Rectangle--triangle soft-matter quasicrystals with hexagonal symmetry

TL;DR

This paper demonstrates the design of soft-matter quasicrystals with hexagonal symmetry using particles interacting through pair potentials, expanding the types of quasicrystals beyond the commonly observed dodecagonal structures.

Contribution

It introduces a method to create aperiodic soft-matter quasicrystals with hexagonal symmetry based on rectangle-triangle tilings, including the bronze-mean tiling and its generalization.

Findings

Successfully designed stable aperiodic states with rectangle-triangle tilings.

Demonstrated formation of quasicrystals with hexagonal symmetry in soft-matter systems.

Expanded the potential for creating diverse quasicrystal structures beyond dodecagonal types.

Abstract

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.