Superconducting phase boundary of aperiodic networks in a magnetic field

We have used electron-beam lithography to fabricate superconducting ‘‘wire’’ arrays in a variety of patterns ranging from periodic to random and including the intermediate quasicrystalline and incommensurate configurations. Sweeping an applied magnetic field while observing the critical temperature reveals which fields are favorable or commensurate with the pattern. We find sharp dips in the $T_c$(H) curve for periodic, incommensurate (quasiperiodic), and quasicrystalline arrays reflecting a lock-in of the flux lattice with the underlying network. We find no similar fine structure for random arrays. This allows us to generalize the concept of commensurability to nonperiodic structures.