Stability and electronic properties of hexagonal boron nitride monolayer with irregular graphene domains embedded

Using density functional theory, we investigated the stability, magnetism and band structures of hexagonal boron nitride (h-BN) monolayer with graphene domains (h-BNC heterostructure). The number of the carbon atoms in the graphene domain is fixed with shapes and locations in the h-BN monolayer different. We found that these h-BNC heterostructures exhibit different stability, magnetism and energy band gap. Our results show that the stability of the system is related to the number of C-C/C-N/C-B bonds and unpaired sublattices in the graphene domains. Some h-BNC heterostructures are magnetic with the magnetic moment equal to the difference of the nonequivalent sublattices in graphene domains, which obeys Lieb's theorem. Because of the spin splitting of the mid-gap states, the band gaps of the magnetic heterostructures are smaller than that of the nonmagnetic ones.