We study Weyl nodes in materials with broken inversion symmetry. We find based on first-principles calculations that trigonal Te and Se have multiple Weyl nodes near the Fermi level. The conduction bands have a spin splitting similar to the Rashba splitting around the H points, but unlike the Rashba splitting the spin directions are radial, forming a hedgehog spin texture around the H points, with a nonzero Pontryagin index for each spin-split conduction band. The Weyl semimetal phase, which has never been observed in real materials without inversion symmetry, is realized under pressure. The evolution of the spin texture by varying the pressure can be explained by the evolution of the Weyl nodes in k space.
@article{arxiv.1409.7517,
title = {Weyl Node and Spin Texture in Trigonal Tellurium and Selenium},
author = {Motoaki Hirayama and Ryo Okugawa and Shoji Ishibashi and Shuichi Murakami and Takashi Miyake},
journal= {arXiv preprint arXiv:1409.7517},
year = {2015}
}