Anomalous microwave response in YBa 2 Cu 3 O 7 − δ resonators beyond the two-level-system model

We report the microwave response of coplanar-waveguide (CPW) resonators fabricated from YBa₂Cu₃O7-δ (YBCO) thin films over temperatures from approximately 70~mK to 40~K. The resonators exhibit internal quality factors Qᵢ in the range of 4×10³ to 10⁴ at 70 mK, which increase to a maximum of approximately 8×10³ to 1.2×10⁴ near 6~K. At low temperatures, both Qᵢ and the fractional shift of the resonance frequency Δfᵣ/fᵣ increases with temperature, qualitatively resembling behavior commonly associated with two-level-system (TLS) defects. However, neither response saturates on the temperature scale set by the resonator frequency, and the loss exhibits no observable microwave-power dependence. We show that low-temperature frequency upturn may be better described by an additional paramagnetic response associated with defect-induced local moments or Andreev bound states, while the low-temperature loss follows an approximately logarithmic temperature dependence whose microscopic origin remains unresolved. These measurements establish the millikelvin performance of patterned YBCO resonators and show that their low-temperature response cannot be understood within the conventional TLS framework alone.