Microwave study of superconducting Sn films above and below percolation

The electronic properties of superconducting Sn films ($T_c \approx$ 3.8 K) change significantly when reducing the film thickness down to a few nm, in particular close to the percolation threshold. The low-energy electrodynamics of such Sn samples can be probed via microwave spectroscopy, e.g. with superconducting stripline resonators. Here we study Sn thin films, deposited via thermal evaporation -ranging in thickness between 38 nm and 842 nm- which encompasses the percolation transition. We use superconducting Pb stripline resonators to probe the microwave response of these Sn films in a frequency range between 4 GHz and 20 GHz at temperatures from 7.2 K down to 1.5 K. The measured quality factor of the resonators decreases with rising temperature due to enhanced losses. As a function of the sample thickness we observe three regimes with significantly different properties: samples below percolation, i.e. ensembles of disconnected superconducting islands, exhibit dielectric properties with negligible losses, demonstrating that macroscopic current paths are required for appreciable dynamical conductivity of Sn at GHz frequencies. Thick Sn films, as the other limit, lead to low-loss resonances both above and below $T_c$ of Sn, as expected for bulk conductors. But in an intermediate thickness regime, just above percolation and with labyrinth-like morphology of the Sn, we observe a quite different behavior: the superconducting state has a microwave response similar to the thicker, completely covering films with low microwave losses; but the metallic state of these Sn films is so lossy that resonator operation is suppressed completely.