Kondo effect in graphene: single vs. two-channel character

TL;DR

This paper models the Kondo effect in graphene with magnetic impurities, analyzing different impurity positions and their coupling to conduction electrons, revealing single vs. multi-channel Kondo behaviors.

Contribution

It provides a detailed theoretical analysis of impurity coupling and symmetry representations for magnetic impurities in graphene, considering various impurity configurations and their effects on the Kondo phenomenon.

Findings

Coupling differs between ADA and ADC impurity positions.

Explicit symmetry representations for impurity orbitals are derived.

Kondo temperature is calculated for ADA configuration.

Abstract

Based on the tight-binding formalism, we investigate the Anderson and the Kondo model for an adaom magnetic impurity above graphene. Different impurity positions are analyzed. Employing a partial wave representation we study the nature of the coupling between the impurity and the conducting electrons. The components from the two Dirac points are mixed while interacting with the impurity. Two configurations are considered explicitly: the adatom is above one atom (ADA), the other case is the adatom above the center the honeycomb (ADC). For ADA the impurity is coupled with one flavor for both A and B sublattice and both Dirac points. For ADC the impurity couples with multi-flavor states for a spinor state of the impurity. We show, explicitly for a 3d magnetic atom, $d_{z^{2}}$, ($d_{xz}$,$d_{yz}$), and ($d_{x^{2}-y^{2}}$,$d_{xy}$) couple respectively with the $\Gamma_{1}$, $\Gamma_{5} (E_{1})$, and $\Gamma_{6} (E_{2})$ representations (reps) of $C_{6v}$ group in ADC case. The basses for these reps of graphene are also derived explicitly. For ADA we calculate the Kondo temperature.