Wigner crystals for a planar, equimolar binary mixture of classical, charged particles

Antlanger Antlanger

doi:10.5488/cmp.16.43501

Abstract

We have investigated the ground state configurations of an equimolar, binary mixture of classical charged particles (with nominal charges $Q_1$ and $Q_2$) that condensate on a neutralizing plane. Using efficient Ewald summation techniques for the calculation of the ground state energies, we have identified the energetically most favourable ordered particle arrangements with the help of a highly reliable optimization tool based on ideas of evolutionary algorithms. Over a large range of charge ratios, $q = Q_2 / Q_1$, we identify six non-trivial ground states, some of which show a remarkable and unexpected structural complexity. For $0.59 \lesssim q < 1$ the system undergoes a phase separation where the two charge species populate in a hexagonal arrangement spatially separated areas.

Highlights

The identification of the ordered ground state configurations of classical charged particles is known in literature as the Wigner problem [1]
In an effort to identify the complete set of ordered ground state configurations of our system specified in section 2, we have performed extensive evolutionary algorithms (EAs)-runs, taking into account up to 20 particles per species and per unit cell
1⁄4 The table provides an overview of the ground state configurations that we have identified for Õ 1⁄2; the structures themselves are depicted in figures 2–5

Summary

Introduction

The identification of the ordered ground state configurations of classical charged particles is known in literature as the Wigner problem [1]. The parameters of these lattices are optimized in such a way as to minimize the lattice sum In this contribution we have used an optimization tool that is based on ideas of evolutionary algorithms (EAs) [8, 9]. Within this concept, any possible two-dimensional lattice is considered as an individual, to which a fitness value is assigned. Any possible two-dimensional lattice is considered as an individual, to which a fitness value is assigned These individuals are exposed on the computer to an artificial evolution: via creation and mutation operations a large number of individuals is produced; in the former procedure a pair of new individuals is created from a pair of parent individuals that are selected according to their fitness values. EA-based optimization algorithms have turned out to be highly efficient and

Methods

Results

Conclusion