Third nearest neighbor parameterized tight binding model for graphene nano-ribbons

The existing tight binding models can very well reproduce the ab initio band structure of a 2D graphene sheet. For graphene nano-ribbons (GNRs), the current sets of tight binding parameters can successfully describe the semi-conducting behavior of all armchair GNRs. However, they are still failing in reproducing accurately the slope of the bands that is directly associated with the group velocity and the effective mass of electrons. In this work, both density functional theory and tight binding calculations were performed and a new set of tight binding parameters up to the third nearest neighbors including overlap terms is introduced. The results obtained with this model offer excellent agreement with the predictions of the density functional theory in most cases of ribbon structures, even in the high-energy region. Moreover, this set can induce electron-hole asymmetry as manifested in results from density functional theory. Relevant outcomes are also achieved for armchair ribbons of various widths as well as for zigzag structures, thus opening a route for multi-scale atomistic simulation of large systems that cannot be considered using density functional theory.