  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
4-band kp 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, accessible to transport already 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
wavevector. For spatially dispersive media, such an induced hedgehog
texture/carrier rotation stabilizes two novel, 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
work demonstrates how Weyl signatures generally appear in transport on
enantiomorphic materials with natural optical activity.
