ac and dc properties of Josephson-junction arrays with long-range interaction

We present an experimental investigation of arrays with long-range interaction, together with a model to explain observed deviations from the predictions of earlier theoretical work. These arrays consist of N horizontal and N vertical superconducting filaments arranged in two parallel planes separated by an oxide layer, so that every wire is Josephson coupled to every other wire in the array as nearest- or next-nearest neighbors. We have performed ac-susceptibility and dc-transport measurements on both ordered and disordered arrays. Our ac measurements show a strong feature at a temperature ${\mathit{T}}_{\mathit{c}}$, which we interpret as a transition to the macroscopically phase-coherent state. We find that this feature is field dependent in ordered arrays, but not in disordered arrays. dc-transport measurements reveal that these arrays have unexpectedly low critical currents and show voltage steps in their I-V curves; moreover, they are hysteretic despite the fact that they consist of nonhysteretic junctions. Our analysis of these results shows that the finite ratio of the wire inductance to the Josephson inductance cannot be ignored since it limits the effective number of Josephson junctions along a wire to ${\mathit{N}}_{\mathit{e}\mathit{f}\mathit{f}}$≪N.