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We investigate the resistivity and dephasing rate in the Kondo regime due tomagnetic impurities in graphene with different chemial potentials ($\mu$). TheKondo effect due to either carbon vacancies or magnetic adatoms in graphene isdescribed by the single-orbital pseudo-gap asymmetric Anderson impurity model.We find that although the Anderson impurity model considered here is a mixedvalence system, it can be drived into either the Kondo [$\mu > \mu_c$ (criticalvalue) $>0$] or mixed valency ($\mu \approx \mu_c$) or empty orbital ($\mu <\mu_c$) regime by a gate voltage, giving rise to characteristic features inresistivity and dephasing rate in each regime. Specifically, in the case of$\mu < \mu_c$, the shapes of the resistivity (dephasing rate) curves fordifferent $\mu$ are nearly identical. However, as temperature decreases, theystart 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, thedephasing 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 distinctpeak above the saturation value near $T_K$. In the case of $\mu > \mu_c$, incontrast, the resistivity curve has an additional broad shoulder above 10$T_K$and the dephasing rate exhibits an interesting shoulder-peak shape. In thenarrow boundary region ($\mu \approx \mu_c$), both the resistivity anddephasing rate curves are similar to the corresponding ones in normal metals.This explains the conventional Kondo like resistivity from recent experimentson graphene with defects. The resistivity and dephasing rate are analysized interms of the calculated $T$-dependent spectral function, correlationself-energy and renormalized impurity level.

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