Weakening effect of defects on the metallicity of graphene nanoribbons

Graphene nanoribbon (GNR), one of the most common graphene derivatives, has gradually become a research hotspot with its unique properties of high carrier concentration, high conductivity, atomic-level thickness plane structure, and large carrier mobility. However, in the current manufacturing process, various defects inevitably exist in the synthesis of GNRs. Many studies have shown that defects have a substantial effect on the properties of GNRs. However, the effect of defects on the metallicity of GNRs has never been reported. Recently, Rizzo et al. achieved the regulation of the metallicity of metallic GNRs by inducing the formation of only two new C-C bonds per GNR unit cell and successfully fabricated them using a bottom-up approach. This seemingly insignificant and small change causes a chemical bond rearrangement that causes a substantial change in the electronic structure, which has attracted widespread attention in the scientific community. This kind of GNR with metallic properties has extremely high application value as a connecting device. At the same time, it is also of scientific significance to explore its metallicity and metal bandwidth by exploring the Luttinger liquid of 1-dimensional materials, plasma, charge density wave, and superconductivity. Inspired by this research, this paper hopes to clarify the mechanism and law of the effect of defects on the metallicity of GNRs to design the defect molecular structure with atomically precise control and regulate the metal bandwidth. First, a pair of zero modes with equal jump parameters is introduced into GNRs to construct the metal GNR model. The electronic properties of the model are calculated based on density functional theory. Next, GNR models with single-vacancy defect concentrations of 1.429% and 2.857% were constructed, and the electronic properties of the models were calculated based on density functional theory. Then, the effect of defect location on its metallic character was investigated. Studies have shown that by introducing the zero modes, the GNR exhibits a much wider metal bandwidth that increases from 91.49 to 452.92 meV. This method induces changes in the metal bandwidth because the five-membered ring formed in the GNR after the introduction of the zero modes causes the polarization loss of the sublattice, thereby enhancing the metallicity. Introducing single-vacancy defects into metallic GNRs has little effect on their stability, and the geometry does not distort greatly. When a single-vacancy defect is introduced into the GNR supercell, the effect of the defect on the C-C bonds is much stronger in the close zero mode than in the distant zero mode, destroying the geometrical symmetry of the GNR, and the localized charge transfer is intensified. The electronic properties of GNRs are prone to change when defect sites are near the edge of the nanoribbons. A part of the GNR band gap is opened, and the defect model completes the transition from metal to semiconductor. For GNRs with two symmetric single-vacancy defects in the supercell, the GNRs generally retain their original symmetry in terms of geometry and charge transfer because of the symmetrical arrangement of defect sites. This arrangement ensures that the hopping amplitude between the two zero modes is the same to the greatest extent so that the GNR keeps the metallicity unchanged. All metallic bandwidths of the GNR defect models are lower than those of the GNR model that only introduces zero mode C-C bonds. This comparison shows that defects have a non-negligible weakening effect on the metallicity of GNRs, which not only easily converts the original metallic GNRs into semiconductors but also weakens their metallicity.