Apical oxygen electron-phonon coupling and poor screening in the cuprates

A theory of the effect of screening in anisotropic planar materials on the electron-phonon coupling for phonon vibrations out of the plane is presented. Specifically it is shown that the poor ability of electrons to propagate along the c-axis has consequences on the screened electron-phonon interaction. A theory for the coupling of charge-transfer excitations to apical oxygen phonons in the cuprates is presented, and strong doping dependence of the magnitude and anisotropy of the electron-phonon coupling is demonstrated.