▎ 摘　　要

The in-plane combination of graphene (G) and hexagonal-boron nitride (h-BN) leads to lateral h-BN/G heterostructures, which are promising candidates for novel two-dimensional electronics. The quality of the interface between G and h-BN domains is crucial for the device performance. By comprehensive first-principles calculations, we explore the heteroepitaxial growth of graphene along the edge of an h-BN domain on a Cu(111) surface and compare it with that on a Cu(111) terrace. We find that the graphene nucleation site strongly depends on the chemical potential of carbon and predeposited h-BN coverage. Under the suitable carbon concentration and coverage of h-BN, graphene mainly grows along the h-BN edge, leading to a sharp and straight h-BN/G interface. Our results provide insightful knowledge to synthesize well-defined h-BN/G and other lateral heterostructures.