We study the electronic structure of finite armchair graphene nanoribbons using density-functional theory and the Hubbard model, concentrating on the states localized at the zigzag termini. We show that the energy gaps between end-localized states are sensitive to doping, and that in doped systems, the gap between the end-localized states decreases exponentially as a function of the ribbon length. Doping also quenches the antiferromagnetic coupling between the end-localized states leading to a spin-split gap in neutral ribbons. By comparing dI/dV maps calculated using the many-body Hubbard model, its mean-field approximation and density-functional theory, we show that the use of a single-particle description is justified for graphene π states in case spin properties are not the main interest. Furthermore, we study the effect of structural defects in the ribbons on their electronic structure. Defects at one ribbon terminus do not significantly modify the electronic states localized at the intact end. This provides further evidence for the interpretation of a multipeak structure in a recent scanning tunneling spectroscopy (STS) experiment resulting from inelastic tunneling processes [van der Lit et al., Nat. Commun. 4, 2023 (2013)]. Finally, we show that the hydrogen termination at the flake edges leaves identifiable fingerprints on the positive bias side of STS measurements, thus possibly aiding the experimental identification of graphene structures.
- Hubbard model
- localized states