CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES: Fifth-Nearest-Neighbor Tight-Binding Description of Electronic Structure of Graphene

An analytic expression for pi and pi* electronic structure of graphene is derived within the tight-binding approximation. Including up to fifth-nearest neighbors, the tight-binding description of electronic dispersion quite accurately reproduces the first-principle calculation result over the entire Brillouin zone. The maximal deviation of the fifth-nearest tight-binding result from the first-principle result is only 6 meV for pi band, and 25 meV for pi* band. This 25 meV deviation is only one-tenth of the maximal deviation of the third-nearest tight-binding result. It is more important that the fitted parameters exponentially approach to zero as the distance between interacting atoms increases.