Dynamical renormalization of electron-phonon coupling in conventional superconductors

The adiabatic Born-Oppenheimer approximation is considered to be a robust approach that very rarely breaks down. Consequently, it is predominantly utilized to address various electron-phonon properties in condensed matter physics. By combining many-body perturbation and density functional theories we demonstrate the importance of dynamical (nonadiabatic) effects in estimating superconducting properties in various bulk and two-dimensional materials. Apart from the expected long-wavelength nonadiabatic effects, we found sizable nonadiabatic Kohn anomalies away from the Brillouin zone center for materials with strong intervalley electron -phonon scatterings. Compared to the adiabatic result, these dynamical phonon anomalies can significantly modify electron-phonon coupling strength lambda and superconducting transition temperature Tc. Further, the dy-namically induced modifications of lambda have a strong impact on transport properties, where probably the most interesting is the rescaling of the low-temperature and low-frequency regime of the scattering time 1/r from about T3 to about T2, resembling the Fermi liquid result for electron-electron scattering. Our goal is to point out the potential implications of these nonadiabatic effects and reestablish their pivotal role in computational estimations of electron-phonon properties.