Geometrically induced transitions between semimetal and semiconductor in graphene

How the long-range ordering and local defect configurations modify the electronic structure of graphene remains an outstanding problem in nanoscience, which precludes the practical method of patterning graphene from being widely adopted for making graphene-based electronic and optoelectronic devices, because a small variation in supercell geometry could change the patterned graphene from a semimetal to a semiconductor, or vice versa. Based on the effective Hamiltonian formalism, here we reveal that a semimetal-to-semiconductor transition can be induced geometrically without breaking the sublattice symmetry. For the same patterning periodicity, however, breaking the sublattice symmetry increases the gap, while phase cancellation can lead to a semiconductor-to-semimetal transition in non-Bravais lattices. Our theory predicts the analytic relationship between long-range defect ordering and band-gap opening/closure in graphene, which is in excellent agreement with our numerical ab initio calculations of graphene nanomeshes, partially hydrogen passivated and boronnitride-doped graphene.