Motivated by the absence of experimental superconductivity in the metallic $\mathit{Pm}\overline{3}\mathit{n}$ phase of ${\mathrm{AlH}}_3$ despite the predictions, we reanalyze its vibrational and superconducting properties at pressures $P\ge 99$ GPa making use of first-principles techniques. In our calculations based on the self-consistent harmonic approximation method that treats anharmonicity beyond perturbation theory, we predict a strong anharmonic correction to the phonon spectra and demonstrate that the superconducting critical temperatures predicted in previous calculations based on the harmonic approximation are strongly suppressed by anharmonicity. The electron-phonon coupling concentrates on the lowest-energy hydrogen-character optical modes at the X point of the Brillouin zone. As a consequence of the strong anharmonic enhancement of their frequency, the electron-phonon coupling is suppressed by at least 30%. The suppression in $\lambda$ makes $T_c$ smaller than 4.2 K above 120 GPa, which is well consistent with the experimental evidence. Our results underline that metal hydrides with hydrogen atoms in interstitial sites are subject to huge anharmonic effects.

• Received 29 January 2021
• Revised 26 March 2021
• Accepted 6 April 2021

DOI:https://doi.org/10.1103/PhysRevB.103.134305