Electronic states of coupled graphene nanoribbons

Abstract

Electronic states of laterally coupled graphene nanoribbons (GNRs) have been calculated within a nearest-neighbor tight-binding approximation with varying inter-GNR coupling strength γ from γ = 0 to t (intra-GNR transfer integral). For a coupled zigzag-edge GNR array, both almost flat bands and anisotropic Dirac cones appear near the Fermi level. For a coupled armchair-edge GNR array with a ribbon width N = 3n or 3n + 1, the system is semiconducting with a finite bandgap at γ = 0, which decreases as γ increases. For N = 3n, it becomes metallic with a zero bandgap only at γ = t. On the other hand, for N = 3n + 1, it becomes metallic when γ ≥ t/2. At γ = t/2, a peculiar energy dispersion emerges; the energy dispersion is parabolic perpendicular to the GNR axis and linear parallel to the GNR axis. When N = 3n + 2, the system is always metallic regardless of γ.