Local Moment Formation and Kondo Effect in Defective Graphene

We study the local moment formation and the Kondo effect at single-atom vacancies in Graphene. We develop a model accounting for the vacancy reconstruction as well as non-planarity effects induced by strain and/or temperature. Thus, we find that the dangling $\sigma$ orbital localized at the vacancy is allowed to strongly hybridize with the $\pi$-band since the scattering with the vacancy turns the hybridization into singular function of the energy ($\sim [|\epsilon| \ln^2 \epsilon/D]^{-1}$, $D\sim$ the bandwidth). This leads to several new types of impurity phases, which control the magnitude of the vacancy magnetic moment and the possibility of Kondo effect depending on the strength of the local Coulomb interactions, the Hund's rule coupling, the doping level, and the degree of particle-symmetry breaking.