Hartree model of electrons in a two-dimensional Wigner lattice on a dielectric substrate

The wave functions and energies of electrons in a two-dimensional Wigner lattice above the surface of a dielectric (He, Ar) are determined in the Hartree approximation and compared with the classical result. The lattice sum is performed with the Ewald transformation, which is modified to include the effective electron-electron interaction in a rather general form. The electron binding energies are enhanced compared to the point-electron results due to electron delocalization perpendicular and parallel to a dielectric surface. The perpendicular delocalization is strongly correlated with the lateral electron interaction.