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

摘要

We study the ground state properties of classical Coulomb charges interactingwith a 1/r potential moving on a plane but confined either by a circular hardwall boundary or by a harmonic potential. The charge density in the continuumlimit is determined analytically and is non-uniform. Because of the non-uniformdensity there are both disclinations and dislocations present and theirdistribution across the system is calculated and shown to be in agreement withnumerical studies of the ground state (or at least low-energy states) of Ncharges, where values of N up to 5000 have been studied. A consequence of thesedefects is that although the charges locally form into a triangular latticestructure, the lattice lines acquire a marked curvature. A study is made ofconformal crystals to illuminate the origin of this curvature. The scaling ofvarious terms which contribute to the overall energy of the system of chargesviz, the continuum electrostatic energy, correlation energy, surface energy(and so on) as a function of the number of particles N is determined. "Magicnumber" clusters are those at special values of N whose energies take thembelow the energy estimated from the scaling forms and are identified withcharge arrangements of high symmetry.