Energy gaps in graphene nanomeshes

We report on the band gap opening and electronic structures of graphene nanomeshes (GNMs), the defected graphene containing a high-density array of nanoscale holes, from first-principles calculations. As expected, quantum confinement at the GNM necks leads to a sizable band gap; however, surprisingly, the appearance of a gap depends sensitively on the hole arrangement and periodicity. For the simplest hexagonal zigzag-edged holes passivated by hydrogen, two-thirds of GNMs remain semimetallic while the rest are semiconductors. Furthermore, we show that the energy gap opening in GNM results from the combination of quantum confinement and the periodic perturbation potential due to perforation.