Upper critical fields of regular superconductive networks. Surfaces and impurities

The upper critical field of several defect structures is studied using the de Gennes—Alexander theory of superconductive networks. The systems considered include a terminated ladder, an impurity site within the ladder, and a square lattice with a surface. Localized modes of condensation appear in all the structures considered. Four different methods have been used alternatively or concurrently: direct diagonalization, continuousfraction expansion, transfer matrix, and a renormalization-group decimation procedure. This last method has proved very useful to study irrational values of the ratio flux to flux quantum in the square lattice. The case of the square lattice with a surface shows several characteristics in common with surface superconductivity ($H_{c3}$) in bulk materials.