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

TL;DR

This paper reveals a hedgehog orbital texture in p-type tellurium caused by spin-orbit interactions, leading to novel nonreciprocal Hall effects, confirmed through theoretical modeling and AC magnetotransport experiments.

Contribution

It demonstrates how Weyl-like textures emerge in tellurium's valence bands and induce unique Hall responses, linking topological features to observable transport phenomena.

Findings

Hedgehog orbital magnetic texture exists at the top valence band.

Induces nonreciprocal, antisymmetric Hall components.

Experimental confirmation via AC magnetotransport measurements.

Abstract

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.