Estimation of the Josephson critical current of a single grain: percolation model of the resistive transition

The granular HTS is treated here as a S-N mixture. Experimental data are used to determine the percolation threshold f0 (the volume fraction of superconducting grains at zero resistance) and fp (corresponding to the appearance of the first spanning superconducting cluster). The latter consists of percolating channels, each carrying the Josephson critical current Ich. We demonstrate that, knowing f0 and fp as well as the morphology and orientation of the grains, one can derive realistic estimates of Ich. This is realized by assuming a parallel resistive combination, one resistor being the spanning superconducting cluster, the other the nonspanning network. The former is treated as a percolation problem while the later is described within the effective-medium theory