Hyperuniformity variation with quasicrystal local isomorphism class

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.