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<p>Aperiodic systems, such as quasiperiodic structures, exhibit properties distinct from those of periodic structures. In 2023, Smith et al. discovered an aperiodic structure based on a single tile shape that can tessellate the plane only aperiodically, known as an aperiodic monotile. Here, by using this monotile tiling, we propose a quasiperiodic structure which possesses perfect threefold rotational (<i>C</i><sub>3</sub>) symmetry but lacks mirror symmetry. Diffraction experiments reveal quasicrystalline properties of the proposed aperiodic structure through observation of clear Bragg peaks and independence of illumination position. Furthermore, we observe chiral properties including pinwheel-like diffraction patterns and unconventional circular-polarization-dependent behavior, which is absent in conventional quasiperiodic structures with mirror symmetry. These findings establish chiral quasiperiodic structures as a platform for studying aperiodic systems beyond traditional quasicrystals, broadening the study of nonperiodic structures.</p>

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Chiral diffraction from aperiodic monotile structure

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月29日

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  • Yuto Moritake,
  • Masato Takiguchi,
  • Takuma Aihara,
  • Masaya Notomi

摘要

Aperiodic systems, such as quasiperiodic structures, exhibit properties distinct from those of periodic structures. In 2023, Smith et al. discovered an aperiodic structure based on a single tile shape that can tessellate the plane only aperiodically, known as an aperiodic monotile. Here, by using this monotile tiling, we propose a quasiperiodic structure which possesses perfect threefold rotational (C3) symmetry but lacks mirror symmetry. Diffraction experiments reveal quasicrystalline properties of the proposed aperiodic structure through observation of clear Bragg peaks and independence of illumination position. Furthermore, we observe chiral properties including pinwheel-like diffraction patterns and unconventional circular-polarization-dependent behavior, which is absent in conventional quasiperiodic structures with mirror symmetry. These findings establish chiral quasiperiodic structures as a platform for studying aperiodic systems beyond traditional quasicrystals, broadening the study of nonperiodic structures.