Measurements of Microwave Vortex Response in DC Magnetic Fields in Tl$_2$Ba$_2$CaCu$_2$O$_{8+x}$ Films

There is a renewed interest in superconductors for high-frequency applications, leading to a reconsideration of already known low-T
_c
, and high-T
_c
materials. In this view, we present an experimental investigation of the millimeter-wave response in moderate magnetic fields of Tl
₂
Ba
₂
CaCu
₂
O
_8+x
superconducting films with the aim of identifying the mechanisms of the vortex-motion-induced response. We measure the dc magnetic-field-dependent change of the surface impedance, ΔZ
₈
(H) = ΔR
₈
(H) + iΔX
₈
(H) at 48 GHz by means of the dielectric resonator method. We find that the overall response is made up of several contributions, with different weights depending on the temperature and field: a possible contribution from Josephson or Abrikosov-Josephson fluxons at low fields; a seemingly conventional vortex dynamics at higher fields; a significant pair breaking in the temperature region close to T
_c
. We extract the vortex motion depinning frequency f
_p
, which attains surprisingly high values. However, by exploiting the generalized model for relaxational dynamics we show that this result comes from a combination of a pinning constant k
_p
arising from moderate pinning, and a vortex viscosity η with anomalously small values. This latter fact, implying large dissipation, is likely a result from a peculiar microscopic structure and thus poses severe limits to the application of Tl
₂
Ba
₂
CaCu
₂
O
_8+x
in a magnetic field.