Symmetry induced semimetal-semiconductor transition in doped graphene.

Substitutional chemical doping is one way of introducing an electronic bandgap in otherwise semimetallic graphene. A small change in dopant arrangement can convert graphene from a semiconducting to a semimetallic state. Based on ab initio Density Functional Theory calculations, we discuss the electron structure of BN-doped graphene with Bravais and non-Bravais lattice-type defect patterns, identifying semiconducting/semimetallic configurations. Semimetallic behavior of graphene with non-Bravais lattice-type defect patterns can be explained by a phase cancellation in the scattering amplitude. Our investigation reveals for the first time that the symmetry of defect islands and the periodicity of defect modulation limit the phase cancellation which controls the semimetal-semiconductor transition in doped graphene.