# Taking one charge off a two-dimensional Wigner crystal

### Moritz Antlanger 1, 2 Martial Mazars 1 Ladislav Šamaj 3, 4 Gerhard Kahl 2 Emmanuel Trizac 4

#### LPT-ORSAY 14-10. 17 pages, 11 figures. 2014

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 six-fold coordination (center of a hexagon) for small distances to a three-fold arrangement (center 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 minimization and Monte Carlo simulations), together with an analytical treatment, are presented. Our results indicate that the $d=0$ and $d\to\infty$ 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.

• 1. LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
• 2. Institut für Theoretische Physik and Center for Computational Materials Science
• 3. Institute of Physics
• 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques