Commensurate states in disordered quasiperiodic networks

In this paper, we report measurements of the normal-metal-superconductor phase boundary Tc(H) in disordered quasiperiodic wire networks. The initially ordered network is an eightfold quasiperiodic array of the type previously constructed by Ammann, and several types of disorder have been introduced. One series of arrays is areally disordered by stretching and contracting individual worm segments in the network, and the resulting phase boundary exhibits a gradual decay of all phase-boundary structure with increasing field. A second series is perturbed by phason disorder, which amounts to the local flipping of small symmetric clusters of tiles and destroys the local ordering inherent in the inflation symmetry of the ordered network. This type of disorder wipes out higher-order commensurate states but has no effect on the major structure of the phase boundary. A third type of array is created by a special modification of the ordered eightfold lattice and results in a fourfold geometry that is approximately inflation symmetric. Its phase boundary exhibits commensurate states that can be related to the approximate inflation symmetry. We use the J2 model, in which one considers only the kinetic energy of the supercurrents induced by fluxoid quantization, to describe accurately the overall behavior of the measured phase boundaries. The experimental results presented here show that commensurate states based on inflation symmetry are strongly favored in these particular quasicrystal geometries (even when the inflation symmetry is only approximate).