Microstructure dependence of the critical current density of superconducting granular systems

We analyse the dependence of the critical current density Jc of granular superconductors from the grain dimensions by means of a Josephson junctions network description of this class of material. In the analysis of the physical properties of these superconducting systems, the Josephson junctions network approach is justified by the presence of weak superconducting coupling between adjacent grains. In particular, starting from an idealised two-dimensional square lattice of identical cylindrical grains, we adopt, as a model, a two dimensional square network of inductively coupled Josephson junction. From the knowledge of the Josephson coupling energy of a single junction, we give the expression of the effective Jc of the whole system, taking into account the co-operative effect of the junctions in the network. We find that the effective critical current density depends on the microstructural properties of the sample in a non-trivial way.