Magnetic-field dependence of the surface impedance in the mixed state of type-II superconductors

The surface impedance of type-II superconductors in the mixed state has been measured as a function of the magnetic field in the low-frequency limit. At the low magnetic fields close to the lower critical field the surface impedance was observed to be proportional to the vortex density, whereas at higher fields a crossover to the square-root dependence on the vortex density was observed. This behavior agrees with the two-mode electrodynamics in which the penetration of electromagnetic fields into the superconductor in the mixed state is governed by two space scales: (i) the skin-layer width, and (ii) the screening length of the order of the intervortex distance arising from the elasticity of the vortex array.