Contribution of Residual Quasiparticles to the Characteristics of Superconducting Thin-Film Resonators

We studied the effect of these quasiparticles on the temperature and microwave power dependence of the characteristics of superconducting thin-film resonator, assuming that there are a significant number of quasiparticles in the superconductor even at
$T \ll T_c$
. It is demonstrated that the temperature dependence of both the internal quality factor and resonance frequency are well described by that of the normal conductivity of quasiparticles including the contributions from Kondo effect, phonon, and electron-electron scatterings. It also found that the readout microwave power dependence of the internal quality factor is well explained by the change of quasiparticle density due to the energy re-distribution of quasiparticles under microwave field in the resonator.