Effects of interfacial alignments on the stability of graphene on Ru(0001) substrate

Structure and electronic properties of two-dimensional materials could be tuned by interfacial misfit or orientation angles. However, graphene grown on Ru(0001) substrate usually shows stable moiré superlattice with a periodicity of 3.0 nm indicating an aligned geometry. The reason for the absence of misaligned structure is still unknown. We have performed first-principles calculation to investigate the microstructure and morphology of graphene on Ru(0001) substrate in both aligned and misaligned geometries with rotation angles of 0°, 7.6°, and 23.4°, respectively. Our results indicate that both the graphene corrugation and moiré superlattice periodicity decrease as the rotation angle increases. Meanwhile the interaction energy between graphene and Ru(0001) substrate also becomes weakened with the rotation angle, as the decrease and discretization of intense charge transfer sites at the graphene/Ru interface, which is closely related to the interface stacking structure. Counterintuitively, the strain energy in graphene also increases anomalously with the rotation angle, which is attributed to the highly distorted local deformation of graphene due to the strong but discrete covalent bonding with Ru substrate. The simultaneous increase in both the interaction energy and strain energy in graphene/Ru(0001) heterostructure with rotation angle contributes to the preferred configuration in the aligned state.