Energetics of nanoscale graphene ribbons: Edge geometries and electronic structures

The energetics of nanometer-scale ribbon edges of a monolayer graphite sheet (graphene) is studied by using the local spin density approximation in the density functional theory. The formation energy of an armchair edge is found to be smaller by 1 eV per edge atom than that of a zigzag edge in clean graphene edges. For hydrogenated edges, we also find that the armchair edge is more stable in energy by 0.2 eV per edge atom than the zigzag edge. Atomic configurations at edges and electronic structures near the Fermi level of ribbons are crucial to determine their energetics.