Critical current of a percolating superconductor

The critical current of a percolating superconductor is analyzed in the vicinity of the superconducting transition temperature and near the percolation threshold. The analysis is based on the Landau-Ginzburg formulation and on the self-similar fractal structure of the infinite cluster on a length scale smaller than the connectivity length ${\xi }_p$. The penetration depth of the percolating cluster is explicitly taken into consideration. The results are compared with previous theories and with experimental results. The dc paraconductivity above $T_c$ is discussed.