Anharmonic and nonadiabatic electron-phonon effects in hydride superconductors

Recent discoveries of high-pressure hydrides have identified these materials as promising candidates for room-temperature superconductivity. Due to the light mass of hydrogen, they exhibit high-frequency phonons, resulting in pronounced nonadiabatic effects when the phonon and electronic energy scales become comparable. In addition, strong lattice anharmonicity from hydrogen vibrations further modifies the electron-phonon interaction. In this work, we examine the combined influence of anharmonic phonons and nonadiabatic electron-phonon vertex corrections on the superconducting properties of hydrides, including H₃S and YH₆. Our results indicate that both effects have a significant impact on the theoretical prediction of the superconducting critical temperature T_c, improving agreement with experimental observations.