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

Abstract

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 highenergy 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.

Screening of long-range Coulomb interaction in graphene nanoribbons: Armchair versus zigzag edges

“…The latter is presented in Table I for the case of 6-ZGNR from the firstto third-nearest neighbors obtained from Wannier functions. The results are in good agreement with reported values of t 01 , t 02 , and t 03 , which are in the range of 2.5-3, 0.1-0.5, and 0.3-0.5 eV, respectively [73][74][75][76][77][78].…”

Braiding of edge states in narrow zigzag graphene nanoribbons: Effects of third-neighbor hopping on transport and magnetic properties

“…In the following calculations, we employ the realistic tight-binding parameters obtained in reference [23] that fit ribbon graphene structures to density functional theory (DFT) results: t = 2.8eV , t = 0.025t, and t = 0.15t. It is interesting to observe that the absolute value of the N3 hopping is much larger than the N2, which reinforces our earlier supposition of only considering hopping that preserves chiral symmetry.…”

“…We think this is the reason why these braiding effects have not been receiving much attention up to now. The majority of the papers are focused on TB calculations for pristine graphene, large N nanoribbons and in the context of the Kane-Mele [17] generalized model [14,18,19,21,22,[24][25][26], or more complete numerical LDA calculations for a N = 11 zigzag ribon [23], in which the numerical resolution blurs the braiding effects of the edge states, which according to our calculations only occur for low N ZGNRs. It is important to mention here that the edge braiding states are not affected by the intrinsic spin-orbit interaction (SO), since this interaction (λ so ) is negligible in graphene; λ so = 1.3µeV [34].…”

Effect of randomly distributed asymmetric stone-wales defect on electronic and transport properties of armchair graphene nanoribbon

“…functional theory (DFT) works. These differences were compared and discussed before [49]. After the calculation of band dispersion, transport properties of these ASW defected AGNRs are going to be discussed.…”