Cubic structures of Josephson coupled superconducting spheres: three-dimensional models of granular superconductors (*)

The transport critical current in high-Tc superconducting systems is considerably limited by the microstructural characteristics of these materials [1]. Indeed, if we schematize these systems as a collection of weakly-coupled superconducting islands, we may adopt Josephson junction network models to describe their electrodynamic response. With the aid of these models one can show that the maximum Josephson currents of the single junctions are natural upper bounds for the transport critical current [2]. Even though granularity in high-Tc superconducting systems plays against large scale and practical applications of these materials, new and interesting phenomena may arise from the study of the magnetic properties of granular systems. For example, one can show that the particular multiply connected structure of granular samples may give rise to the so-called Wohlleben effect [3, 4], which is sometimes referred to as paramagnetic Meissner effect. As far as the magnetic properties of these materials are concerned, one usually adopts one-dimensional (1D) [5, 6] or two-dimensional (2D) [7-9] junction arrays. Only few recent works have appeared on three-dimensional (3D) Josephson junction arrays [10, 11]. In the present work we study the magnetic response of a particular 3D Josephson junction network: twelve junctions, each one located at the midpoint of a cube side. This