Anomalous electron-phonon coupling in the proximity of a ferroelectric phase transition.

We study the problem of electron-phonon coupling in a framework of effective correlated electron-ion dynamics, hence going beyond the standard adiabatic approximation for electrons and Ehrenfest dynamics for ions' vibrations. We focus on the coupling with the transverse optical (TO) branch, a mode that plays a crucial role in the ferroelectric phase transition -- its softening drives the system to the transition. This softening results in an anomalously strong dispersion of the optical mode and brings it very close to acoustic branches. Our study is motivated by recent experimental findings in PbTe where hybridization with the LA mode and the so-called 'waterfall' of spectral weight were detected. By accounting for a strong anharmonicity present in the system close to the transition, we are able to identify a novel scattering mechanism which is driven by the presence of fluctuations of the order parameter in the critical regime. Subsequently, we consider the coupling of TO phonons with electrons as well as TO-LA phonon-phonon scattering. Since our study is dedicated to intermediate temperatures, where the phonon drag effect is the largest, we conclude with a discussion of possible implications for thermoelectric coefficients.