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The structural and dynamical properties of small three-dimensional (3D) anisotropically confined Wigner crystals of particles interacting via a Coulombic interparticle potential are investigated. Varying the degree of anisotropy of the confinement potential drives the system from a 3D to a one-dimensional configuration intermediated by a sequence of first and second order structural phase transitions. We classified the ground state configurations with respect to their symmetry resulting in three different groups of configurations: multiple ring, degenerate multiple ring, and nonsymmetric structures. The results are summarized in a phase diagram where the different configurations are identified for systems ranging from $N=4$ to 25 particles. The behavior of the ground state symmetry of large systems was investigated for the cases of $N=50$, 60, and 70 particles. A normal mode analysis reveals that multiple ring structures exhibit inter-ring and∕or vortex∕antivortex excitation modes of oscillations.

Multiple rings in a 3D anisotropic Wigner crystal: Structural and dynamical properties