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Dirac fermions and Kondo effect

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 $H_k= v{\bf k}\cdot σ+m σ_0$ for the wave number ${\bf k}$ where $σ_j$ are Pauli matrices and $σ_0$ 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 $T_K\propto \exp(-{\rm const}/ρ|J|)$ when $ρ|J|$ is small. The Kondo effect will disappear when the Fermi surface is point like because $T_K$ vanishes as the chemical potential $μ$ approaches the Dirac point.