Zigzag graphene nanoribbons: bandgap and midgap state modulation.

We study zigzag graphene nanoribbons with periodic edge roughness and report significant band gap opening. Interestingly, such nanoribbons have a near-midgap state with a small band width. We extensively study the electronic structure and the electric-field modulation of the conduction/valence bands and the near-midgap state. We summarize the important electronic-structure features like the band gap, the band width and the effective mass. We show that by applying an external electric field in the width direction, the band width of the near-midgap state varies linearly due to the edge localization, whereas the band gap remains almost constant. Additionally, the effective mass of these states can switch polarity from negative (hole-like) to positive (carrier-like) at the Γ-point with the field modulation.