Separation of Wigner structures for two-dimensional equimolar binary mixtures of Coulomb particles

We study the lowest energy configurations of an equimolar binary mixture of classical pointlike particles with charges Q₁ and Q₂, such that q=Q₂/Q₁∈[0,1]. The particles interact pairwise via three-dimensional (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 [Condens. Matter Phys. 16, 43501 (2013)], using numerical computations based on an evolutionary algorithm, six fully mixed structures were identified for 0≤q0.59, while the separation of Q₁ and Q₂ pure hexagonal phases minimizes the energy for 0.59q<1. Here, we introduce a structure which consists of the separation of two phases: a pure hexagonal one formed by a fraction of particles with the larger charge Q₁ and the other a mixed one containing different numbers of Q₁ and Q₂ charges. Using an analytic method based on an expansion of the interaction energy in Misra functions, we show that this structure provides the lowest energy in two intervals of q values, 0<q0.0470.16em0ex07 and 0.5880.16em0ex95q0.6130.16em0ex67. 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.