Band engineering in graphene with superlattices of substitutional defects

We investigate graphene superlattices of nitrogen and boron substitutional defects and by using symmetry arguments and electronic structure calculations we show how such superlattices can be used to modify graphene band structure. Specifically, depending on the superlattice symmetry, the structures considered here can either preserve the Dirac cones (D_{6h} superlattices) or open a band gap (D_{3h}). Relevant band parameters (carriers effective masses, group velocities and gaps, when present) are found to depend on the superlattice constant n as 1/n^{p} where p is in the range 1-2, depending on the case considered. Overall, the results presented here show how one can tune the graphene band structure to a great extent by modifying few superlattice parameters.