| Abstract: | Significant interest has lately been devoted to the study of vacancies in graphene obtained by removing a neutral carbon atom. The presence of a single vacancy has interesting and unexpected consequences. It leads to the occurrence of a stable charge of order unity localized at the vacancy site and interacting with other charges of the conductor by means of a Coulomb potential. It also breaks the symmetry between the two triangular graphene sublattices hence inducing zero energy states at the Dirac point. These features have been noticed, however, their precise underlying mechanism and its relation to Dirac physics, if any, are yet to be investigated. Here we show the fractional and pseudo-scalar nature of this stable vacancy charge originating from the vacuum and insensitive to screening effects. A continuous Dirac model is presented which relates zero modes to vacuum fractional charge and to parity symmetry breaking. This relation constitutes an Index theorem and is achieved by using particular chiral boundary conditions, which map the vacancy problem onto edge state physics and link zero energy states to topological features of the bulk alike the Hall effect or physics of kinks, vortices, and monopoles. Vacancies in graphene thus allow to realize prominent features of 2+1 quantum electrodynamics, e.g., charge fractionalization and parity breaking, but without coupling to a gauge field. This essential difference makes vacancy physics relatively easy to implement and an interesting playground for topological charge switching.
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