# Kondo effect due to a hydrogen impurity in graphene: a multichannel Kondo problem with diverging hybridization

## TL;DR

This paper investigates the Kondo effect caused by a hydrogen impurity in graphene, revealing a complex multichannel Kondo problem with diverging hybridization and analyzing its ground states using numerical renormalization group methods.

## Contribution

It introduces a detailed model of hydrogen impurity-induced Kondo effect in graphene, highlighting the diverging hybridization and analyzing the resulting multi-channel Kondo physics.

## Key findings

- Ground state is a spin-1/2 doublet with ferromagnetic coupling at weak scattering.
- Moderate scattering leads to a spin singlet with antiferromagnetic coupling.
- Diverging local density of states influences the Kondo behavior.

## Abstract

We consider the Kondo effect arising from a hydrogen impurity in graphene. As a first approximation, the strong covalent bond to a carbon atom removes that carbon atom without breaking the $C_{3}$ rotation symmetry, and we only retain the Hubbard interaction on the three nearest neighbors of the removed carbon atom which then behave as magnetic impurities. These three impurity spins are coupled to three conduction channels with definite helicity, two of which support a diverging local density of states (LDOS) $\propto 1/ [ | \omega \ | \ln ^{2}( \Lambda /| \omega \ | \ ) \ ] $ near the Dirac point $\omega \rightarrow 0$ even though the bulk density of states vanishes linearly. We study the resulting 3-impurity multi-channel Kondo model using the numerical renormalization group method. For weak potential scattering, the ground state of the Kondo model is a particle-hole symmetric spin-$1/2$ doublet, with ferromagnetic coupling between the three impurity spins; for moderate potential scattering, the ground state becomes a particle-hole asymmetric spin singlet, with antiferromagnetic coupling between the three impurity spins. This behavior is inherited by the Anderson model containing the hydrogen impurity and all four carbon atoms in its vicinity.