The Emergence of the Hexagonal Lattice in Two-Dimensional Wigner Fragments.

At very low density, the electrons in a uniform electron gas spontaneously break symmetry and form a crystalline lattice called a Wigner crystal. But which type of crystal will the electrons form? We report a numerical study of the density profiles of fragments of Wigner crystals from first principles. To simulate Wigner fragments, we use Clifford periodic boundary conditions and a renormalized distance in the Coulomb potential.

Solution to the Thomson Problem for Clifford Tori with an Application to Wigner Crystals.

In its original version, the Thomson problem consists of the search for the minimum-energy configuration of a set of point-like electrons that are confined to the surface of a two-dimensional sphere () that repel each other according to Coulomb's law, in which the distance is the Euclidean distance in the embedding space of the sphere, i.e., .