Second-order phase transitions in metals are a longstanding question, often linked to charge-density waves, Peierls distortions, or Kohn anomalies in the phonon spectrum. Such a phase transition has recently been observed in cubic ${\mathrm{LaH}}_{10}$, a material that exhibits superconductivity with exceptionally high critical temperature up to 260 K. Previous work has shown that this phase is unstable below 200 GPa if quantum effects and anharmonicity are not present. Here, we study the instabilities occurring in this material at such pressures. Lowering the electronic temperature to 0 K softens the phonon branches along the $\mathrm{\Gamma }-X, K-\mathrm{\Gamma }, \mathrm{\Gamma }-L-U$, and $W-L-K$ directions. We relate these softenings to the linewidths predicted in the electronic high-temperature phonon band structure of ${\mathrm{LaH}}_{10}$ at specific wave vectors. The correspondence is striking: both functions are either large or small for all investigated wave vectors. In contrast, the Fermi nesting function, often invoked for such structural phase transitions, provides little insight. The phase transition in ${\mathrm{LaH}}_{10}$ is found to be similar to the one previously observed for paradigmatic charge-density-wave materials, $2H-{\mathrm{NbSe}}_2, {\mathrm{TaTe}}_4$, and $1T-{\mathrm{VSe}}_2$. Going beyond the observation of a simple coincidence between the softening and the linewidth, we highlight the similarities and differences between the equations describing the Fermi surface nesting function, the phonon linewidth, and the temperature dependence of the phonon frequencies. Furthermore, we analyze the contributions to the calculated phonon linewidth from the four electronic bands crossing the Fermi surface of ${\mathrm{LaH}}_{10}$. One specific intra-band contribution clearly dominates. However, the corresponding variation in the charge density of that specific band with temperature is negligible.

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• Charge density waves
• Electron-phonon coupling
• Fermi surface
• Phonons
• Superconductivity
• Hydrides
• Density functional calculations