Dirac fermions and Kondo effect

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 $H_k=v\mathbf{k}\cdot \sigma +m{\sigma }_0$ for the wave number $\mathbf{k}$ 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 $T_K\propto \exp (-\mathrm{const}/\rho |J|)$ 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.

This is a short note on the Kondo effect in a Dirac system

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• Kondo effect driven by chirality imbalance
• Two relativistic Kondo effects: Classification with particle and antiparticle impurities
• Kondo effect with Wilson fermions
• Dirac Kondo effect under magnetic catalysis
• Zero-energy modes, fractional fermion numbers and the index theorem in a vortex-Dirac fermion system
• Magnetic Susceptibility of Dirac Fermions, Bi-Sb Alloys, Interacting Bloch Fermions, Dilute Nonmagnetic Alloys, and Kondo Alloys
• QCD Kondo effect for single heavy quark in chiral-symmetry broken phase