Higher-order nonadiabaticity governs the temperature dependence of the phonon spectrum

Abstract

Nonadiabatic effects determine the frequency and linewidth of coupled phonon modes, shape of Kohn anomalies and have important implications on many material properties. State-of-the-art ab-initio nonadiabatic phonon self-energy relies on an infinite electron lifetime approximation, which cannot capture the temperature dependence of the phonon spectrum, neglects long-wavelength intraband phonon decay, and exhibits exaggerated phonon splitting. In MgB${}_2$, we show how the higher-order nonadiabatic phonon corrections mitigate these deficiencies, yielding linewidths in a closer experimental agreement and a dome-like coupling strength temperature dependence.