Formation of quasicrystals and other exotic crystal structures in a soft-core fluid: a tale of two length scales

A two-dimensional system of soft particles interacting via a two-length-scale potential is studied. Density functional theory reveals the existence of a fluid phase and two crystalline phases with different lattice spacing. Of these the larger lattice spacing crystalline phase takes the form of a `crystal liquid' state with a small fraction of mobile particles. Near the transition between this phase and the smaller lattice spacing crystalline phase, quasicrystalline structures may be created by a competition between linear instability at one scale and nonlinear selection of the other. The results are confirmed using Brownian dynamics simulations.