Superconductivity on networks : II. The London approach

Abstract

The magnetic energies and critical fields of networks of thin wires are calculated for the square net and the Sierpinski gasket and the results are applied to percolation clusters. The results are obtained by a systematic expansion of the Landau Ginzburg equations around the constant amplitude London limit. The role of flux quantization and local critical currents are included in a systematic way. For percolation we assume a short distance self similar fractal structure of the clusters with proper crossovers and inclusion of the Stauffer cluster distribution. Simple scaling forms for the magnetic energy and for the superconducting coherence length, and for the critical field of finite clusters and of the infinite cluster are obtained. The results are compared with other studies of the same problem and the origin of the discrepancies is discussed. We also discuss existing experiments and suggest some new experimental approaches