Studies of quasicrystalline superconducting networks

We have studied a variety of different periodic and quasiperiodic superconducting networks both theoretically and experimentally with an eye toward seeing whether quasicrystalline structures have physical properties distinct from either random or periodic structures. We are also interested in the question of whether there can be a sense of "commensurability" of a particle or fluxoid arrangement on a quasicrystalline substrate. Experimentally we find cusp-like dips in -δT_c(H) for the quasicrystalline networks at H H₁ = n + mσ, where H₁ is the field which would put 1 flux quanta in every tile an d σ is the irrational number which characterizes the inflation symmetry of the network. This suggests that the commensurate states are associated with the inflation properties of the network. Using several theoretical models and Monte Carlo simulated annealing we have found that the ground state configurations are particular fillings of inflated tilings. We then redefine commensurability in terms of inflation symmetry and indicate how this applies to periodic and quasicrystalline networks.