Key pairing interaction in layered doped ionic insulators

A controversial issue on whether the electron-phonon interaction (EPI) is crucial for high-temperature superconductivity or it is weak and inessential has remained one of the most challenging problems of contemporary condensed matter physics. We employ a continuum random phase approximation for the dielectric response function allowing for a self-consistent semianalytical evaluation of the EPI strength, electron-electron attractions, and the carrier mass renormalization in layered high-temperature superconductors. We show that the Fr?hlich EPI with high-frequency optical phonons in doped ionic lattices is the key pairing interaction, which is beyond the BCS-Migdal-Eliashberg approximation in underdoped superconductors, and it remains a significant player in overdoped compounds.