DC magnetic field dependence of the surface impedance in superconducting parallel plate transmission line resonators

The authors have measured the real and imaginary parts of the surface impedance of cuprate superconducting films in the parallel plate resonator geometry at 11 GHz as a function of perpendicular DC magnetic field. Above a temperature-dependent crossover field, a linear increase of the surface resistance and reactance with field, up to 4 kG, is found. The authors extract the microscopic vortex dynamical parameters-the viscosity and the pinning-potential restoring force constant-along with their temperature dependences, using the low-temperature and low-field limit of the unified model of M.W. Coffey and J.R. Clem (1991). It is found that the pinning frequency is above 40 GHz for temperatures below 60 K. Consequently, a complete understanding of the field dependence of the microwave surface impedance of the cuprates must include both vortex pinning and viscosity. The vortex viscosity is temperature dependent and, in the context of the Bardeen-Stephen model, is consistent with a temperature-dependent normal-state resistivity below T/sub c/.<>