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We study the lowest energy configurations of an equimolar binary mixture ofclassical 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 Coulombpotential and are confined to a 2D plane with a homogeneous neutralizingbackground charge density. In a recent paper by M. Antlanger and G. Kahl [Cond.Mat. Phys. {\bf 16}, 43501 (2013)], using numerical computations based onevolutionary algorithm, six fully mixed structures were identified for $0\leq\lesssim 0.59$, while the separation of $Q_1$ and $Q_2$ pure hexagonal phasesminimizes the energy for $0.59\lesssim q<1$. Here, we introduce a novelstructure which consists in the separation of two phases, the pure hexagonalone formed by a fraction of particles with the larger charge $Q_1$ and theother fixed one containing different numbers of $Q_1$ and $Q_2$ charges. Usingan analytic method based on an expansion of the interaction energy in Misrafunctions we show that this novel structure provides the lowest energy in twointervals of $q$ values, $0<q\lesssim 0.04707$ and $0.58895\lesssim q\lesssim0.61367$. This fact might inspire numerical methods, for both Coulomb andYukawa interactions, to test more general separations which go beyond theseparation of two pure phases.

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