Structural studies of local environments in high-symmetry quasicrystals

Alan Rodrigo Mendoza Sosa, Atahualpa S. Kraemer, Erdal C. Oğuz, Michael Schmiedeberg

Research output: Contribution to journalArticlepeer-review


The statistics of how the local environment of a particle looks like, e.g., given by the distribution of nearest neighbor distances or the sizes of Voronoi cells, is important as a starting point for the calculation of many material properties like electronic or photonic band structures. Here we study local environments that occur in quasicrystals with large rotational symmetry. Both with analytical considerations based on geometric arguments and with an analysis of a large number of numerically created patches of high-symmetry quasicrystals we find that the Voronoi area's distribution reaches a bimodal curve and that in the limit of large rotational symmetries the distribution of nearest neighbor distance converges against a universal curve, where [Formula: see text] of the vertices have their nearest neighbor at a normalized distance equal to 1, while for the other [Formula: see text] the nearest neighbor is at a distance less than 1. Therefore, the statistics of local environments is non-trivial but independent of the specific rotational symmetry. Thus properties that only depend on local environments are expected to be universal for all high-symmetry quasicrystals.

Original languageEnglish
Pages (from-to)16696
Number of pages1
JournalScientific Reports
Issue number1
StatePublished - 4 Oct 2023
Externally publishedYes


Dive into the research topics of 'Structural studies of local environments in high-symmetry quasicrystals'. Together they form a unique fingerprint.

Cite this