Electronic structure of zigzag graphene nanoribbons with nanometer scale corners

We have demonstrated that graphene intrinsically possesses edges with substantial roughness. Graphene frequently exhibits zigzag edges with corners with an angle of 120° in transmission electron microscopy images. Theoretical calculations showed that the edge formation energy of a zigzag edge is larger by 0.2 eV per edge than that of an armchair edge due to the emergence of the edge state. The higher energy of the zigzag edge induces structural reconstruction to reduce the energy associated with the electron system, albeit with an increase in the lattice energy. A theoretical work based on the tight binding approximation has suggested to explain the emergence of the zigzag edges with corner edges of 120°, the edge states are absent near the 120° corner even though the two edges have a zigzag arrangement, while they emerge with sufficient distance from the corner. The result showed that the zigzag edges of graphene possessing 120° corners with a moderately straight region are thermodynamically stable. Besides the 120° corner, a 150° corner has also observed an graphene edges in experiments. The stability of the 150° corner is ascribed to the small formation energy of the armchair edges of the corner. In our study, we have shown the energies and electronic structure of graphene edges with 120° and 150 ° corners using first principles total energy calculations in the framework of the density functional theory. Our calculations showed that the formation energies of a zigzag edge of graphene ribbon with a 120° corner are similar than those of a straight zigzag graphene nanoribbon indicating the stability of graphene edges with nanometer scale 120° corners. The obtained results are in good agreement with previously obtained result of the theoretical and experimental works. (author)