Dirac fermions and Kondo effect

TL;DR

This paper studies the Kondo effect in systems with Dirac fermions, deriving the Kondo temperature formula and showing it vanishes at the Dirac point, highlighting the impact of linear dispersion on magnetic impurity screening.

Contribution

It introduces a Green's function approach to derive the Kondo temperature for Dirac fermions, revealing the conditions under which the Kondo effect disappears.

Findings

Kondo temperature formula derived for Dirac fermions

Kondo effect vanishes at the Dirac point

Linear dispersion influences magnetic impurity screening

Abstract

In this study, we investigate the Kondo effect induced by the s-d interaction where the conduction bands are occupied by Dirac fermions. The Dirac fermion has the linear dispersion and is described typically by the Hamiltonian such as $H_k= v{\bf k}\cdot {\sigma}+m \sigma_0$ for the wave number ${\bf k}$ where $\sigma_j$ are Pauli matrices and $\sigma_0$ is the unit matrix. We derived the formula of the Kondo temperature $T_K$ by means of the Green's function theory for Green's functions including Dirac fermions and the localized spin. The $T_K$ was determined from a singularity of Green's functions in the form $T_K\propto \exp(-{\rm const}/\rho|J|)$ when $\rho|J|$ is small. The Kondo effect will disappear when the Fermi surface is point like because $T_K$ vanishes as the chemical potential $\mu$ approaches the Dirac point.