Magnetic impurity in a Weyl semimetal

We utilize the variational method to study the Kondo screening of a 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 vertical bar mu vertical bar. The spin-spin correlation function J(uv) (r) between the spin v component of the magnetic impurity at the origin and the spin u component of a conduction electron at spatial point 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 (y) component of the correlation function in the spatial direction of the z axis.