▎ 摘　　要

Constructing a van der Waals (vdW) heterostructure is a promising approach to tackle the bandgap hurdle of graphene meanwhile preserving its excellent electronic properties. The unique symmetry of atomic arrangement in C3B and C3N monolayers could induce interesting properties in the graphene/C3B (C3N) heterostructure. Based on the density functional theory calculation, we demonstrate that the bandgap near the Dirac cone depends sensitively on the stacking order in the graphene/C3B (C3N) vdW heterostructure. The bandgap is opened in the AB stacking order, but is completely closed in the AA stacking order. The bandgap closing is protected by the AA stacking order even under vertical strain, while the bandgap increases in the AB stacking order with a positive vertical strain. Based on the tight-binding model, the origin of the bandgap opening and closing is explained by the stacking-order dependent charge transfer. Moreover, the transport properties of the devices assembled by the graphene/C3B vdW heterostructures are investigated based on the non-equilibrium Green's function method plus the density functional theory. The conductance can be turned on or off depending on the stacking order. This finding is useful for the future design of on/off devices based on graphene/C3B (C3N) heterostructures.