Quantum impurity in topological multi-Weyl semimetals

Abstract

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 ${J}_{uv}(\mathbf{r})\phantom{\rule{4pt}{0ex}}(u,v=x,y,z)$ show strong anisotropy in the coordinate space. The spin-spin 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 $\ensuremath{-}{J}_{yx}$ can be related through a $\ensuremath{\pi}/(2J)$ rotation.