Local Moment Formation of an Anderson Impurity on Graphene

We study the property of a magnetic impurity on a single-layer graphene within an Anderson impurity model. Due to the vanishing local density of states at the Fermi level in graphene, the impurity spin cannot be effectively screened out. Treating the problem within the Gutzwiller approximation, we found a region in the parameter space of $U$-$E^f$ where the impurity is in the local moment state, which is characterized by a zero effective hybridization between the bath electron and the magnetic impurity. Here $U$ is the onsite Coulomb repulsion of the impurity electrons and $E^f$ the impurity energy level. The competition between $U$ and $E^f$ is also discussed. While larger $U$ reduces double occupation and favors local moment formation, a deeper impurity level prefers double occupation and a nonzero hybridization and thus a Kondo screened state. For a fixed $U$, by continuously lowering the impurity level, the impurity first enters from a Kondo screened state into a local moment state and then departs from this state and re-enters into the Kondo screened state.