Nonadiabatic Theory of Chiral Phonon Splitting

Chiral phonon, carrying finite angular momentum, can activate numerous intriguing physical phenomena, such as circular dichroism, phonon magnetic moment, thermal Hall effect, and spin Seebeck effect. They emerge when time reversal symmetry is broken and are often detected in experiments through the splitting of previously degenerate modes into left- and right-handed ones. In this study, we develop a nonadiabatic framework for studying the splitting, which originates from electron-phonon coupling in the presence of spin or orbital magnetization, whether spontaneous or magnetic-field-induced. The theory can be applied to both insulators and metals, demonstrated by model and first-principles calculations.