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

Abstract: In this work, we resolve conflicting experimental and theoretical findings related to the dynamical stability and superconducting properties of $Fm\overline{3}m$-LuH$3$, 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 $Fm\overline{3}m$ phase near ambient pressures is suppressed for temperatures above $200\,\text{K}$. We provide a $p\,\unicode{x2013}\,T$ phase diagram for stability up to pressures of $6\,\text{GPa}$, where the required temperature for stability is reduced to $T>80\,\text{K}$. We also determine the superconducting critical temperature $T\text{c}$ of $Fm\overline{3}m$-LuH$3$ within the Migdal-Eliashberg formalism, using temperature- and quantum-anharmonically-corrected phonon dispersions, finding that the expected $T\text{c}$ for electron-phonon mediated superconductivity is in the range of $50$ $\unicode{x2013}$ $60\,\text{K}$, i.e., well below the temperatures required to stabilize the lattice. When considering moderate doping based on rigidly shifting the Fermi level, $T_\text{c}$ decreases for both hole and electron doping. Our results thus provide evidence that any observed room-temperature superconductivity in pure or doped $Fm\overline{3}m$-LuH$_3$, if confirmed, cannot be explained by a conventional electron-phonon mediated pairing mechanism.