Comprehensive study of phonon chirality under symmetry constraints

Phonons are quanta of lattice vibrations, and their modes (linear, circular, or stationary) are symmetry-determined. Circularly polarized phonons, possessing nonzero angular momentum (AM), have drawn widespread attention recently. Despite widespread use of pseudo-angular momentum (PAM) and circularly polarized light polarization flips to identify chiral phonons in Raman scattering, their reliability is debated due to symmetry dependence, and experimental verification standards remain lacking. Here, we systematically study phonon chirality and associated phenomena across magnetic point groups. We establish that the AM-PAM correlation is governed by both crystalline symmetry and Wyckoff positions, dictating conditions where nonzero AM manifests in PAM signatures. Crucially, phonons belonging to distinct irreducible representations exhibit distinct experimental benchmarks, enabling direct determination of crystalline chirality and symmetry classification. Furthermore, we report the discovery of a signature for symmetry-induced phenomena, notably a half-wave plate-analogous effect induced by mirror-odd phonons. Meanwhile, we conducted five experiments to validate our theory.