Weyl Nodes in Trigonal Tellurium and Selenium

Singular points in the momentum space (Dirac nodes) have been under intensive investigation recently. Among various Dirac systems, materials having three-dimensional Dirac nodes without spin degeneracy (Weyl nodes) are of particular interest because of their topological nature. We study trigonal Te and Se as systems having both strong spin-orbit interaction (SOI) and broken inversion symmetry, which is necessary for the Weyl node. We calculate the electronic structure by using QMAS [1] based on relativistic density functional theory, and add the self-energy correction in the GW approximation. Te and Se are insulating at ambient pressure. 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. The energy gap decreases with increasing pressure. In the metallic phase, the spin rotates twice around H on the k$_{\mathrm{z}} = \pm \pi$/c plane, which can be explained by the motion of the Weyl nodes under pressure [2]. We also find that trigonal Te shows the Weyl semimetal phase with time-reversal symmetry under pressure [2].\\[4pt] [1] http://www.qmas.jp/\\[0pt] [2] M. Hirayama, R. Okugawa, S. Ishibashi, S. Murakami, and T. Miyake: arXiv 1409.6399.