Nonlinear surface impedance Z(T,f,Hrf) of Tl-Ba-Ca-Cu-O thin films

YBa₂Cu₃O₇ (YBCO) film quality has reached a stage enabling rf applications at T≤80 K. Higher operating temperatures or better power handling are very much desired. Tl₂Ba₂CaCu₂O₈ (Tl-2212) is a perfect candidate with its higher transition temperature T_c>100 K. We studied the rf field dependence of the impedance Z_s of epitaxial Tl-2212, which shows already surface resistances at low fields superior to YBCO and promising power handling with a nonlinearity onset above μ₀H^*≃3 mT. Defective Tl-2212 films show anomalous nonlinear behavior for μ₀H_rf≤μ₀H^*∼0.3 to 1 mT, extremely pronounced at T<40 K, indicating the presence of very weak-links yielding flux-flow, followed at higher fields μ₀H_rf≥0.5 mT by hysteresis losses with a linear field dependence δR_s(H_rf)∞H_rf. Better quality Tl-2212 films show δR_s(H_rf)∞H_rf² up to fields of about 5 to 10 mT. The δR_s(H_rf)∞H_rfⁿ (n=1,2) dependencies together with the ratios r(T)=δX_s/δR_s∼1 to 10 hint to hysteresis losses of Josephson fluxons enhanced by slits or holes in the films.