Analytic theory of hexagonal monolayer interacting with hexagonal substrate

Analytic theory of the infinite rigid hexagonal monolayer interacting with hexagonal substrate is developed. The interaction potential is described by a Fourier series with up to six shells of the reciprocal cell vectors. It is rigorously shown that energy of minimum structures is directly related to their symmetry, assuming a decaying behavior of Fourier coefficients. Preliminary comparison with real systems of halogens and alkalis adsorbed on metal surfaces is encouraging and indicates that the adsorbate-substrate interaction is one of the main driving forces in the monolayer formation. The need of detailed ab initio calculations to obtain the Fourier coefficients for different complex adsorption systems is emphasized. Our results indicate the importance of accurate description of the adsorbate-substrate interactions for quantitative theory of monolayer epitaxy on well-ordered surfaces.