Nonreciprocal Acoustic and Optical Phonon Dispersion Mediated by Berry Curvature in Chiral Weyl Semimetals

Abstract: We investigate the phonon magnetochiral effect (PMCE) in chiral Weyl semimetals by deriving the nonreciprocal dispersion relations of both acoustic and non-polar optical phonons in the presence of a magnetic field. Using a semiclassical Boltzmann kinetic framework that incorporates Berry curvature, orbital magnetic moment, and node-dependent electronic structure, we obtain analytic expressions for the magnetic-field-induced corrections to the phonon dynamical matrix. Inequivalent Weyl nodes with distinct Fermi velocities, Fermi energies, and relaxation times generate a dynamical chiral imbalance that alters the phonon dispersion. For acoustic phonons, the formalism yields the magnetic-field-dependent corrections to the longitudinal mode, while for optical phonons we identify an optical analogue of the PMCE that produces a corresponding shift in the optical branch. Together, these results provide a unified theoretical description of how band-geometric properties of Weyl fermions influence both acoustic and optical phonon dispersions in chiral Weyl semimetals.