Examining the Long-Range Effect in Very Long Graphene Nanoribbons: A First-Principles Study

The role of long-range effect on the modulation of the electronic structure of graphene nanoribbons has been little studied due to the limitations of existing theoretical and computational methods. By splitting a molecule top-down and calculating and jointing the Fock matrix of fragments, we developed a computational method suitable for large-size molecules with random doping and arbitrary geometry. Utilizing this method, we achieved the study of the effects of dopants and curvature on graphene nanoribbons (GNRs). It reveals that both dopants and curvature can change the charge distribution of GNRs, while the influence of dopants is more significant and can extend up to 1-3 nm. The electronic excitation properties of GNRs are also largely modified by the doping state or nonuniform curvature. Our findings provide not only a feasible approach for studying the electronic structure of large-size molecules but also the possibility to improve the properties of graphene-based materials by dopants and local curvature.