Divacancy in graphene nano-ribbons

We have investigated the reconstruction and electronic structure of divacancy in chiral and achiral graphene nanoribbons as the defect moves to the ribbon edge. The new healing bonds introduce strain dictating the structure and its energetics. Unlike in infinite graphene, the ribbons can take advantage of the edge flexibility in relieving stress. The total energy depends on the defect orientation and its distance to the ribbon edge, and the disposal of the divacancy through the edge results in the energy gains up to approximate to 7.7 eV. This energy gain is closely related to the pentagon count in the final edge morphology. The divacancy has lower energy near the edge, and thus it is more likely to occur at the edges in the thermodynamic equilibrium. We find that the zigzag portions at the edge induce spin polarization even though the whole edge is not zigzag. However, the spin polarization from discontinuous zigzag portions are not strong and can be modified by the spin polarization around the defect. Moving the divacancy closer to an edge modifies the spin polarization on one side, and the magnetic structure becomes diverse especially in the achiral ribbons. The divacancy induces defect states near E-F. The defect level and the extent of its mixing with native ribbon states depend on the defect orientation and distance to the edge.