Taking one charge off a two-dimensional Wigner crystal

Abstract

A planar array of identical charges at vanishing temperature forms a Wigner crystal with hexagonal symmetry. We take off one (reference) charge in a perpendicular direction, hold it fixed, and search for the ground state of the whole system. The planar projection of the reference charge should then evolve from a sixfold coordination (centre of a hexagon) for small distances to a threefold arrangement (centre of a triangle), at large distances d from the plane. The aim of this paper is to describe the corresponding non-trivial lattice transformation. For that purpose, two numerical methods (direct energy minimisation and Monte Carlo simulations), together with an analytical treatment, are presented. Our results indicate that the d = 0 and d → ∞ limiting cases extend for finite values of d from the respective starting points into two sequences of stable states, with intersecting energies at some value d_t; beyond this value the branches continue as metastable states.

Keywords:

• 2D Wigner crystal
• lattice sums
• vacancy
• polarisation

Acknowledgements

It is a pleasure to dedicate this work to Pierre Turq, who has made seminal contributions to Coulombic systems, in particular ionic liquids and electrolyte solutions. The authors acknowledge also the computation facilities (iDataPlex - IBM) provided by Direction Informatique of Université Paris-Sud. This work was granted access to the HPC resources of IDRIS under the allocation 2013097008 made by GENCI.

Additional information

Funding

The authors acknowledge financial support from the projects PHC-Amadeus-2012/13 [project number 26996UC]; Projekt Amadée [project number FR 10/2012]; Austrian Research Foundation FWF [project number P23910-N16 and the SFB ViCoM, FWF-Spezialforschungsbereich F41]; Grant VEGA [grant number 2/0049/12].