Tellurium is a gyrotropic, $p$-type Weyl semiconductor with remarkable electronic, optical, and transport properties. It has been argued that some of these properties might stem from Weyl nodes at crossing points in the band structure and their nontrivial topological textures. However, Weyl nodes in time-reversal invariant semiconductors are split up in energy, rather than in momentum, and located deep below (far above) the top (bottom) of the valence (conduction) band, challenging such an interpretation. Here, instead, we use a four-band$\mathbf{k}·\mathbf{p}$ Hamiltonian for $p$-type tellurium to show how the k-dependent spin-orbit interaction mixes up the top two (Weyl node free) and bottom two (Weyl-node-containing) valence bands, generating a 3D hedgehog orbital magnetic texture at the uppermost valence band, already accessible to transport at the lowest doping. Hedgehog textures are important signatures of Weyl fermion physics, in general, and in the context of condensed matter physics arise form the carriers' wave packet rotation being locked to their propagation wave vector. For spatially dispersive media, such an induced hedgehog texture/carrier rotation stabilizes two nonreciprocal and antisymmetric components to the Hall transport within different weak-localization (antilocalization) relaxation regimes: the anomalous and planar Hall effects, usually forbidden by time-reversal symmetry. Our AC magnetotransport measurements on Sn-doped tellurium confirm the theoretical predictions and our paper demonstrates how Weyl signatures generally appear in transport on enantiomorphic materials with natural optical activity.

• Received 7 August 2022
• Revised 14 November 2022
• Accepted 14 December 2022

DOI:https://doi.org/10.1103/PhysRevMaterials.7.014204