Twofold quadruple Weyl nodes in chiral cubic crystals
Tiantian Zhang, Ryo Takahashi, Chen Fang, Shuichi Murakami
Abstract
Unlike conventional Weyl nodes, unconventional ones carry a quantized monopole charge $\mathcal{C}>1$, and their existence needs the protection of crystalline symmetries in addition to translation symmetry. There have been many studies on unconventional Weyl nodes, yet we have so far missed one, which is the twofold Weyl node with $\mathcal{C}=4$. In this paper, we study the relationship between the winding number and pseudospin texture in all twofold Weyl nodes, and offer an intuitive way to understand the complex pseudospin texture of the twofold quadruple Weyl node. We not only list all the possible space groups and corresponding momenta, where the twofold quadruple Weyl node can be stabilized, but also propose a series of LaIrSi-type materials that have the Weyl node with $\mathcal{C}=4$ in both the electronic band structure and the phonon spectra. In the electronic band structure, the twofold quadruple Weyl node will evolve into a fourfold quadruple Weyl node and change both the chirality and the monopole charge after considering spin-orbit coupling, which is uncommon in the known Weyl semimetals. In the phonon spectra, we propose a platform having a Weyl node with $\mathcal{C}=4$.