We utilize the variational method to study the Kondo screening of a $\text{spin}-1/2$ magnetic impurity in a three-dimensional (3D) Weyl semimetal with two Weyl nodes along the $k_z$ axis. The model reduces to a 3D Dirac semimetal when the separation of the two Weyl nodes vanishes. When the chemical potential lies at the nodal point, $\mu =0$, the impurity spin is screened only if the coupling between the impurity and the conduction electron exceeds a critical value. For finite but small $\mu$, the impurity spin is weakly bound due to the low density of states, which is proportional to ${\mu }^2$, contrary to that in a 2D Dirac metal such as graphene and 2D helical metal, where the density of states is proportional to $\left|\mu \right|$. The spin-spin correlation function $J_{uv}\left(\mathbf{r}\right)$ between the spin $v$ component of the magnetic impurity at the origin and the spin $u$ component of a conduction electron at spatial point $\mathbf{r}$ is found to be strongly anisotropic due to the spin-orbit coupling, and it decays in the power law. The main difference of the Kondo screening in 3D Weyl semimetals and in Dirac semimetals is in the spin $x\left(y\right)$ component of the correlation function in the spatial direction of the $z$ axis.

• Received 17 September 2015

DOI:https://doi.org/10.1103/PhysRevB.92.195124