Electronic structure of the substitutional vacancy in graphene

Details Electronic structure of the substitutional vacancy in graphene Electronic structure of the substitutional vacancy in graphene

2011-05-05

arxiv.org/abs/1105.1129v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

12 pages, 15 figures

Scientific paper

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. We find that the dangling $sp^2\sigma$ bonds on the three carbon atoms adjacent to the vacancy introduce localized states ($V\sigma$) in the mid-gap region, which split due to a Jahn-Teller distortion, while the $p_z \pi$ states introduce a vacancy-mediated zero-mode state ($V\pi$), which also splits due to spin-polarization. Symmetry forbids interaction between the $\sigma$ and the $\pi$ states, so that the $V\sigma$ states are localized, while the $V\pi$ states form sharp resonances due to the interaction with the $\pi$ bands. Hund's-rule coupling makes the vacancy center magnetic with a net magnetic moment of about $2 \mu_B$. These features are confirmed from density-functional calculations using the linear augmented plane wave (LAPW) method. The origin of the zero-mode $V\pi$ state and its wave function are studied using the Dyson and the Lippmann-Schwinger equations and from direct numerical diagonalization of the tight-binding Hamiltonian. The wave function of the zero-mode state contains interference terms from the two Dirac points in the Brillouin zone and it decays slowly with distance as $\sim 1/r$ in the nearest-neighbor tight-binding approximation and linear-band limit.

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