Separation of Wigner structures for 2D equimolar binary mixtures of Coulomb particles

TL;DR

This paper introduces a new phase separation structure for 2D Coulomb binary mixtures that minimizes energy in specific charge ratio intervals, expanding understanding of their lowest energy configurations.

Contribution

The paper presents an analytic method revealing a novel phase separation structure that minimizes energy in certain charge ratio ranges, beyond previously known mixed and pure phases.

Findings

Identified a new phase separation structure with lowest energy in specific charge ratios.

Analytic expansion method based on Misra functions used to determine energy minima.

Results suggest potential for more complex phase separation configurations in Coulomb systems.

Abstract

We study the lowest energy configurations of an equimolar binary mixture of classical pointlike particles with charges $Q_1$ and $Q_2$, such that $q=Q_2/Q_1\in [0,1]$. The particles interact pairwisely via 3D Coulomb potential and are confined to a 2D plane with a homogeneous neutralizing background charge density. In a recent paper by M. Antlanger and G. Kahl [Cond. Mat. Phys. {\bf 16}, 43501 (2013)], using numerical computations based on evolutionary algorithm, six fully mixed structures were identified for $0\le q\lesssim 0.59$, while the separation of $Q_1$ and $Q_2$ pure hexagonal phases minimizes the energy for $0.59\lesssim q<1$. Here, we introduce a novel structure which consists in the separation of two phases, the pure hexagonal one formed by a fraction of particles with the larger charge $Q_1$ and the other fixed one containing different numbers of $Q_1$ and $Q_2$ charges. Using an analytic method based on an expansion of the interaction energy in Misra functions we show that this novel structure provides the lowest energy in two intervals of $q$ values, $0<q\lesssim 0.04707$ and $0.58895\lesssim q\lesssim 0.61367$. This fact might inspire numerical methods, for both Coulomb and Yukawa interactions, to test more general separations which go beyond the separation of two pure phases.