▎ 摘　　要

We report the electronic structure of armchair graphene nanoribbons (acGNRs) with periodic edge roughness. For the unpassivated edges, due to the dangling-bond states, we find, for both pristine and periodically rough acGNRs, the width dependence does not exhibit the hyperbolic trend in the band gap, which is otherwise a characteristic of the passivated acGNRs. The effective mass also does not follow the hyperbolic dependence for the passivated acGNRs with edge roughness. Furthermore, the distinct nonpristine edges, discussed in this paper, have a band-gap opening with and without passivation, since the probability of crossing the quantized wave vector and one of the two Dirac points becomes quite small due to the mixed boundary conditions. We finally report the electronic-structure modulation by applying an external electric field to decrease the band gap to a few meV.