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

School of Mathematical Sciences, Queen Mary University of London - London E1 4NS, UK, EU

Received: 27 October 2012
Accepted: 11 January 2013

Abstract

In this paper we characterize the superconductor-insulator phase transition on a network of 2d percolation clusters. Sufficiently close to the percolation threshold, for p ≃ p_c, 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 Λ of the adjacency matrix of the network. At the percolation threshold, p = p_c, we find that the maximal eigenvalue Λ 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.