Energetics and electronic structure of graphene nanoribbons under a lateral electric field

We studied the energetics and electronic structure of graphene nanoribbons with hydrogenated and clean edges with respect to the detailed edge shapes using density functional theory. Our calculations showed that the stability of graphene edges strongly depends on the length of the zigzag edge portion. Near-zigzag edges are less stable than near-armchair edges because of the large number of states at the Fermi level (EF) in nanoribbons with near-zigzag edges. The edge formation energy retains a constant value up to the edge angle of 16°, after which it monotonically increases with increasing zigzag portion or edge angle. We also found that the edge stability strongly correlates with the electronic structures near the EF of graphene nanoribbons. Nanoribbons with a small zigzag portion already possess edge localized π electronic states near the EF. We also demonstrate that a lateral electric field increases the energy gap of ribbons with/without hydrogen termination, resulting in a decrease in edge formation energy.