Anomalous Microwave Response in YBCO Resonators beyond the Two-Level-System Model

Abstract

We report the microwave response of coplanar-waveguide (CPW) resonators fabricated from $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{7-\delta }$ (YBCO) thin films over temperatures from approximately $70\mathrm{mK}$ to $40\mathrm{K}$. The resonators exhibit internal quality factors $Q_{\mathrm{i}}$ in the range of $4\times 10^3$ to $10^4$ at 70 mK, which increase to a maximum of approximately $8\times 10^3$ to $1.2\times 10^4$ near $6\mathrm{K}$. At low temperatures, both $Q_{\mathrm{i}}$ and the fractional shift of the resonance frequency $\Delta f_{\mathrm{r}}/f_{\mathrm{r}}$ 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.

8 pages, 5 figures