Ordered equilibrium structures of soft particles in thin layers

Considering a system of gaussian particles confined between two hard, parallel plates, we investigate at T = 0, ordered equilibrium configurations that the system forms as the distance D between the plates gradually increases. Using a very sensitive and reliable optimization technique that is based on ideas of genetic algorithms, we are able to identify the emerging sequences of the energetically most favorable structures. Although the resulting phase diagram is rather complex, its essential features can be reduced to the discussion of two archetypes of structural transitions: (i) a continuous transformation at a fixed number of layers, leading from a square to a centered rectangular and then to a hexagonal lattice; (ii) a discontinuous transition, transforming a hexagonal to a square lattice via complex intermediate structures, i.e., the so-called buckling transition, which is encountered as the system forms a new layer. Detailed Monte Carlo simulations are able to confirm the theoretical predictions on a semiquantitative level but are not able to grasp the tiny energetic differences between competing structures.