Electronic states of coupled graphene nanoribbons

• Published in: Japanese Journal of Applied Physics Vol. 56; no. 4; p. 45001
• Main Authors: Hashimoto, Futo, Mori, Nobuya, Kubo, Osamu, Katayama, Mitsuhiro
• Format: Journal Article
• Language: English
• Published: The Japan Society of Applied Physics 01.04.2017
• Subjects: Approximation; Arrays; Dispersion; Electron states; Energy gaps (solid state); Graphene; Mathematical analysis; Nanostructure
• ISSN: 0021-4922; 1347-4065
• DOI: 10.7567/JJAP.56.045001

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.