Selection rule for the optical absorption of graphene nanoribbons

We demonstrate that the optical absorption of zigzag-edge graphene nanoribbons is qualitatively different from that of armchair nanotubes. Unlike the selection rule for nanotubes, when the incident beam is polarized along the longitudinal direction, the interband transitions at direct gaps are forbidden for graphene nanoribbons. This selection rule is due to the finite width of graphene nanoribbons. We also demonstrate that the edge states of graphene nanoribbons play an important role in the optical absorption. They are involved in many of the absorption peaks within optical range ( ω<0.12 a.u.) and have no contribution to the absorption peaks beyond optical range.