Rectangle-triangle soft-matter quasicrystals with hexagonal symmetry

Andrew J. Archer, Tomonari Dotera, and Alastair M. Rucklidge

Editors' Suggestion: Physical Review E106, 044602 (2022).


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Aperiodic (quasicrystalline) tilings, such as Penrose’s tiling, can be built up from e.g. kites and darts, squares and equilateral triangles, rhombi or shield shaped tiles and can have a variety of different symmetries. However, almost all quasicrystals occurring in soft-matter are of the dodecagonal type. Here, we investigate a class of aperiodic tilings with hexagonal symmetry that are based on rectangles and two types of equilateral triangles. We show how to design soft-matter systems of particles interacting via pair potentials containing two length-scales that form aperiodic stable states with two different examples of rectangle–triangle tilings. One of these is the bronze-mean tiling, while the other is a generalization. Our work points to how more general (beyond dodecagonal) quasicrystals can be designed in soft-matter.

Editors' Suggestion: Editor's summary

This paper describes an investigation of soft-matter quasicrystals with hexagonal symmetry. Examining two different examples of rectangle-triangle tilings, the authors demonstrate how to design stable aperiodic soft-matter systems containing two length scales. Their work suggests ways to find a wider variety of quasicrystals in soft matter systems.

編集者のお薦め: 編集者のサマリー

この論文では6回対称性を持つソフトマター準結晶の研究が述べられます。 長方形と3角形からなる2種のタイリングを調べて、著者らは 2つの長さスケールを含む安定した非周期的なソフトマター系をデザインする方法を示します。 彼らの研究は、ソフトマター系でより多様な準結晶を見つける方法を示唆しています。