Effect of charge fluctuations on the phonon dispersion and electron-phonon interaction inLa2CuO4

In this paper we propose a formulation of the electronic density response that is well suited to investigate the influence of localization and delocalization properties of the electrons on the phonon dispersion and the electron-phonon interaction. The formalism is applied to study nonlocal, long-range, electron-phonon-interaction effects of the charge-fluctuation type in high-temperature superconductors, using ${\mathrm{La}}_2$ ${\mathrm{CuO}}_4$ as an example. Some important features in the experimental phonon spectrum can be understood within such an approach. We discuss the modification of the usual picture of electron pairing, taking into account these nonlocal effects. In this context the symmetric apical oxygen breathing mode at the Z point is of special importance. In this vibration, nonlocal electron-phonon-interaction effects of the charge-fluctuation type are shown to generate in the metallic phase of ${\mathrm{La}}_2$ ${\mathrm{CuO}}_4$ an interplane charge transfer that is blocked completely in the insulating phase if a strictly two-dimensional electronic structure is assumed. Very recently we became aware of unpublished experimental results where this previously undetected mode appears, unusually broad, as the highest ${\mathrm{\Lambda }}_1$ mode at the Z point, in agreement with our theoretical predictions for the insulating phase. Finally, our considerations point towards a simple structure that could be very effective for high-temperature superconductivity.