Hexagonal two-dimensional layers of $A_{N}B_{8-N}$ compounds on metals

Analytical expressions for densities of states of free graphene-like $A_{N}B_{8-N}$ compounds and flat and buckled epitaxial monolayers on a metallic substrate have been obtained by the tight-binding method using a low-energy approximation. Characteristic features of the densities of states as functions of the layer–substrate coupling constant and the buckling factor have been analyzed. The energy gaps and the binding energy between the epitaxial layer and the substrate have been estimated.