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Superconductor-insulator transition in a network of 2d percolation clusters

In this paper we characterize the superconductor-insulator phase transition on a network of 2d percolation clusters. Sufficiently close to the percolation threshold, this network has a broad degree distribution, and at p=p_c the degree distribution becomes scale-free. We study the Transverse Ising Model on this complex topology in order to characterize the superconductor-insulator transition in a network formed by 2d percolation clusters of a superconductor material. We show, by a mean-field treatment, that the critical temperature of superconductivity depends on the maximal eigenvalue of the adjacency matrix of the network. At the percolation threshold, we find that the maximal eigenvalue of the adjacency matrix of the network of 2d percolation clusters has a maximum. In correspondence of this maximum the superconducting critical temperature T_c is enhanced. These results suggest the design of new superconducting granular materials with enhanced critical temperature.