Quasi-flat bands in armchair graphene nanoribbons produced by topological junction states

Abstract Nearly dispersionless energy bands are realized in armchair graphene nanoribbons by a periodic repetition of segments characterized by two different widths. The quasi-flat bands are created when interfacial junction states emerge due to the topological dissimilarity between the nanoribbon segments. With the elongation of the period of the nanoribbon superlattice, the band energies approach the Dirac point of graphene with increasing the flatness of the dispersion. The topological winding number is utilized in designing the junctions to control the presence and the number of the topological junction states (TJSs). The existence of the TJSs and the exclusive localization of their wavefunctions in the sublattices of graphene are shown to be maintained when the second-nearest-neighbour hopping in the honeycomb lattice is taken into account with the hopping strength expected for graphene.