Dislocations, vacancies and interstitials in the two-dimensional one-component plasma

TL;DR

This study investigates the energetics and stability of various defects in a two-dimensional one-component plasma on a curved surface, revealing insights into defect interactions, energies, and implications for phase transition theories.

Contribution

It provides the first numerical analysis of defect energetics in the 2D OCP, challenging the applicability of KTHNY theory and suggesting the absence of phase transitions.

Findings

Vacancy-interstitial pair energies cancel at long distances

Bound dislocation pairs depend on their formation history

Isolated dislocations have finite energies, implying thermal excitation

Abstract

The energetics and stability of dislocations, vacancies and, interstitials in the one-component plasma (OCP), where the charges interact with a log potential and move on the curved surface of a cylinder have been investigated numerically. For vacancy-interstitial pairs, the log term of the direct Coulomb attraction and the elastic displacement energy cancel exactly at long distances, resulting in a defect energy of O(1). The numerical results confirm the predicted asymptotic behavior but also identify critical distances below which pairs evolve to different forms. We have found that bound pairs of dislocations - created by adding or removing 120 degree zig-zags of particles - have a dependence on their preparation history which is not accounted for in the usual starting point of the KTHNY theory. Furthermore, isolated dislocations, whose presence disrupts crystalline order, have energies of O(1) at some values of N, the number of particles in the system, and therefore will be thermally excited, raising questions about the applicability of standard KTHNY theory to the OCP, and supporting older suggestions that there are no phase transitions at all in the two-dimensional OCP.