Anisotropic electrical conductivity tensor of granular high-Tc superconductors in an effective-medium theory

The earliest high-Tc oxide superconductors were generally studied in the form of porous polycrystalline pellets. As material preparation technology improved, resulting in samples with orientational order and a smaller concentration of impurity phases, the effects of granular behaviour did not disappear. In both the cases of disordered and partially-ordered structures, an important question arises as to how to interpret measured low-field resistivities in terms of the underlying anisotropic single-crystal values. This paper provides the answer to this question within the context of an effective-medium theory. Our version of the effective-medium approximation attempts to describe the electrical properties of an inhomogeneous medium, consisting of a mixture of several types of anisotropic polycrystals with different degrees of orientational order.