Electronic states in finite graphene nanoribbons: Effect of charging and defects

TL;DR

This study investigates the electronic properties of finite graphene nanoribbons, focusing on end-localized states, effects of doping and defects, and comparing theoretical models to experimental observations.

Contribution

It demonstrates the impact of doping and defects on end-localized states and validates the use of single-particle models for graphene π states.

Findings

Doping decreases the energy gap between end-localized states exponentially with ribbon length.

Doping quenches antiferromagnetic coupling, leading to a spin-split gap.

Defects at one end do not significantly affect the electronic states at the other end.

Abstract

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 {\pi} states. Furthermore, we study the effect of structural defects in the ribbons on their electronic structure. Defects at one ribbon termini do not significantly modify the electronic states localized at the intact end. This provides further evidence for the interpretation of a multi-peaked structure in a recent scanning tunneling spectroscopy (STS) experiment resulting from inelastic tunneling processes [J. van der Lit et al., Nature Commun., in press (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.