Electron-Chiral Phonon Coupling, Crystal Angular Momentum, and Phonon Chirality

We explicitly derive the wavefunctions of chiral phonons propagating along the helical axis in chiral crystals and clarify the characteristics of electron-phonon interactions in chiral helical crystals. In particular, we elucidate how the conservation of not only the crystal momentum (CM) but also the crystal angular momentum (CAM) manifests in the interaction vertex. This formulation provides a microscopic framework for describing physical processes involving chiral phonons. Furthermore, we construct a phononic analogue of Zilch, a known measure of chirality carried by light, and discuss its relationship with phonon angular momentum.