Quantum phase transitions to Kondo states in bilayer graphene

We study a magnetic impurity intercalated in Bernal-stacked bilayer graphene described by a multiband Anderson Hamiltonian. Through a properly generalized Schrieffer-Wolff transformation, it reduces to a single-channel Kondo model with a strongly energy-dependent exchange coupling. The form of this effective Kondo Hamiltonian suggests the possibility of driving the system through quantum phase transitions via tuning of the chemical potential through doping or electrical means. The microscopic coupling of the impurity to the graphene layers determines symmetries and details of the various phases. We use the numerical renormalization group to accurately access the many-body physics of this system. Our calculations reveal zero-temperature transitions under variation of the band filling and/or the energy of the impurity level between a local-moment phase and a pair of singlet strong-coupling phases. The latter have conventional Kondo, pseudogap Kondo, and local-singlet regimes that can be distinguished through their thermodynamic and spectral properties, as well as their different rates of variation of the Kondo temperature with the chemical potential.