Electromagnetic response of high-Tcsuperconductors

The effective-medium approach is used to calculate the penetration depth, surface resistance, and infrared reflectivity of materials consisting of uniaxial grains embedded in an isotropic background. The grains are taken to be superconducting in the ab plane. The mean-free-path dependence of the ac conductivity in the superconducting state is explicitly taken into account. In the c direction the grains are assumed to be either insulating or poorly conducting. The background is either insulating or normal conducting. In the normal state, all conductivities reduce to Drude expressions. This model should present a reasonable description of high-${\mathit{T}}_{\mathit{c}}$ materials. We predict an increase in the penetration depth by a temperature-independent scale factor. The microwave surface resistance can be fitted, if the samples contain 10–20 % of a background material that is a good conductor. This assumption would also explain the less than perfect reflectivity below the absorption edge. If the background is a dielectric, then the absorption edge appears to be shifted to lower frequencies due to void resonances. The shift of this apparent absorption edge with temperature is less than predicted by BCS theory. There seems to be no way to explain large energy gaps sometimes observed in ir reflectivity by invoking granularity.