Upper Critical Field of Regular Superconductive Networks

Abstract

The de Gennes-Alexander theory of superconductive networks is used to study the upper critical fields of two-dimensional square lattices built from $N$ equally spaced infinite wires joined by transverse strands. Phase diagrams and current-flow patterns for representative cases are shown. A critical value is found of the magnetic flux per square below which the current flow resembles the Meissner state, and above which an ordered array of vortices appears, in general incommensurate with the underlying lattice. The critical flux decreases for increasing $N$.