Inhomogeneous superconducting state of superconducting networks in a magnetic field

Making use of de Gennes--Alexander's network equation, we have investigated the transition temperature of superconducting honeycomb and square lattice networks in magnetic field. We found that the decrease of the transition temperature TC of the finite cluster due to the external field is small compared with that of the periodic networks. At TTC, the superconducting order parameter becomes inhomogeneous for the finite clusters with edge in contrast to the case of the infinite lattice with periodic boundary condition. Also we obtained the distribution of quantized fluxoids from the winding number of the phase of the order parameter.