Critical currents of composite superconductors: Model calculations

We calculate the I-V characteristics of composite superconductors modeled as random three-dimensional arrays of resistively shunted Josephson junctions at zero temperature, in zero and finite applied magnetic fields. Two types of disorder are considered: site dilution of a simple cubic lattice to a concentration p and a random displacement of grains in an ordered lattice. In the site-diluted lattice, we find that there exists a critical current density Jc(p), below which the voltage becomes very small, and which varies as a power law in (p-pc), Jc(p){∝}(p-pc{)}ᵛwith v1.7, in agreement with previous static estimates and in qualitative agreement with experimental studies on Ag/{YBa}₂Cu₃{O}_{7{{-}}{{δ}}}$ composites. Near the percolation threshold ${p}c$, we find a scaling relation between the current density J and the electric field E, analogous to that proposed by Fisher et al. near the vortex-glass transition in superconductors with microscopic disorder. In the presence of an applied magnetic field, we find numerically that the critical current initially decreases with field, then reaches a plateau. We present qualitative arguments to estimate both the crossover field HX at which the plateau is approached, and the value of the critical current density on the plateau. Possible connections between these results and the large plateau fields and critical currents observed by Sato et al. [IEEE Trans. Magn. MAG-27, 1231 (1991)] are discussed.