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.

16 pages, 3 figures