Probing the Chirality of Trigonal Selenium and Tellurium by Spin and Orbital Hall Effects

TL;DR

This study uses first-principles calculations to reveal how the spin and orbital Hall conductivities in chiral trigonal selenium and tellurium depend on their handedness, showing opposite signs for enantiomers due to mirror symmetry effects.

Contribution

It demonstrates the symmetry-based origin of handedness-dependent spin and orbital Hall effects in chiral semiconductors, linking tensor sign reversal to mirror operations.

Findings

Opposite signs of SHC/OHC tensor elements between enantiomers.

Sign reversal of specific tensor components due to mirror symmetry.

Correlation of tensor signs with structural handedness.

Abstract

Chiral crystals exhibit enantiomer-dependent transport phenomena that generate pure spin or orbital currents, while the handedness sensitivity of spin and orbital Hall conductivities (SHC/OHC) remains insufficiently understood. Using first-principles calculations, we demonstrate that trigonal selenium and tellurium -- prototypical chiral semiconductors -- exhibit opposite signs of the SHC/OHC tensor elements $\sigma_{yx}^{S_y}$ and $\sigma_{yx}^{L_y}$ between their left- and right-handed enantiomers. This behavior originates from the mirror operation relating the two structures, described by space groups $P3_221$ (left-handed) and $P3_121$ (right-handed). Although both enantiomers share identical band structures and four nonzero SHC/OHC tensor components, $\sigma_{yx}^{S_y}$ and $\sigma_{yx}^{L_y}$ reverse sign due to the antisymmetric transformation of the spin/orbital Berry curvature under the $M_{xy}$ mirror operation. More generally, for mirror-related enantiomorphic structures, selected SHC/OHC tensor components can exhibit symmetry-governed sign reversal. For trigonal Se and Te, the calculated signs of these components can be directly correlated with the left- and right-handed structures under the chosen coordinate convention. These results clarify the symmetry origin of handedness-dependent SHC/OHC and suggest a possible route for correlating measurable SHC/OHC signals with structural handedness in specific chiral materials.