Electron-phonon interactions in the high-temperature superconductors

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Abstract
A characterization of the electron-phonon coupling in the high-temperature superconductors is important both in helping to ascertain the role of phonons in the superconductivity and in helping to characterize the phonon ‘‘background’’ contribution to the temperature-dependent resistivity. Here we present a ‘‘frozen phonon’’ and equivalent diagrammatic scheme for calculating the electron-phonon coupling in the presence of very strong Coulomb correlations. The inclusion of these correlations is essential for creating the insulating state at half-filling. Furthermore, these effects substantially reduce the electron-phonon contribution to the resistivity, so that the experimentally measured coupling constant of the resistivity λ≃0.2–0.4 can be reconciled with the necessarily smaller electron-phonon contribution. Our frozen-phonon scheme is based on a Coulomb renormalized band structure of the copper-oxygen plane alone. Coulomb correlations lead to a suppression of charge fluctuations as the insulator is approached and thereby a significant reduction in the electron-phonon coupling.