Andrew Archer: Rectangle-triangle soft-matter quasicrystals with hexagonal symmetry

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. Joint work with Tomonari Dotera (Kindai) and Alastair Rucklidge (Leeds).

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