Abstract
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.
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