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We study Weyl nodes in materials with broken inversion symmetry. We findbased on first-principles calculations that trigonal Te and Se have multipleWeyl nodes near the Fermi level. The conduction bands have a spin splittingsimilar to the Rashba splitting around the H points, but unlike the Rashbasplitting the spin directions are radial, forming a hedgehog spin texturearound the H points, with a nonzero Pontryagin index for each spin-splitconduction band. The Weyl semimetal phase, which has never been observed inreal materials without inversion symmetry, is realized under pressure. Theevolution of the spin texture by varying the pressure can be explained by theevolution of the Weyl nodes in k space.

Weyl Node and Spin Texture in Trigonal Tellurium and Selenium