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There is a renewed interest in superconductors for high-frequencyapplications, leading to a reconsideration of already known low-$T_c$ andhigh-$T_c$ materials. In this view, we present an experimental investigation ofthe millimeter-wave response in moderate magnetic fields ofTl$_2$Ba$_2$CaCu$_2$O$_{8+x}$ superconducting films with the aim of identifyingthe mechanisms of the vortex-motion-induced response. We measure the dcmagnetic-field-dependent change of the surface impedance, $\Delta Z_s(H) =\Delta R_s(H) + i\Delta X_s(H)$ at 48 GHz by means of the dielectric resonatormethod. We find that the overall response is made up of several contributions,with different weights depending on the temperature and field: a possiblecontribution from Josephson or Abrikosov-Josephson fluxons at low fields; aseemingly conventional vortex dynamics at higher fields; a significant pairbreaking in the temperature region close to $T_c$. We extract the vortex motiondepinning frequency $f_p$, which attains surprisingly high values. However, byexploiting the generalized model for relaxational dynamics we show that thisresult come from a combination of a pinning constant $k_p$ arising frommoderate pinning, and a vortex viscosity $\eta$ with anomalously small values.This latter fact, implying large dissipation, is likely a result from apeculiar microscopic structure and thus poses severe limits to the applicationof Tl$_2$Ba$_2$CaCu$_2$O$_{8+x}$ in a magnetic field.

Measurements of microwave vortex response in dc magnetic fields in Tl$_2$Ba$_2$CaCu$_2$O$_{8+x}$ films