Orbitally controlled Kondo effect of Co ad-atoms on graphene

TL;DR

This paper uses ab-initio calculations to explore how the Kondo effect in graphene with Co ad-atoms depends on orbital and spin degrees of freedom, revealing complex behaviors influenced by symmetry, spin-orbit coupling, and graphene's band structure.

Contribution

It provides a detailed theoretical analysis of the orbital and spin-controlled Kondo effects of Co ad-atoms on graphene, highlighting the role of symmetry and spin-orbit interactions.

Findings

Kondo effect is quenched by spin-orbit coupling below ~15 K for Co on top of a carbon atom.

An SU(4) Kondo model describes Co in the hexagon center at higher energies.

Spin-orbit coupling leads to a transition from SU(4) to SU(2) Kondo behavior below ~60 meV.

Abstract

Based on ab-initio calculations we identify possible scenarios for the Kondo effect due to Co ad-atoms on graphene. General symmetry arguments show that for magnetic atoms in high-symmetry positions, the Kondo effect in graphene is controlled not only by the spin but also by the orbital degree of freedom. For a Co atom absorbed on top of a carbon atom, the Kondo effect is quenched by spin-orbit coupling below an energy scale of $\sim 15$\,K. For Co with spin $S=1/2$ located in the center of a hexagon, an SU(4) Kondo model describes the entanglement of orbital moment and spin at higher energies, while below \sim 60$\,meV spin-orbit coupling leads to a more conventional SU(2) Kondo effect. The interplay of the orbital Co physics and the peculiar band-structure of graphene is directly accessible in Fourier transform tunneling spectroscopy or in the gate-voltage dependence of the Kondo temperature displaying a very strong, characteristic particle-hole asymmetry.