High-Field Surface Impedance of Dirty Type-II Superconductors in the Vortex State

Surface-impedance data, obtained in the vortex state of dirty type-II superconductors, are presented. In the geometry considered, the dc magnetic field H is perpendicular to the sample surface. The data are explained in terms of the mechanism of flux-flow resistance. A theoretical expression is derived which predicts a frequency-independent surface resistance $R\left(H\right)\mathrm{}$ in the vicinity of the upper critical field $H_{c2\mathrm{}}$. This theoretical expression accounts well for the experimental $R\left(H\right)\mathrm{}$ data at temperatures such that the microwave energy $\hslash \omega$ is below the intrinsic pair-breaking energy ${\epsilon }_0\mathrm{}\left(t\right)\mathrm{}$. The quantitative comparison of experiments and theory indicates that strong-coupling effects can be taken into account, replacing the weak-coupling relation ${\left(4\mathrm{}\pi \sigma D\right)}^{-1\mathrm{}}=4\mathrm{}{{\kappa }_1}^2\mathrm{}\left(0\right)=4\mathrm{}{{\kappa }_2}^2\mathrm{}\left(0\right)\mathrm{}$ by ${\left(4\mathrm{}\pi \sigma D\right)}^{-1\mathrm{}}=4\mathrm{}{{\kappa }_2}^2\mathrm{}\left(0\right)\mathrm{}\ne 4{{\kappa }_1}^2\mathrm{}\left(0\right)\mathrm{}$. At high temperatures, when $\hslash \omega \geqq {\epsilon }_0\mathrm{}\left(t\right)\mathrm{}$, the absorption is larger than predicted by the flux-flow mechanism, because near $T_c$ dynamical fluctuations of the order parameter provide an additional, frequency-dependent mechanism of absorption. This is satisfactorily accounted for if one retains the frequency-dependent terms in the expression derived for the conductivity.