Microwave impedance of thin-film superconductor–normal metal hybrid structures with a high conductivity ratio

The temperature dependence of the linear electrodynamic response of thin-film superconductor (MoN)–normal metal (Al) hybrid structures with a high conductivity ratio in the normal state has been theoretically and experimentally investigated. Low-frequency measurements of the coefficient of mutual induction of two coils with a sample placed between them indicate an increase in the magnetic screening of the superconductor–normal metal (SN) structures with an increase in the Al layer thickness $d_{\mathrm{Al}}$ near liquid-helium temperatures. Measurements of the frequency shift $\delta f$ of a microwave dielectric resonator, brought into contact with the sample, as a function of temperature and $d_{\mathrm{Al}}$ showed that (i) the character of the dependence $\delta f(T)$ depends strongly on $d_{\mathrm{Al}}$ and (ii) the resonance frequency shift of SN structures at temperatures close to the critical temperature $T_c$ is not described by dependence $\operatorname{const}/(1-T/T_{c})$, which is typical of thin superconducting films. Numerical calculations performed within the Usadel model well describe the observed effects. Thus, these anomalies of the electrodynamic properties of SN structures can be explained by the presence of a minigap in the spectrum of quasiparticles due to the proximity effect in a normal-metal layer, which depends on $d_{\mathrm{Al}}$, and by the high conductivity of the Al layer.