  The ab initio band structure of 2D graphene sheet is well reproduced by the
third nearest neighbor tight binding model proposed by Reich et al [Phys. Rev.
B 66, 035412]. For ribbon structures, the existing sets of tight binding
parameters can successfully explain semi-conducting behavior of all armchair
ribbon structures. However, they are still failing in describing accurately the
slope of the bands while this feature is directly associated to 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 density functional theory.
Relevant outcomes are also demonstrated for armchair ribbons of various widths
as well as for zigzag structures, thus opening a route for multi-scale
simulations.
