Anharmonicity and Nonadiabaticity in Hydride Superconductors

Abstract

We study superconductivity in representative hydrides using anharmonic phonons, electron-phonon vertex corrections, and full-bandwidth Eliashberg theory. The high-pressure binary hydrides H3S, YH6, and YH9 must be treated with both anharmonic and nonadiabatic corrections, whereas the ambient-pressure PdH/PdD/PdT series is strongly anharmonic but remains adiabatic, reproducing the inverse isotope effect without sizable vertex contributions. LaBeH8 exhibits weak anharmonicity, while vertex corrections reduce the critical temperature (Tc) by approximately 4 K, leaving the predicted Tc above experiment. To identify when treatments beyond harmonic, adiabatic Migdal-Eliashberg theory are required, we introduce the anharmonic renormalization $A_{\lambda}$ and the vertex ratio $R_{V}$ as material-specific diagnostics.