Large Band Gap in Graphene Induced by Inhomogeneous Mechanical Deformation

Graphene is a prospective material for future electronics. However, in order to become useful and work in electronic chips, graphene should have a semiconducting energy gap. The seemingly simplest way to induce a gap is to subject the graphene to a strain. Recently, it was predicted within tight-binding approximation that by combining shear deformations and uniaxial strains one can open the gap up at moderate strains ($\sim $12{\%}), well before the elastic limit of the material is reached. Here, we show with the help of ab-initio calculations that, in fact, the gap \textit{cannot} be opened up by any kind of homogeneous deformations smaller that the graphene failure strain. The gap, however, can be opened up by \textit{inhomogeneous} deformation, e.g. by the periodic out-of-plane atomic displacements with an ``amplitude-to-wavelength'' ratio on the order of 0.1, similar to Ref. [2], which translates roughly to only 10{\%} elongation. The gap can be quickly pushed to values up to 1 eV by further increase of strain still far enough from the point of mechanical failure. \\[4pt] [1] G. Cocco, E. Cadelano, and L. Colombo, Phys. Rev. B \textbf{81}, 241412 (2010). \\[0pt] [2] I. Naumov, A. M. Bratkovsky, and V. Ranjan, Phys. Rev. Lett. \textbf{102}, 217601 (2009).