From Kondo to local singlet state in graphene nanoribbons with magnetic impurities

TL;DR

This paper investigates the transition from Kondo screening to local singlet formation in graphene nanoribbons with magnetic impurities, revealing two distinct regimes influenced by impurity coupling strength and edge states.

Contribution

It provides a detailed numerical analysis of the Kondo effect and local singlet states in graphene nanoribbons with magnetic impurities, highlighting the dependence on coupling regimes and impurity position.

Findings

Two screening regimes identified: weak coupling enhances Kondo temperature, strong coupling favors local singlet formation.

Kondo temperature $T_K$ increases exponentially with impurity coupling in the weak regime.

Characteristic temperature $T^*$ scales linearly with impurity coupling in the strong regime.

Abstract

A detailed analysis of the Kondo effect of a magnetic impurity in a zigzag graphene nanoribbon is addressed. An adatom is coupled to the graphene nanoribbon via a hybridization amplitude $\Gamma_{imp}$ in a hollow or top site configuration. In addition, the adatom is also weakly coupled to a metallic STM tip by a hybridization function $\Gamma_{tip}$ that provides a Kondo screening of its magnetic moment. The entire system is described by an Anderson-like Hamiltonian whose low-temperature physics is accessed by employing the numerical renormalization group approach, which allows us to obtain the thermodynamic properties used to compute the Kondo temperature of the system. We find two screening regimes when the adatom is close to the edge of the zigazag graphene nanoribbon: (1) a weak coupling regime ($\Gamma_{imp}\ll \Gamma_{tip}$), in which the edge states produce an enhancement of the Kondo temperature $T_K$ and (2) a strong coupling regime ($\Gamma_{imp}\gg \Gamma_{tip}$), in which a local singlet is formed, in detriment to the Kondo screening by the STM tip. These two regimes can be clearly distinguished by the dependence of their characteristic temperature $T^*$ on the coupling between the adatom and the carbon sites of the graphene nanoribon ($V_{imp}$). We observe that in the weak coupling regime $T^*$ increases exponentially with $V_{imp}^2$. Differently, in the strong coupling regime, $T^*$ increases linearly with $V_{imp}^2$.