Spatial anisotropy of the Kondo screening cloud in a type-II Weyl semimetal

We theoretically study the Kondo screening of a spin-1/2 magnetic impurity in the bulk of a type-II Weyl semimetal (WSM) by use of the variational wave-function method. We consider a type-II WSM model with two Weyl nodes located on the k_z axis, and the tilting of the Weyl cones are along the k_x direction. Due to coexisting electron and hole pockets, the density of states at the Fermi energy becomes finite, leading to a significant enhancement of the Kondo effect. Consequently, the magnetic impurity and the conduction electrons always form a bound state; this behavior is distinct from that in type-I WSMs, where the bound state is only formed when the hybridization exceeds a critical value. Meanwhile, the spin-orbit coupling and unique geometry of the Fermi surface lead to a strongly anisotropic Kondo screening cloud in coordinate space. The tilting terms break the rotational symmetry of the type-II WSM about the k_z axis, but the system remains invariant under a combined transformation T R^y(π ) , where T is the time-reversal operation and R^y(π ) is the rotation about the y axis by π . Largely modified diagonal and off-diagonal components of the spin-spin correlation function on three principal planes reflect this change in band symmetry. Most saliently, on the x -z plane, tilting terms trigger the emergence of nonzero off-diagonal spin-spin correlation function J_{y z}(r ) and J_{x y}(r ) , while in a type-I WSM they vanish on the x -z plane.