Anharmonic and screening corrections to the melting of a two-dimensional charged colloidal crystal

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Abstract
The Kosterlitz-Thouless-Halperin-Nelson-Young theory of melting is applied to a two-dimensional charged colloidal crystal. The renormalization of elastic constants due to anharmonic and dislocation pair-screening effects is calculated. For colloidal spheres (‘‘polyballs’’) suspended in a thin film of water confined between two glass plates whose surfaces are highly charged, as in recent experimental configurations, the corrections to the harmonic results simply require an altered effective polyball charge to reproduce virtually the identical melting curve of the harmonic approximation (which agrees well with experiment). The effect on the melting curve of added salt is also calculated; the corresponding experiments have yet to be performed. For a film between uncharged surfaces the anharmonic correction again softens the lattice significantly. Dislocation pair screening causes an additional but minor reduction of the elastic constants. Neither correction eliminates a nonmelting behavior characteristic of the two-dimensional screened Coulomb system in this configuration.