Microscopic Theory of Chiral-Phonon-Induced Orbital Selectivity in Helical Crystals

We present a microscopic theory of chirality-induced orbital selectivity (CIOS) in helical crystals, in which truly chiral phonons selectively transfer angular momentum to electronic orbital degrees of freedom. For a threefold helical crystal with line-group symmetry $L3_1$, we show that phonon-induced local rotations generate a rotational electron-phonon interaction proportional to $\hat{L}^{\pm}$, which drives the orbital transfer $m_{\ell}\to m_{\ell}-m_{s}$ in accordance with crystal angular momentum (CAM) conservation, where $m_{s}=\pm 1$ denotes the eigenvalue of the phonon rotational mode. Evaluating $\langle\hat{L}^{z}\rangle$ to leading order in perturbation theory, we find that the orbital response is suppressed near the $\Gamma$ point and the BZ boundary, and enhanced at intermediate wave vectors -- a feature intimately tied to the degeneracy structure of the phonon bands.