Ordered equilibrium structures in soft matter systems between two and three dimensions

We identify the sequences of emerging ordered equilibrium structures as a three-dimensional crystal grows in thickness, starting from a two-dimensional lattice. To this end, we consider a system of particles that interact via a Gaussian potential and are confined between two parallel plates separated by a distance D. Using optimization tools that are based on genetic algorithms, we identify the T = 0, ground state configurations of the system. Based on these results, we investigate and interpret in detail two archetypes of structural transitions occurring in the diagram of states: one of them is a sequence of square --> centered rectangular --> hexagonal transitions at fixed confinement D as the density grows and the other is the often-discussed buckling transition, which emerges at fixed density as the system forms a new layer with increasing thickness D. These theoretical investigations are complemented and confirmed by Monte Carlo simulations.