Electronic structure of graphene under periodic uniaxial tensile strain

Using density functional theory with the generalized gradient approximation, we investigate the electronic structure of graphene with uniaxial tensile strain in terms of its direction and homogeneity. A uniform strain does not affect the conical dispersion band of pristine graphene but simply shifts its position in the two-dimensional Brillouin zone. Graphene with periodic tensile strain along the armchair and chiral directions is a semiconductor with a tiny gap of a few meV, which is slightly dependent on the strain direction.