Random mixtures with orientational order, and the anisotropic resistivity tensor of high-Tc superconductors

By generalizing effective-medium theory to the case of orientationally ordered but positionally disordered two-component mixtures, it is shown that the anisotropic dielectric tensor of oxide superconductors can be extracted from microwave measurements on oriented crystallites of YBa, Cu, 0, _ x embedded in epoxy. Surprisingly, this technique appears to be the only one which can access the resistivity perpendicular to the copper-oxide planes in crystallites that are too small for depositing electrodes. This possibility arises in part because the real part of the dielectric constant of oxide superconductors has a large magnitude. The validity of the effective-medium approach for orientationally ordered mixtures is corroborated by simulations on two-dimensional anisotropic random resistor networks. Analysis of the experimental data suggests that the zero-temperature limit of the finite-frequency resistivity does not vanish along the c axis, a result which would imply the existence of states at the Fermi surface, even in the superconducting state.