▎ 摘　　要

To solve a challenging issue, i.e., the gap opening of graphene, we designed several heterojunctions of graphene and other two-dimensional carbonitride materials with natural holes in their monolayers, namely, nitrogenated holey graphene (NHG), g-C3N4, and g-CN, to destroy graphene's sublattice symmetry and we investigated their electronic structures by first-principles calculations, in which the external electric field effect was also considered. We found that the heterojunctions, except for that with g-CN, have a direct band gap and that their important band edge states are dominated mainly by their graphene layer. The electric field can open band gaps and reduce the effective mass of electron and hole. The graphene/NHG has a large band gap (186.6 meV) and electron effective mass, which can be reduced from 1.31 to 0.014 m(0) by applying an electric field of 0.4 V/angstrom. The NHG/graphene/NHG has the largest band gap of 250.7 meV among all of the graphene-based heterojunctions. The band gap of g-C3N4/graphene/g-C3N4 can be enlarged from 76.8 to 85.5 meV by applying a perpendicular electric field (0.6 V/angstrom). Interestingly, the external electric field can also convert the indirect band gap of graphene/g-CN into a direct one of 83.3 meV. Our results are useful for fast graphene-based nano-optoelectronic devices.