Hierarchical ground-state crystals underlying Hertzian quasicrystals

Abstract

Abstract As a simple physics model for crystal and quasicrystal formation, the Hertzian potential describes the interaction between two soft-core colloidal particles. However, explaining why quasicrystals emerge in such a minimal model remains a theoretical challenge. Here, using analytically exact approaches, we reveal multiple layers of hierarchical crystal patterns that serve as the energy ground states underlying quasicrystals found by computer simulations. Our findings offer a new perspective on quasicrystal formation.