Single or multi-flavor Kondo effect in graphene

TL;DR

This paper investigates the Kondo effect in graphene with magnetic impurities, analyzing different impurity positions and their coupling to conduction electrons, revealing multi-flavor interactions and calculating the Kondo temperature.

Contribution

It provides a detailed analysis of impurity coupling in graphene, considering multiple impurity configurations and symmetry representations, advancing understanding of the Kondo effect in this material.

Findings

Impurity coupling varies with position and symmetry.

Multi-flavor interactions are significant in the ADC configuration.

Kondo temperature is explicitly calculated for ADA case.

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.