二维渗流团簇网络中的超导体-绝缘体转变
Superconductor-insulator transition in a network of 2d percolation clusters
摘要：
本文研究了二维渗流团簇网络上的超导体-绝缘体相变。在足够接近逾渗阈值的情况下，该网络具有较宽的度分布，并且在p=p_c时，度分布变为无标度。我们在这个复杂的拓扑结构上研究了横向伊辛模型，以描述超导体材料的二维渗流团簇形成的网络中的超导体-绝缘体转变。通过平均场处理，我们证明了超导电性的临界温度依赖于网络邻接矩阵的最大本征值。在逾渗阈值处，我们发现二维逾渗团簇网络的邻接矩阵的最大特征值有一个极大值。对应于此极大值，超导临界温度T_c提高。这些结果为设计具有高临界温度的新型超导颗粒材料提供了依据。
英文摘要：
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.
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