Toward an Accurate Tight-Binding Model of Graphene's Electronic Properties under Strain

In this work, the effect of strain on the electronic structure of graphene modeled by several single-orbital third-nearest-neighbors tight-binding models is examined. The Hasegawa et al. conditions for gap opening in graphene under uniform tensile strain are revised to include up to third-nearest-neighbor interactions using parameters available in the literature. A comparison with ab initio density functional theory (DFT) calculations shows discrepancies. Based on the DFT calculations and through the projection of the Kohn-Sham wavefunctions into localized orbitals, the disagreement is explained by an angular dependence of the second- and third-nearest-neighbors tight-binding parameters.