Symmetry arguments are used to describe all possible two-dimensional periodic corrugations of graphene ("nanomeshes") capable of inducing tangible semiconducting gap. Such nanomeshes or superlattices break the initial graphene translational symmetry in a way that produces mixing and subsequent splitting of the Dirac K and K' states. All of them have hexagonal Bravais lattice and are described by space groups that are subgroups of the graphene group. The first-principles calculations show that the gaps of about 0.5 eV can be induced at strains safely smaller than the graphene failure strain.
@article{arxiv.1112.1711,
title = {Semiconducting graphene nanomeshes},
author = {I. I. Naumov and A. M. Bratkovsky},
journal= {arXiv preprint arXiv:1112.1711},
year = {2011}
}