Rapid and high-quality formation of dodecagonal quasicrystals and their approximants using a purely mechanical approach

The conditions for forming quasicrystals and their approximants are stringent, normally requiring multiple length scales to stabilize the quasicrystalline order. Here, we report an unexpected finding that the approximants and motifs of dodecagonal quasicrystals can be spontaneously formed in the simplest system of identical hard disks, utilizing the unstable feature of the initial square packing subject to mechanical perturbations. Because only one length scale is involved, this finding advances our knowledge of quasicrystals and their approximants. Remarkably, applying this purely mechanical approach to systems known to form dodecagonal quasicrystals yields quasicrystalline order athermally and even single quasicrystals that exhibit the theoretical tiling patterns of perfect dodecagonal quasicrystals. Our study suggests a paradigm for the rapid synthesis of high-quality quasicrystals.