B. R. K. Nanda, M. Sherafati, Z. Popović, S. Satpathy
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 method. The three $sp^2 \sigma$ dangling bonds adjacent to the vacancy introduce localized states (V$\sigma$) in the mid-gap region, which split due to the crystal field and a Jahn-Teller distortion, while the $p_z \pi$ states introduce a sharp resonance state (V$\pi$) in the band structure. Symmetry strictly forbids hybridization between the $\sigma$ and the $\pi$ states, if the relaxed structure is planar, so that these bands are clearly identifiable in the calculated band structure. Hund's-rule coupling aligns the spins of the V$\sigma$ and the V$\pi$ states resulting in a S=1 state, with a magnetic moment which varies between $1.5 - 2.0 \mu_B$ depending on the lattice relaxation. Using the Lippmann-Schwinger equation, we reproduce the $\sim 1/r$ decay of the localized V$\pi$ wave function with distance and in addition find an interference term coming from the two Dirac points, previously unnoticed in the literature. The long-range nature of the V$\pi$ wave function may be responsible for the widely varying relaxed structures and magnetic moments reported from the band calculations in the literature.
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http://arxiv.org/abs/1105.1129
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