Axionic acoustic phonons from Weyl semimetals

The sound propagation properties resulting from a dynamical axion insulator generated from a Weyl semimetal are explored. Axial electron-phonon coupling in Weyl semimetals hybridizes phonons with the axion field changing their velocity and attenuation. At the random phase approximation (RPA) level, this hybridization gives rise to weaker modification of the speed of sound in longitudinal waves propagating parallel to the axionic charge density wave (ACDW) wave vector than in transverse waves. On the other hand, the attenuation is modified by anharmonic phonon interactions beyond the RPA, but the axionic contribution to this attenuation is negligible. While the corrections on sound attenuation might be too weak to observe, the corrections to the speed of sound should be accessible in ultrasound propagation experiments. In the presence of a magnetic field, these corrections are sensitive to the magnetic field through the value of the ACDW gap and the axion velocity, but not through the axial anomaly, implying that these effects can be observed in the absence of an applied electric field. Finally, we also discuss the importance of axial electron-phonon interactions with respect to the more conventional vector interactions in these systems.