Properties of superconducting networks with large Josephson junctions

Abstract

We derive a new approach to study superconducting Josephson lattices whose size L is large compared to the London penetration depth λ L. When L is larger than the Josephson penetration depth δ, we find the critical magnetic field H c1, the energy E p of pinning and the frequency of free oscillations of vortices about centers of pinning. Josephson lattices with L ⪌ δ are described by the XY model taking into account self-consistently magnetic fields of the Josephson currents. Highly anisotropic Josephson lattices are described by the one dimensional Frenkel-Kontorova model. Finally, in the limit of a high magnetic field, H, the problem is reduced to the modified XY model whose coupling strength has an oscillating dependence on H.