Abstract
A Landau-Ginzburg formulation is presented to describe a series of superconducting islands interacting via Josephson weak links in the presence of a magnetic field. It is demonstrated that the structure of superconducting islands (and the lattice of magnetic vortices), describing by the order parameter envelope, may be commensurate or incommensurate with a superimposed array of weak links via the order parameter phase for each island. A discussion is provided in terms of a Kosterlitz-Thouless transition in the latter structure. A description of space modulation of these phases is given through sine-Gordon equations.
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