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

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

Truly chiral phonons in {\alpha}-HgS

Chirality is a manifestation of the asymmetry inherent in nature. It has been defined as the symmetry breaking of the parity of static objects, and the definition was extended to dynamic motion such that true and false chiralities were distinguished. Recently, rotating, yet not propagating, atomic motions were predicted and observed in two-dimensional materials, and they were referred to as "chiral phonons" . A natural development would be the discovery of truly chiral phonons that propagate while rotating in three-dimensional materials. Here, we used circularly polarised Raman scattering and first-principles calculations to identify truly chiral phonons in chiral bulk crystals. This approach enabled us to determine the chirality of a crystal in a non-contact and non-destructive manner. In addition, we demonstrated that the law of the conservation of pseudo-angular momentum holds between circularly polarised photons and chiral phonons. These findings are expected to help develop ways for transferring the pseudo-angular momentum from photons to electron spins via the propagating chiral phonons in opto-phononic-spintronic devices