Anomalous Temperature Dependence of the Quality Factor in a Superconducting Coplanar Waveguide Resonator

We present the measurements of the temperature dependence of the internal quality factor (Q_i) of a microwave resonator, well below the superconducting transition temperature. The device is a quarter-wavelength niobium (T_c=9.2 K) coplanar waveguide resonator. The measured |S₂₁| parameter shows typically the skewed Lorentzian distributions, from which the fitted quality factor monotonically decreases with the temperature increasing from 30 mK to 900 mK. It is observed that for the lower temperature range (i.e., at T<700 mK) the temperature dependence of the fitted Q_i deviates significantly from the predictions of the usual Mattis–Bardeen theory. The measured 3 dB internal quality factor Q'_i also verifies such an anomalous temperature dependence. Physically, this phenomenon could be attributed dominantly to the effects of the two-level systems in the device, rather than the usual temperature-dependent complex conductance.