Electron-phonon interactions in the high-temperature superconductors.

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 \ensuremath{\lambda}\ensuremath{\simeq}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.Low-frequency modes (\ensuremath{\omega}\ensuremath{\simeq}12 meV) imply a quasilinear phonon resistivitiy down to temperatures of the order of 50 K. This band structure also provides reasonable values for the plasma frequency, which like the experimental measurements show a decrease as the insulator is approached. This can be attributed physically to an enhanced effective mass, which is a precursor to Mott localization at half-filling. The combination of the plasma frequency and electron-phonon coupling leads to a relatively concentration-independent resistivity slope, whose magnitude accounts for a large fraction of the measured linear resistivity at moderate and high hole concentrations x. However, this phonon background is significantly less than the measured resistivity slope as the insulator is approached. This suggests that electron-electron scattering may be playing a more dominant role at small x. Following the Mott-Ioffe-Regel criterion, we analyze the implications of our results for the breakdown of the metallic state at finite concentrations x. We conclude with the observation that the strength of the electron-phonon interaction appears to us from transport data, as well as our microscopic calculations to be too weak to be the primary mechanism responsible for high-temperature superconductivity. On the other hand, we cannot with certainty rule this mechanism out.