The compound ${\mathrm{ZrTe}}_5$ has recently been connected to a charge-density-wave (CDW) state with intriguing transport properties. Here, we investigate quantum oscillations in ultrasound measurements that microscopically originate from electron-phonon coupling and analyze how these would be affected by the presence or absence of a CDW. We calculate the phonon self-energy due to electron-phonon coupling, and from there deduce the sound-velocity renormalization and sound attenuation. We find that the theoretical predictions for a metallic Dirac model resemble the experimental data on a quantitative level for magnetic fields up to the quantum-limit regime.

• Received 8 September 2021
• Revised 22 November 2021
• Accepted 23 November 2021

DOI:https://doi.org/10.1103/PhysRevB.104.245117