Influence of Landau levels in the phonon dispersion of Weyl semimetals

Weyl semimetals display unusual electronic transport properties when placed under magnetic fields. Here, we investigate how magnetic fields alter the dynamics of long wavelength lattice vibrations in these materials. To that end, we develop a theory for the phonon dispersion, which incorporates contributions from chiral and nonchiral Landau levels, electron-phonon interactions, electron-electron interactions, and disorder. We predict (i) a magnetic-field-induced hybridization between optical phonons and plasmons, (ii) avoided crossings between pseudoscalar optical phonons and electronic excitations originating from nonchiral Landau levels, (iii) a sharp dependence of the sound velocity on the relative angle between the sound propagation and the magnetic field. We compare our results to recent theoretical studies on the signatures of the chiral anomaly in phonon dynamics.