Formation and stability of conformal spirals in confined 2D crystals.

We investigate the ground-state and dynamical properties of nonuniform two-dimensional (2D) clusters of long-range interacting particles. We demonstrate that, when the confining external potential is designed to produce an approximate 1/density profile, the particles crystallize into highly ordered structures featuring spiral crystalline lines. Despite the strong inhomogeneity of the observed configurations, most of them are characterized by small density of topological defects, typical of conformal crystals, and the net topological charge induced by the simply-connected geometry of the system is concentrated near the cluster center.