Temperature and quantum anharmonic lattice effects on stability and superconductivity in lutetium trihydride

In this work, we resolve conflicting experimental and theoretical findings related to the dynamical stability and superconducting properties of [Formula: see text]-LuH₃, which was recently suggested as the parent phase harboring room-temperature superconductivity at near-ambient pressures. Including temperature and quantum anharmonic lattice effects in our calculations, we demonstrate that the theoretically predicted structural instability of the [Formula: see text] phase near ambient pressures is suppressed for temperatures above 200 K. We provide a p-T phase diagram for stability up to pressures of 6 GPa, where the required temperature for stability is reduced to T > 80 K. We also determine the superconducting critical temperature T_c of [Formula: see text]-LuH₃ within the Migdal-Eliashberg formalism, using temperature- and quantum-anharmonically-corrected phonon dispersions, finding that the expected T_c for electron-phonon mediated superconductivity is in the range of 50-60 K, i.e., well below the temperatures required to stabilize the lattice. When considering moderate doping based on rigidly shifting the Fermi level, T_c decreases for both hole and electron doping. Our results thus provide evidence that any observed room-temperature superconductivity in pure or doped [Formula: see text]-LuH₃, if confirmed, cannot be explained by a conventional electron-phonon mediated pairing mechanism.