Electron-Phonon Coupling with Spin and Orbital Angular Momentum Transfer

Spin and orbital angular-momentum transfer between lattice vibrations and electrons has become an important focus beyond traditional electron-phonon coupling. Recent studies of spin-rotation coupling have shown that the rotational motion of lattice elastic vibrations can directly interact with the electron spin. Here we develop a microscopic description of the electron-phonon angular momentum coupling beyond spin-rotation coupling, which includes both the electron spin and orbital angular momentum from the relative motion of atoms in a local co-rotating lattice. We relate the lattice angular velocity to the atom-relative angular momentum through the inertia tensor, so that the lattice angular momentum, coupled to total electron angular momentum, contains both phonon spin and orbital angular momentum. The microscopic construction connects with continuum rotation descriptions, extends to non-rigid motion, and reveals discrete-lattice effects beyond the long-wavelength limit. These results provide a microscopic framework of electron-phonon coupling with spin and orbital angular momentum transfer, enabling both studies of phonon-driven electron spin and orbital dynamics and electron-driven phonon spin and orbital dynamics.