Phase separation, charge ordering, and pairing in layered three-dimensional systems

The processes of Coulomb gas ordering in a three-dimensional (3D) layered system are studied by means of the Brownian dynamics approach. It is found that at different densities of the carriers, a 3D lattice of charges, as well as new specific structures, are possible in the system. At small densities, the particles inside the layers can associate into droplets that collectively repel between neighboring layers, creating 3D ordering of the droplets. These droplets possess local stripe structure that orders spontaneously along an arbitrary direction. The density of charge within the droplets is not a constant and changes with the average density. At higher densities, a specific ordering of the charges into the tetragonal-like or hexagonal-like structures is observed visually and described numerically. Specific “pairing” of the charges from neighboring layers plays an essential role in the formation of all above structures.