Rectangle-triangle soft-matter quasicrystals with hexagonal symmetry

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

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



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。