Energy Gaps in Graphene Nanoribbons

TLDR

The study derives scaling rules for graphene nanoribbon band gaps as a function of ribbon width using first‑principles calculations. First‑principles calculations and analytic modeling of hydrogen‑passivated armchair and zigzag graphene nanoribbons, incorporating edge effects, were employed. Both armchair and zigzag ribbons exhibit band gaps; armchair gaps arise from quantum confinement and edge effects, while zigzag gaps result from a staggered sublattice potential due to edge magnetization, reproducing ab initio results and contrasting with simple tight‑binding predictions.

Abstract

Based on a first-principles approach, we present scaling rules for the band gaps of graphene nanoribbons (GNRs) as a function of their widths. The GNRs considered have either armchair or zigzag shaped edges on both sides with hydrogen passivation. Both varieties of ribbons are shown to have band gaps. This differs from the results of simple tight-binding calculations or solutions of the Dirac's equation based on them. Our ab initio calculations show that the origin of energy gaps for GNRs with armchair shaped edges arises from both quantum confinement and the crucial effect of the edges. For GNRs with zigzag shaped edges, gaps appear because of a staggered sublattice potential on the hexagonal lattice due to edge magnetization. The rich gap structure for ribbons with armchair shaped edges is further obtained analytically including edge effects. These results reproduce our ab initio calculation results very well.