Electrical Conductivity in Pure Type-II Superconductors nearHc2

The electrical conductivity for a pure type-II superconductor in high magnetic fields near $H_{c2\mathrm{}}$ is calculated for frequencies and relaxation times that satisfy the limit $\omega \tau >1\mathrm{}$. The conductivity in the absence of fluctuations, i.e., with a static vortex lattice, is calculated in a manner similar to the procedure used by Brandt, Pesch, and Tewordt to obtain the density of states. This direct approach allows us to bypass an ansatz made by Maki for the purpose of calculating transport properties of pure type-II superconductors. The fluctuations of the order parameter are included in the theory by using the calculation by Caroli and Maki of the conductivity due to fluctuations. In the Pippard limit, the conductivity is calculated numerically. From the conductivity, results for the surface resistance are obtained. The theory predicts that, as the magnetic field is lowered below $H_{c2\mathrm{}}$, a highly frequency-dependent decrease in the surface resistance occurs, especially for frequencies in the neighborhood of 0.5 GHz. This frequency dependence is not present in the surface resistance calculated by Caroli and Maki. For frequencies in the megahertz region, where experimental measurements have been made, the theory predicts a sharper decrease in $\frac{R_s}{R_n}$ than is observed experimentally. It is pointed out, however, that for these frequencies the limit $\omega \tau >1\mathrm{}$ is not valid, and higher-frequency measurements are necessary for direct comparison to the theory. The effects on the surface resistance of a smearing-out of the vortex lattice near $H_{c2\mathrm{}}$ are also determined numerically by inserting a phenomenological delocalization factor.