Stable local moments of vacancies and hollow-site impurities in graphene

Taking into account the possibility of a p-wave hybridization function $V(\vec k)$ of ad-atom with Dirac electrons in graphene -- which arises for vacancies and hollow-site impurities -- we study the nature of magnetic moment formation within the single impurity Anderson model (SIAM). Compared to the s-wave hybridization function, we find that the local moments formed within the Hartree mean field are robust against the change in the parameters of the model. Further we investigate the stability of the local moments with respect to quantum fluctuations by going beyond the Hartree approximation. We find that for parameter regimes where local moments formed by top-site ad-atoms are completely washed out by quantum fluctuations, those formed by vacancies (or hollow-site impurities) survive the quantum fluctuations captured by post-Hartree approximation. Hence vacancies and hollow-site ad-atoms are suitable candidates to produce stable local moments.