Interacting loop-current model of superconducting networks

The authors review their recent approximation scheme to calculate the normal-superconducting phase boundary, Tc(H), of a superconducting wire network in a magnetic field in terms of interacting loop currents. The theory is based on the London approximation of the linearized Ginzburg-Landau equation. An approximate general formula is derived for any two-dimensional space-filling lattice comprising tiles of two shapes. Many examples are provided illustrating the use of this method, with a particular emphasis on the fluxoid distribution. In addition to periodic lattices, quasiperiodic lattices and fractal Sierpinski gaskets are also discussed