Flux Quantization on Quasicrystalline Networks

We have measured the superconducting transition temperature $T_c\mathrm{}\left(H\right)\mathrm{}$ as a function of magnetic field for a network of thin aluminum wires arranged in two quasicrystalline arrays, a Fibonacci sequence and the eightfold-symmetric version of a Penrose tiling. The quasicrystals have two periods whose ratio $\sigma$ is irrational and are constructed of two tiles with irrationally related areas. We find a series of dips in $\delta T_c\mathrm{}\left(H\right)\mathrm{}$ corresponding to favorable arrangements of the flux lattice on the quasi-crystalline substrate. The largest dips are found at ${\sigma }^n$ and the dips approach the zero-field transition temperature as $n$ increases.