Dynamical renormalization of electron-phonon coupling in conventional superconductors

TL;DR

This paper highlights the significance of dynamical (nonadiabatic) effects in electron-phonon interactions, showing they can substantially alter superconducting properties and transport behavior in materials, challenging the traditional adiabatic approximation.

Contribution

It demonstrates the importance of including dynamical effects in calculations of electron-phonon coupling and superconductivity, revealing sizable nonadiabatic anomalies and their impact on material properties.

Findings

Nonadiabatic effects cause significant modifications in electron-phonon coupling and $T_c$.

Sizable nonadiabatic Kohn anomalies are found away from the Brillouin zone center.

Dynamical effects alter low-temperature scattering time from $T^3$ to $T^2$, resembling Fermi liquid behavior.

Abstract

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 $T_c$. Further, the dynamically-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 $1/\tau$ from about $T^3$ to about $T^2$, 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.