Flux quantization in periodic networks containing tiles with irrational ratio of areas

We report measurements of the superconducting-normal transition boundary Tc(H) of two-dimensional periodic networks with two different space-group symmetries in a magnetic field. Each network is a mixture of squares and equilateral triangles. In both cases, we observe maxima in Tc(H) with one major period, which does not correspond to the area of either the square or the triangle. We interpret the results in terms of flux configurations whose energies are sensitive to the geometry of a given network. © 1988 The American Physical Society.