We utilize variational method to investigate the Kondo screening of a spin-1/2 magnetic impurity in tilted Dirac surface states with the Dirac cone tilted along the ky-axis. We mainly study about the effect of the tilting term on the binding energy and the spin-spin correlation between magnetic impurity and conduction electrons. The binding energy has a critical value while the Dirac cone is slightly tilted. However, as the tilting term increases, the density of states near the Dirac node becomes significant, such that the impurity and the host material always favor a bound state. The diagonal and the off-diagonal terms of the spin-spin correlation between the magnetic impurity and conduction electrons are also studied. Due to the spin-orbit coupling and the tilting of the spectra, various components of spin-spin correlation show very strong anisotropy in coordinate space, and are of power-law decay with respect to the spatial displacements.

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 kz-axis, and the tilting of the Weyl cones are along the kx direction. Due to co-existing electron and hole pockets, the density of states at the Fermi energy becomes finite, leading to a significant enhancement of Kondo effect. Consequently, the magnetic impurity and the conduction electrons always form a bound state, this behavior is distinct from that in the 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 strongly anisotropic Kondo screening cloud in coordinate space. The tilting terms break the rotational symmetry of the type-II WSM about the kz-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, the tilting terms trigger the emergence of non-zero off-diagonal components of spin-spin correlation function on the x-z principal plane. -1 0 1 J y z ( r ) J y z ( r ) J y z ( r ) J y y ( r ) J y y ( r ) J y y ( r ) J z z ( r ) J z z ( r ) J x x ( r ) J z z ( r ) J z z ( r ) z