Lattice relaxation at the interface of two-dimensional crystals: graphene and hexagonal boron-nitride.

Heteroepitaxy of two-dimensional (2D) crystals, such as hexagonal boron nitride (BN) on graphene (G), can occur at the edge of an existing heterointerface. Understanding strain relaxation at such 2D laterally fused interface is useful in fabricating heterointerfaces with a high degree of atomic coherency and structural stability. We use in situ scanning tunneling microscopy to study the 2D heteroepitaxy of BN on graphene edges on a Ru(0001) surface with the aim of understanding the propagation of interfacial strain. We found that defect-free, pseudomorphic growth of BN on a graphene edge "substrate" occurs only for a short distance (<1.29 nm) perpendicular to the interface, beyond which misfit zero-dimensional dislocations occur to reduce the elastic strain energy. Boundary states originating from a coherent zigzag-linked G/BN boundary are observed to greatly enhance the local conductivity, thus affording a new avenue to construct one-dimensional transport channels in G/BN hybrid interface.