Quantum oscillations in acoustic phonons of nodal-line semimetals

We theoretically investigate the magnetoacoustic oscillation and the attenuation oscillation of long-wavelength acoustic phonons in nodal-line semimetals. Because of the electron-phonon interaction, we observe pronounced oscillatory behaviors in the dispersion modification and attenuation of acoustic phonons at low temperatures. These oscillations, exhibiting unique patterns associated with Fermi surface and magnetic field directions, serve as direct manifestation of both the Fermi-surface geometry and relativistic features of electrons. Our findings propose that these observed oscillations offer discernible signatures for characterizing the electronic structures of the nodal-line semimetals.