Gap opening in graphene by simple periodic inhomogeneous strain

Using ab initio methods we show first that the uniform deformation either leaves graphene (semi) metallic or opens up a small gap (yet only beyond its mechanical breaking point), contrary to claims in the literature based on tight-binding (TB) calculations. It is possible however to open up a global gap by a sine-like inhomogeneous deformation applied along any direction but the armchair one, with the largest gap along the zigzag direction (similar to 1.0 eV) and without any electrostatic gating. The gap opening has a threshold character with very sharp rise when the ratio of the amplitude A and the period of the sine wave deformation lambda exceeds (A/lambda)(c) similar to 0.1 and the inversion symmetry is preserved, while it is thresholdless when the symmetry is broken. The gap opening occurs in graphene mesh on boron-nitride substrate.