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arXiv · 1401.8167

Taking one charge off a two-dimensional Wigner crystal

Moritz Antlanger·Martial Mazars·Ladislav Šamaj·Gerhard Kahl·Emmanuel Trizac
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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 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.

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Moritz Antlanger, Martial Mazars, Ladislav Šamaj, Gerhard Kahl, Emmanuel Trizac. 2014-01-31. Taking one charge off a two-dimensional Wigner crystal. https://doi.org/10.1080/00268976.2014.901569

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