Chiral phonons: circularly polarized Raman spectroscopy and $\textit{ab initio}$ calculations in a chiral crystal tellurium

Abstract: Recently, phonons with chirality (chiral phonons) have attracted significant attention. Chiral phonons exhibit angular and pseudo-angular momenta. In circularly polarized Raman spectroscopy, the peak split of the $\Gamma_3$ mode is detectable along the principal axis of the chiral crystal in the backscattering configuration. In addition, peak splitting occurs when the pseudo-angular momenta of the incident and scattered circularly polarized light are reversed. Until now, chiral phonons in binary crystals have been observed, whereas those in unary crystals have not been observed. Here, we observe chiral phonons in a chiral unary crystal Te. The pseudo-angular momentum of the phonon is obtained in Te by an $\textit{ab initio}$ calculation. From this calculation, we verified the conservation law of pseudo-angular momentum in Raman scattering. From this conservation law, we determined the handedness of the chiral crystals. We also evaluated the true chirality of the phonons using a measure with symmetry similar to that of an electric toroidal monopole.