TY - JOUR

T1 - Structural studies of local environments in high-symmetry quasicrystals

AU - Sosa, Alan Rodrigo Mendoza

AU - Kraemer, Atahualpa S.

AU - Oğuz, Erdal C.

AU - Schmiedeberg, Michael

N1 - Publisher Copyright:
© 2023. Springer Nature Limited.

PY - 2023/10/4

Y1 - 2023/10/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85173182734&partnerID=8YFLogxK

U2 - 10.1038/s41598-023-42145-7

DO - 10.1038/s41598-023-42145-7

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C2 - 37794114

AN - SCOPUS:85173182734

SN - 2045-2322

VL - 13

SP - 16696

JO - Scientific Reports

JF - Scientific Reports

IS - 1

ER -