Kondo effect in Dirac systems

TL;DR

This paper analyzes the Kondo effect in Dirac materials, deriving the Kondo temperature formula and showing how it vanishes at the Dirac point, with specific predictions for resistivity and heat capacity behaviors.

Contribution

It provides a theoretical derivation of the Kondo temperature in Dirac systems and explores its dependence on chemical potential and the disappearance at the Dirac point.

Findings

Kondo temperature formula derived for Dirac systems.

T_K vanishes at the Dirac point where the Fermi surface shrinks to zero.

Logarithmic temperature dependence of resistivity and heat capacity in certain regimes.

Abstract

We investigate the Kondo effect in Dirac systems, where Dirac electrons interact with the localized spin via the s-d exchange coupling. The Dirac electron in solid state has the linear dispersion and is described typically by the Hamiltonian such as $H_k= v{\bf k}\cdot {\sigma}$ for the wave number ${\bf k}$ where $\sigma_j$ are Pauli matrices. We derived the formula of the Kondo temperature $T_{\rm K}$ by means of the Green's function theory for small $J$. The $T_{\rm K}$ is determined from a singularity of Green's functions in the form $T_{\rm K}\simeq \bar{D}\exp(-{\rm const.}/\rho |J|)$ when the exchange coupling $|J|$ is small where $\bar{D}=D/\sqrt{1+D^2/(2\mu)^2}$ for a cutoff $D$ and $\rho$ is the density of states at the Fermi surface. When $|\mu|\ll D$, $T_{\rm K}$ is proportional to $|\mu|$: $T_{\rm K}\simeq |\mu|\exp(-{\rm const.}/\rho |J|)$. The Kondo screening will, however, disappear when the Fermi surface shrinks to a point called the Dirac point, that is, $T_{\rm K}$ vanishes when the chemical potential $\mu$ is just at the Dirac point. The resistivity and the specific heat exhibit a log-$T$ singularity in the range $T_{\rm K} < T\ll |\mu|/k_{\rm B}$. Instead, for $T\sim O(|\mu|)$ or $T>|\mu|$, they never show log-$T$.