Influence of ab initio derived site-dependent hopping parameters on electronic transport in graphene nanoribbons

Graphene Nano Ribbons (GNRs) have been studied extensively due to their potential applications in electrical transport, optical devices, etc. The Tight Binding (TB) model is a common method used to theoretically study the properties of GNRs. However, the hopping parameters of two-dimensional graphene (2DG) are often used as the hopping parameters of the TB model of GNRs, which may lead to inaccuracies in the prediction of GNRs. In this work, we calculated the site-dependent hopping parameters from density functional theory and construction of Wannier orbitals for use in a realistic TB model. It has been found that due to the edge effect, the hopping parameters of edge C atoms are markedly different from the bulk part, which is prominently observed in narrow GNRs. Compared to graphene, the change of hopping parameter of edge C atoms of zigzag GNRs (ZGNRs) and armchair GNRs (AGNRs) is as high as 0.11 and 0.08 eV, respectively. Moreover, we investigated the impact of the calculated site-dependent (SD) hopping parameters on the electronic transport properties of GNRs in the absence and presence of the perpendicular electric field and dilute charged impurities using the Green function approach, Landauer-Büttiker formalism and self-consistent Born approximation. We find an electron-hole asymmetry in the electronic structure and transport properties of ZGNRs with SD hopping parameters. Furthermore, AGNRs with SD hopping energies show a band gap regardless of their width, while AGNRs with 2DG hopping parameters exhibit metallic or semiconductor phases depending on their width. In addition, electric field-induced 4-ZGNR with SD hopping parameters undergoes a metallic to n-doped semiconducting phase transition whereas for 4-ZGNR with 2DG hopping parameters and 8-AGNRs with 2DG or SD hopping parameters, the application of an electric field opens the band gap in both conduction and valence bands simultaneously. Our findings provide evidence for the electron-hole symmetry breaking in ZGNR with SD hopping parameters and make ZGNRs a suitable candidate in valleytronic devices.