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

Abstract

The resistive transition $\ensuremath{\rho}(T,H)$ 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 ${f}_{p}$ and of the zero-resisitivity threshold ${f}_{0}.$ The model describes successfully the experimental $\ensuremath{\rho}(T,H)$ dependence at different relative directions of the c axis, the current j and the magnetic field H in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8\ensuremath{-}x}$ 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 $H<750\mathrm{Oe}.$ This results in the appearance of the field-induced excess resistivity $\ensuremath{\Delta}\ensuremath{\rho}$ that obeys the dependence $1/\ensuremath{\Delta}\ensuremath{\rho}\ensuremath{\simeq}{1+H}_{\ensuremath{\varphi}}/H,$ where ${H}_{\ensuremath{\varphi}}$ is the characteristic field trapped by a single Josephson contact.