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

TL;DR

This paper introduces a new third nearest neighbor tight binding model for graphene nanoribbons that accurately reproduces band structures, including electron-hole asymmetry, aligning well with density functional theory results across various ribbon types.

Contribution

A novel tight binding parameter set up to third nearest neighbors, including overlap terms, improves accuracy in modeling graphene nanoribbons' electronic properties.

Findings

Excellent agreement with density functional theory in band structure predictions.

Accurately captures electron-hole asymmetry.

Effective for various ribbon widths and types.

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 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.