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.