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-$T$.
Categories: cond-mat.str-el