Gate-tunable Kondo resistivity and dephasing rate in graphene studied by numerical renormalization group calculations

Abstract

Motivated by the recent observation of the Kondo effect in graphene in transport experiments, we investigate the resistivity and dephasing rate in the Kondo regime due to magnetic impurities in graphene with different chemical potentials ($\ensuremath{\mu}$). The Kondo effect due to either carbon vacancies or magnetic adatoms in graphene is described by the single-orbital pseudogap asymmetric Anderson impurity model which is solved by the accurate numerical renormalization group method. We find that although the Anderson impurity model considered here is a mixed-valence system, it can be driven into either the Kondo [$\ensuremath{\mu}>{\ensuremath{\mu}}_{c}$ (critical value) $>0$], mixed-valency ($\ensuremath{\mu}\ensuremath{\approx}{\ensuremath{\mu}}_{c}$), or empty-orbital ($\ensuremath{\mu}<{\ensuremath{\mu}}_{c}$) regime by a gate voltage, giving rise to characteristic features in resistivity and dephasing rate in each regime. Specifically, in the case of $\ensuremath{\mu}<{\ensuremath{\mu}}_{c}$, the shapes of the resistivity (dephasing rate) curves for different $\ensuremath{\mu}$ are nearly identical. However, as temperature decreases, they start to increase to their maxima at a lower $T/{T}_{K}$, but more rapidly [as ${({T}_{K}/T)}^{3/2}$] than in normal metals [here, $T$ (${T}_{K}$) denotes the (Kondo) temperature]. As $T$ further decreases, after reaching the maximum, the dephasing rate drops more quickly than in normal metals, behaving as ${(T/{T}_{K})}^{3}$ instead of ${(T/{T}_{K})}^{2}$. Furthermore, the resistivity has a distinct peak above the saturation value near ${T}_{K}$. In the case of $\ensuremath{\mu}>{\ensuremath{\mu}}_{c}$, in contrast, the resistivity curve has an additional broad shoulder above 10${T}_{K}$ and the dephasing rate exhibits an interesting shoulder-peak shape. In the narrow boundary region ($\ensuremath{\mu}\ensuremath{\approx}{\ensuremath{\mu}}_{c}$), both the resistivity and dephasing rate curves are similar to the corresponding ones in normal metals. This explains the conventional Kondo-like resistivity from recent experiments on graphene with defects, although the distinct features in the resistivity in the other cases ($\ensuremath{\mu}<{\ensuremath{\mu}}_{c}$ or $\ensuremath{\mu}>{\ensuremath{\mu}}_{c}$) were not seen in the experiments. The interesting features in the resistivity and dephasing rate are analyzed in terms of the calculated $T$-dependent spectral function, correlation self-energy, and renormalized impurity level.