Characteristics of Very High Q Nb Superconducting Resonators for Microwave Kinetic Inductance Detectors

We have prepared superconducting resonators using high-quality Nb thin films with $RRR = 48$ and studied their resonance characteristics in detail. It was observed that the measured internal quality factor $Q_i$ reached as high as $4\times 10^7$, which might be the highest value obtained among the Nb thin film superconducting resonators ever reported. It is demonstrated that the temperature dependence of the internal quality factors can be well explained by considering the temperature dependence of the residual resistance due to phonon scattering, electron–electron scattering, and the Kondo effect of the residual quasiparticle in addition to the extended Mattis–Bardeen theory. It is also found that the change of the resonance frequency of the Nb thin film resonator with respect to temperature can be well explained by considering the temperature dependence of both the Kondo effect and the kinetic inductance of the residual quasiparticles. These results strongly indicate that a finite number of quasiparticles are present in the superconducting gap of the high-quality Nb film even at a sufficiently low temperature of $T/T_c < 0.15$ and form a Fermi liquid state.