Hyperuniformity variation with quasicrystal local isomorphism class

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Hyperuniformity is the suppression of long-wavelength density fluctuations, relative to typical structurally disordered systems. In this paper, we examine how the degree of hyperuniformity [λ(∞)] in quasicrystals depends on the local isomorphism class. By studying the continuum of pentagonal quasicrystal tilings obtained by direct projection from a five-dimensional hypercubic lattice, we find that λ(∞)) is dominantly determined by the local distribution of vertex environments (e.g. as measured by Voronoi cells) but also exhibits a non-negligible dependence on the restorability. We show that the highest degree of hyperuniformity [smallest λ(∞))] corresponds to the Penrose local isomorphism class. The difference in the degree of hyperuniformity is expected to affect physical characteristics, such as transport properties.

Original languageEnglish (US)
Article number204003
JournalJournal of Physics Condensed Matter
Issue number20
StatePublished - Apr 13 2017

All Science Journal Classification (ASJC) codes

  • General Materials Science
  • Condensed Matter Physics


  • Penrose tiling
  • hyperuniformity
  • local isomorphism class
  • quasicrystals
  • restorability


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