Theory of interacting Josephson junctions (Josephson lattices)

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Abstract
A theoretical approach is derived to describe a Josephson junction of complex form with self-crossings. Results of the approach are used to study properties of granular superconducting systems with Josephson junctions between grains (Josephson networks or lattices). The authors show that properties of Josephson lattices depend on the grain size (L). If L is smaller than the Josephson length ( delta ), then the lattices are described by the energy functional of the XY model in which internal magnetic fields are taken into account self-consistently. On the basis of the functional they find the low critical field (H*cl) and the pinning energy of vortices. They study also a case of high magnetic fields (H>>H*cl). In this case the lattices are also described by the XY model but the coupling strength between grains may depend strongly on H.