayer films

Abstract

The surface resistance and magnetic penetration depth in proximity-coupled superconductor/normal-metal (Nb/Al) bilayers are examined to study the electrodynamics of layered structures with spatially inhomogeneous superconducting order parameter. The effective penetration depth ${\ensuremath{\lambda}}_{\mathrm{eff}}$(T) obeys \ensuremath{\Delta}${\ensuremath{\lambda}}_{\mathrm{eff}}$(T)\ensuremath{\sim}${\mathit{T}}^{\mathit{n}}$, where n\ensuremath{\le}1, at low temperatures, distinctly different from the exponential behavior of Nb. An accompanying drop in the surface resistance ${\mathit{R}}_{\mathit{s}}$ occurs in the same temperature range. A model of the bilayer electrodynamics explicitly including the effects of proximity coupling is developed, and the behavior of both ${\ensuremath{\lambda}}_{\mathrm{eff}}$ and ${\mathit{R}}_{\mathit{s}}$ is consistently described. We find that a treatment of coherence effects in the proximity-coupled normal-metal layer is necessary to properly describe the behavior of ${\mathit{R}}_{\mathit{s}}$(T).