Lattice dynamics with molecular Berry curvature: Chiral optical phonons

Under the Born-Oppenheimer approximation, electronic ground state evolves adiabatically and can accumulate geometrical phases characterized by molecular Berry curvature. In this work, we study effect of curvature on lattice dynamics in a system with broken time-reversal symmetry. The is formulated based single-particle Bloch states. It manifests as nonlocal effective magnetic field equations motion ions that are beyond widely adopted Raman spin-lattice coupling model. We employ Bogoliubov transformation to solve quantized obtain phonon polarization vectors. apply our formula Haldane model honeycomb find large around Brillouin zone center. As result, degeneracy optical branches at point lifted intrinsically. phonons show circular polarizations, possess curvature, have nearly angular momentum modifies Einstein-de Haas effect.