Topological defects in the crystalline state of one-component plasmas of non-uniform density

TL;DR

This paper analyzes the ground state properties of non-uniformly distributed classical Coulomb charges confined in a plane, revealing defect structures, lattice curvature, and energy scaling, supported by analytical and numerical methods.

Contribution

It provides an analytical and numerical study of topological defects and lattice curvature in non-uniform 2D Coulomb systems, including energy scaling and special symmetric configurations.

Findings

Presence of disclinations and dislocations due to non-uniform density

Lattice lines exhibit marked curvature explained by conformal crystal analysis

Identification of 'magic number' clusters with high symmetry and lower energy

Abstract

We study the ground state properties of classical Coulomb charges interacting with a 1/r potential moving on a plane but confined either by a circular hard wall boundary or by a harmonic potential. The charge density in the continuum limit is determined analytically and is non-uniform. Because of the non-uniform density there are both disclinations and dislocations present and their distribution across the system is calculated and shown to be in agreement with numerical studies of the ground state (or at least low-energy states) of N charges, where values of N up to 5000 have been studied. A consequence of these defects is that although the charges locally form into a triangular lattice structure, the lattice lines acquire a marked curvature. A study is made of conformal crystals to illuminate the origin of this curvature. The scaling of various terms which contribute to the overall energy of the system of charges viz, the continuum electrostatic energy, correlation energy, surface energy (and so on) as a function of the number of particles N is determined. "Magic number" clusters are those at special values of N whose energies take them below the energy estimated from the scaling forms and are identified with charge arrangements of high symmetry.