High-temperature superconductivity: the role of dielectricity

The large ionic dielectric constant observed in the cuprates and in organic superconductors has drastic effects on both superconducting and normal-state properties. Specifically, the electron-phonon coupling is enhanced to an extent that it can account for high-temperature superconductivity via a phonon-mediated interaction. The electron-phonon scattering becomes very large for forward scattering accounting for the d-wave symmetry of the gap parameter. We generalized the Eliashberg equations for the case of a renormalized, frequency-dependent coupling constant arising from this huge ionic polarizability. The solution of the generalized Eliashberg equations along the imaginary-ω axis is straightforward. Extension of the solutions to the real-ω axis requires an elaborate algorithm. We worked it out, and find highly unusual spectroscopic properties, accounting for the experimentally observed extended Van Hove singularity, overdamping of electronic states, and the unusually large values of 2Δ₀/T_c. Thus, electron-phonon coupling can account for the various unusual properties of 'exotic' superconductors, when the proximity to a ferroelectric transition, characteristic of the perovskites, is taken into account.