Vortex Motion and Quasiparticle Resistivity in Superconductors at Microwave Frequencies

At nonzero frequencies both the normal and superfluid fractions, as well as moving vortices, contribute to the electrical transport, resulting in intricate expressions for the resistivity. We present an extended study of microwave resistivity data measured on YBa$\text{}_{2}$Cu$\text{}_{3}$O$\text{}_{7-δ}$, SmBa$\text{}_{2}$ Cu$\text{}_{3}$O$\text{}_{7-δ}$, and MgB$\text{}_{2}$ by means of a broad-band technique between 2 and 20 GHz and of a resonant system at 50 GHz. We discuss the main experimental fingerprints that allow one to identify the relevance of the different contributions from the measured microwave response as a function of frequency, temperature, and magnetic field. We show that the field-dependent superfluid/quasiparticles dynamics cannot be in general neglected with respect to the vortex motion, albeit its relative importance is different in different materials: in high temperature superconductors vortex motion prevails at high fields, but at low fields a significant superfluid/quasiparticle contribution exists (ascribed to the presence of lines of nodes). In MgB$\text{}_{2}$ the two contributions are comparable even at high fields. In this general frame, we derive from the measurements vortex and superfluid parameters in agreement with theoretical predictions and independent measurements.