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/r²density 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. These crystals are shown to be robust with respect to thermal fluctuations up to a certain threshold temperature, above which the net charge is progressively redistributed from the center to the rest of the system and the topological order is lost. The crystals are also resilient to the shear stress produced by a small nonuniform azimuthal force field, rotating as a rigid body (RB). For larger forces, topological defects proliferate and the RB rotation gives place to plastic flow.