Computational Self-Assembly of a Six-Fold Chiral Quasicrystal

Quasicrystals are unique materials characterized by long-range order without periodicity. They are observed in systems such as metallic alloys, soft matter, and particle simulations. Unlike periodic crystals, which are invariant under real-space symmetry operations, quasicrystals possess symmetry described by a space group in reciprocal space. In this study, we report the self-assembly of a six-fold chiral quasicrystal using molecular dynamics simulations of a two-dimensional particle system. These particles interact via the Lennard-Jones-Gauss pair potential and are subjected to a periodic substrate potential. Our findings confirm the presence of chiral symmetry through diffraction patterns and order parameters, revealing unique local motifs in both real and reciprocal space. We demonstrate that the quasicrystal's properties, including the tiling structure and symmetry and the extent of diffuse scattering, are influenced by substrate potential depth and temperature. Our results provide insights into the mechanisms of chiral quasicrystal formation and the role of external fields in tailoring quasicrystal structures.