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

## TL;DR

This paper investigates how the unique electronic structure of a type-II Weyl semimetal influences the Kondo screening cloud around a magnetic impurity, revealing anisotropic features and enhanced binding due to electron-hole pockets.

## Contribution

It introduces a theoretical analysis of Kondo screening in a type-II Weyl semimetal, highlighting the effects of tilting and Fermi surface geometry on anisotropic spin correlations and bound state formation.

## Key findings

- Finite density of states enhances Kondo effect in type-II WSMs.
- Magnetic impurity always forms a bound state, unlike in type-I WSMs.
- Tilting induces non-zero off-diagonal spin-spin correlations on the x-z plane.

## Abstract

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 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 $k_z$-axis, but the system remains invariant under a combined transformation $\mathcal{T}R^{y}(\pi)$, where $\mathcal{T}$ is the time-reversal operation and $R^{y}(\pi)$ is the rotation about the $y$-axis by $\pi$. 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.