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 Fröhlich 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.

Figure 1

Diagrammatic representation of the screened EPI vertex (a): solid lines correspond to polaron propagators, wavy lines are the exact phonon propagator, and the dashed line is the Coulomb repulsion. (b) long-wave dispersion of zeros of the dielectric function of quasi-2D carriers with the 3D Coulomb repulsion. An optical phonon with the energy 80 meV is also shown.

Figure 2

The on site, $V(0)$ (upper curve), the nearest-neighbor, $V(1)$ (middle curve), and the next-nearest-neighbor, $V(\sqrt{2})$ (lower curve), attractions induced by the Fröhlich EPI for different doping $x$ and two characteristic phonon frequencies, $\hslash {\omega }_0=80\mathrm{meV}$ and $\hslash {\omega }_0=60\mathrm{meV}$.

Figure 3

The carrier mass (in units of the band mass $m=m_e$) as a function of doping for two characteristic phonon frequencies, $\hslash {\omega }_0=80\mathrm{meV}$ and $\hslash {\omega }_0=60\mathrm{meV}$.