Wigner crystallization in a magnetic field: single electrons versus electron pairs at the lattice sites

The ground state energy of a two-dimensional Wigner crystal in a perpendicular magnetic field with one and two electrons per cell is investigated. The electron–electron interaction between the cells is treated in second-order (dipole) van der Waals approximation. In case of two electrons per lattice site, the interaction of the electrons within each cell is taken into account exactly (including exchange and correlation effects). No further approximations are made, in particular Landau level mixing and incomplete spin polarization are accounted for. The phase diagram shows that the paired phase is energetically more favorable than the single electron phase for large filling factors and high densities.