Unified bandgap engineering of graphene nanoribbons

Abstract

Unified bandgap engineering, valid both for the armchair and zigzag graphene nanoribbons (GNRs), is enunciated. Using the boundary condition appropriate for K-K′ points of the Dirac cones, GNRs are shown to exhibit three distinct semiconducting states SC0, SC1, and SC2 with complete absence of metallic state. The experimental bandgap for 7-AGNR and 13-AGNR armchair (A) is found to be in excellent agreement with SC1 state. Similar associations are pointed out for other configurations. Both the experimental data and theoretical results show bandgap and effective mass inversely proportional to the GNR width. The effective mass is directly proportional to the bandgap. The indexing scheme connects chiral index of carbon nanotubes (CNTs) to that used for GNR by making edge corrections for the dangling bonds.