Nonadiabatic and Anharmonic Effects in High‐Pressure H 3 S and D 3 S Superconductors

ABSTRACT Superconductivity in compressed arises from the interplay between high‐frequency phonons and a pronounced van Hove singularity near the Fermi level. Using first‐principles calculations, we investigate the superconducting properties of and at 160 and 200 GPa, explicitly incorporating anharmonic lattice dynamics and first‐order vertex corrections to electron‐phonon (e‐ph) interactions, thereby going beyond the Migdal approximation underlying conventional Migdal‐Eliashberg theory. We find that both anharmonicity and nonadiabatic vertex corrections suppress the effective e‐ph coupling and reduce the superconducting critical temperature (). Calculations performed within the energy‐dependent full‐bandwidth Eliashberg formalism, including both anharmonic and vertex effects, yield values in close agreement with experimental measurements for at both pressures and for at 200 GPa.