Taking one charge off a two-dimensional Wigner crystal

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 -> infinity 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.