Quantum impurity in topological multi-Weyl semimetals

Multi-Weyl semimetals are new types of topological semimetals which have anisotropic nonlinear energy dispersion and whose topological charge can be 2 or more depending on the value of the winding number J. Here we investigate the Kondo effect of a spin-1/2 magnetic impurity in a multi-Weyl semimetal of different J by using the variational wave function method. For different J, the binding energy is always positive in the presence of broken inversion symmetry, and a bound state is favored to form between the impurity and the host electrons. It is found that the formed bound state is more stable for larger J. Due to the spin-orbit coupling, the components of spin-spin correlation functions J(uv) (r) (u, v = x, y, z) show strong anisotropy in the coordinate space. The spinspin correlation indicates distinct decay behaviors along different directions due to the anisotropic dispersion in the energy band. In the case of J = 2 and J = 3, the rotational symmetries of the spatial spin-spin correlations are displayed. Especially, the components J(xx) and J(yy) and J(xy) and -J(yx) can be related through a pi/(2J) rotation.