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Magnetic correlation effects by the topological zero mode in a hydrogenated graphene vacancy $V_{111}$

Electron correlation effects caused by the topological zero mode of a hydrogenated graphene vacancy, $V_{111}$, with three adsorbed hydrogen atoms is discussed theoretically. A Kondo model is derived from the multi-reference representation of the density functional theory, where exchange scattering processes between the zero mode and low-energy modes in the Dirac cones are estimated. Even when the Dirac cone is slightly off from the charge neutral point, a finite on-site correlation energy, $U_0$, for the zero mode of an isolated $V_{111}$ allows the half-filling of the localized level giving a spin $s=1/2$. The anti-ferromagnetic Kondo screening mediated by higher order scattering processes becomes dominant in the dilute limit of the vacancies. Our estimation of relevant two body interactions certifies appearance of the Kondo effect at low temperatures.