Resistive transition anisotropy in superconducting granular ceramics: Interplay of effective medium approximation and percolation

The resistive transition p(T,H) in granular high-T_c superconductors is described by a combination of the effective-medium approximation for anisotropic mixtures with the percolation theory. We found a single parameter accounting for both the structural anisotropy as well as for the intrinsic resistivity anisotropy of a single grain. We obtained a direct (no fitting parameters) estimate of the superconducting volume fraction f as a function of temperature, as well as of the percolation threshold f_ρ and of the zero-resisitivity threshold f₀. The model describes successfully the experimental ρ(T,H) dependence at different relative directions of the c axis, the current j and the magnetic field H in Bi₂Sr₂CaCu₂O_8-x ceramics. We provided estimates for the value of the Josephson critical current between grains. The latter proves to be strongly suppressed even by weak magnetic fields H < 750 Oe. This results in the appearance of the field-induced excess resistivity Δρ that obeys the dependence 1/Δρ≃1+H_φ/H, where H_φ is the characteristic field trapped by a single Josephson contact.