Electronic structure of the substitutional vacancy in graphene: density-functional and Green's function studies

Abstract

In the original paper, figure 12(b) was incorrect and the caption of figure 12 was also erroneous. The correct figure and caption are shown below. E/t Figure 12. LDOS at the impurity site ρ 0A (top), the NN site ρ 0B (middle) and the next-NN site ρ 1A (bottom) obtained from equations (13) and (14) for different strengths of the impurity potential U 0 /t = 0, 2 and 5, denoted by black dashed, black solid and red dashed lines, respectively. As U 0 → ∞, the top LDOS goes to zero (except for the bound state beyond the top of the band whose energy goes to ∞), and the zero-mode state lives only on the B sublattice, as indicated from the middle and the bottom panels. The prominent zero-mode peak in the middle panel for U 0 /t = 5 will develop into a δ-function peak at E = 0 as the impurity potential U 0 → ∞.Abstract. We study the electronic structure of graphene with a single substitutional vacancy using a combination of the density-functional, tight-binding and impurity Green's function approaches. Density-functional studies are performed with the all-electron spin-polarized linear augmented plane wave (LAPW) method. The three sp 2 σ dangling bonds adjacent to the vacancy introduce localized states (Vσ ) in the mid-gap region, which split due to the crystal field and a Jahn-Teller distortion, while the p z π states introduce a sharp resonance state (Vπ ) in the band structure. For a planar structure, symmetry strictly forbids hybridization between the σ and the π states, so that these bands are clearly identifiable in the calculated band structure. As to the magnetic moment of the vacancy, the Hund's rule coupling aligns the spins of the four localized Vσ 1 ↑↓, Vσ 2 ↑ and Vπ ↑ electrons, resulting in an S = 1 state, with a magnetic moment of 2µ B , which is reduced by about 0.3µ B due to the anti-ferromagnetic spin polarization of the π band itinerant states in the vicinity of the vacancy. This results in the net magnetic moment of 1.7µ B . Using the Lippmann-Schwinger equation, we reproduce the well-known ∼1/r decay of the localized Vπ wave function with distance, and in addition, find an

Structural, mechanical, and electronic properties of defect-patterned graphene nanomeshes from first principles

“…The origin of magnetism in defective graphene sheets and the character of electronic states induced by the vacancy resulting in flat bands around the Fermi level have been investigated in some recent studies. [44][45][46] Upon the removal of C atoms (n > 1), graphene is reconstructed to result in a significant modification of the atomic configuration around the hole. For example, after relaxation of the atomic structure, the C 2 defective region becomes an octagon-shaped hole surrounded by two pentagons and six hexagons.…”

Spin relaxation in disordered graphene: Interplay between puddles and defect-induced magnetism

“…8 for the case of vacancies and hydrogen adatoms. We note that other adatom or molecular species have been proposed to cause a similar π-like magnetism in graphene, such as methyl 69 and fluor 35 . The fact that different sources may lead to a similar mechanism makes more plausible that π-like magnetism is present in different experimental scenarios, even when the defects are not intentionally created.…”

“…Ab initio calculations suggest more involved tightbinding models for vacancies and adatoms 35,52 , that take into account local lattice deformations. We do not investigate such models here, but the approach we have put forward can be easily generalized to incorporate lattice reconstruction effects.…”

Selective Hydrogen Adsorption in Graphene Rotated Bilayers

“…The character of this state is peculiar 25 and has been studied and characterized extensively in model hamiltonians. 3,11,26 It decays like 1/r as it has been proved experimentally in graphite. 7 Beyond model hamiltonians many first principles calculations been performed and there is a large list of published papers.…”