Kondo effect in disordered graphene - Miranda, Vladimir Gonçalves (2014)
Recent experiments found evidences that vacancies give rise to local magnetic moments in graphene sheets. This vacancy-mediated magnetism has renewed the interest on Kondo physics in graphene systems. The Kondo effect is singular in graphene due to its vanishing density of states at low energies, which puts graphene in the class of the socalled pseudogap systems. The pseudogap leads to a Kondo physics that is significantly different than that of the metallic case. There is a recent report on the observation of the Kondo effect in graphene in the literature [1]. However, this result has been contested in favor of a Curie-like paramagnetism persistent down to temperatures as low as 2K [2]. Inthis cloudy scenario, theory can offer valuable support to elucidate this puzzle. In this thesis we put forward a theoretical model to address the Kondo effect in graphene with vacancies. We show that disorder plays a central role for the Kondo physics in graphene being the mechanism responsible for the coupling between the local moment created by the vacancy and the conduction band electrons. Our study shows that graphene's nearest neighbors tight-binding Hamiltonian can, upon inclusion of the long-range disorder term, be mapped into a single impurity Anderson-like model. This Anderson Hamiltonian provides the necessary inputs to implement the Numerical Renormalization Group method (NRG), that allows a full characterization of the low-temperature behavior of the system physical properties. We perform NRG simulations and analyze the system's magnetic susceptibility. We find that disorder "spoils" the pseudogap character of graphene since our results are consistent with those of a "standard" metal. We also use the NRG method to study the distributions of Kondo temperatures P (TK). We find that the resulting P (TK) depends on the disorder strength and, in a more subtle manner, on the chemical potential. We show that disorder can lead to long logarithmic tails in P (TK), consistent with a quantum Griffiths phase, opening the possibility of observation of non-Fermi-liquid behavior in graphene. Finally, we argue that our study can also offer a conciliatory scenario to the contentious experimental results reported in the literature about the low-temperature behavior of local magnetic moments generated by vacancies in graphene.