Percolation thresholds in granular films: non-universality and critical current

The results are reported which should be applicable to the percolation threshold seen in the low temperature properties of inhomogeneous superconductors as the fraction of superconducting material is varied. First, we introduce a simplified model for the deposition of granular films, with an interaction enegy favoring the formation of metal clumps. The percolation problem defined on random samples prepared by this process is nonuniversal: critical exponents are continuous functions of the interaction strength and fiffer from the conventional values. Second, we treat the critical current, using the network model introduced recently by Deutscher and Rappaport[1], and by Huse and Guyer[2], neglecting the effects of structural correlation. Results are presented for 2D and 3D networks. In the course of these calculations, e have obtained a measure of the ’’tortuousity’’ of percolation paths close to threshold. Both results are conveniently expressed in terms of the percolation coherence length, ξp. The critica...