Symmetry-induced band-gap opening in graphene superlattices

We study n x n honeycomb superlattices of defects in graphene. The considered defects are missing p(z) orbitals and can be realized by either introducing C atom vacancies or chemically binding simple atomic species at the given sites. Using symmetry arguments and electronic-structure calculations we show that it is possible to open a band gap without breaking graphene point symmetry. This has the advantage that new Dirac cones appear right close to the gapped region. We find that the induced gaps have an approximate square-root dependence on the defect concentration x = 1/n(2) and compare favorably with those found in nanoribbons at the same length scale.