Gate-tuned two-channel Kondo screening in Graphene: Universal scaling of the nonlinear conductance

We study the nonlinear conductance through magnetic adatoms on Graphene. In particular, we address the finite-temperature crossover from a quantum critical to the two-channel Kondo regime expected to occur in doped Graphene. Based on the non-crossing approximation, We calculate both the linear and nonlinear conductance within the two-lead single-impurity Anderson model where the conduction electron density of states vanishes in a power-law fashion $ \propto |\omega-\mu_F|^r$ with $r=1$ near the Fermi energy, appropriately for Graphene. For given gate voltage, we study the universal crossover from a 2-channel Kondo (2CK) phase to a un-screened local momemt (LM) phase. We extract universal scaling functions governing charge transport through the adatom and discuss our results in the context of a recent scanning tunneling spectroscopy (STM) experiment on Co-doped Graphene.