Renormalization of phonon frequencies by conduction electrons in layer systems with application to YBa2Cu3O7

It is generally assumed that there are free electronic carriers associated with the CuO₂ planes in high-temperature superconductors. Regarding these carriers as confined to these planes their influence on phonon frequencies is studied within the framework of a shell model of lattice dynamics taking into account the long-range part of the electron-phonon coupling. We find a complete suppression of the LO-TO splitting for modes polarized along the planes by metallic screening and a strong coupling of electronic plasmon and particle-hole excitations especially to some To-phonon branches polarized perpendicular to the conducting planes, particularly pronounced in systems with at least two CuO₂ planes per unit cell. Numerical results are presented for YBa₂Cu₃O₇.