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

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 $σ_{yx}^{S_y}$ and $σ_{yx}^{L_y}$ 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, $σ_{yx}^{S_y}$ and $σ_{yx}^{L_y}$ 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.