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Tellurium is a gyrotropic, p-type Weyl semiconductor with remarkableelectronic, optical, and transport properties. It has been argued that some ofthese properties might stem from Weyl nodes at crossing points in the bandstructure, and their nontrivial topological textures. However, Weyl nodes intime-reversal invariant semiconductors are split up in energy, rather than inmomentum, and located deep below (far above) the top (bottom) of the valence(conduction) band, challenging such an interpretation. Here, instead, we use a4-band kp Hamiltonian for $p-$type tellurium to show how the k-dependentspin-orbit interaction mixes up the top two (Weyl node free) and bottom two(Weyl node containing) valence bands, generating a 3D hedgehog orbital magnetictexture at the uppermost valence band, accessible to transport already at thelowest doping. Hedgehog textures are important signatures of Weyl fermionphysics in general and in the context of condensed matter physics arise formthe carriers' wave packet rotation being locked to their propagationwavevector. For spatially dispersive media, such an induced hedgehogtexture/carrier rotation stabilizes two novel, nonreciprocal and antisymmetriccomponents 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 magnetotransportmeasurements on Sn-doped tellurium confirm the theoretical predictions and ourwork demonstrates how Weyl signatures generally appear in transport onenantiomorphic materials with natural optical activity.

Hedgehog orbital texture in p-type tellurium and the antisymmetric nonreciprocal Hall response