Superconducting Transition of Two- and Three-Dimensional Networks in a Magnetic Field

We investigate the superconducting transition temperature TC of two- and three-dimensional superconducting networks in a magnetic field. Making use of the de Gennes–Alexander equation, magnetic field dependence of the TC and quantized fluxoid distributions are obtained. Especially, we calculate phase winding numbers of the superconducting order parameter around each closed path of the networks, and then deduce the fluxoid distributions. Two dimensional square lattice networks with edges have higher TC than periodic square networks. For a three dimensional tetragonal network, TC in the magnetic field perpendicular to the one of its face is much reduced in contrast to the case of a cubic network.