Quantum Critical Transition and Kondo Screening of Magnetic Moments in Graphene

In normal metals, the local moment of a magnetic impurity begins to decrease below a characteristic “Kondo temperature” which marks the formation of an entangled state consisting of the moment surrounded by polarized conduction-band electrons that screen it. In contrast, moments embedded in insulators remain unscreened at all temperatures. This raises the question about the fate of magnetic moments in intermediate pseudogap systems, such graphene or high temperature superconductors. We use scanning tunneling microscopy and spectroscopy, and numerical renormalization group calculations to study the screening of local magnetic moments in graphene introduced by creating single-atom vacancies in its honeycomb structure. Identifying Kondo screening of the vacancy spin by its characteristic spectroscopic signature, we detect and map the existence of a quantum phase transition separating magnetic from non-magnetic states. Furthermore, using the unique properties of this phase transition we show that the local magnetic moment can be turned on or off with either a gate voltage or through the local curvature of the graphene membrane.