Gaps in the spectrum of epitaxial graphene formed on silicon carbide polytypes

Silicon carbide NH-SiC polytypes with $N$ = 2, 4, 6, and 8 are considered as substrates for the epitaxial formation of graphene. The density of states for the substrates is described using the Haldane-Anderson model. It is shown that this model always leads to the appearance of two gaps in the graphene spectrum, which are adjacent to the valence and conduction bands of the substrate. The gap widths are determined by the ratio of the energy of interatomic interaction in the free-standing graphene sheet and the energy of graphene-substrate interaction. If this ratio is very small, the gap widths may increase so as to jointly cover almost the entire bandgap of the substrate; on the contrary, if this ratio is extremely large, both gaps exhibit narrowing and become negligibly small.