Vibronic mechanism of high-Tc superconductivity

The dispersion of the in-plane Cu-O bond-stretching LO phonon mode in the high-$T_{C}$ superconducting cuprates shows strong softening with doping near the zone boundary. We suggest that it can be described with a negative electronic dielectric function that results in overscreening of inter-site Coulomb interaction due to phonon-induced charge transfer and vibronic electron-phonon resonance. We propose that such a strong electron-phonon coupling of specific modes can form a basis for the phonon mechanism of high-temperature superconductivity. With the Eliashberg theory using the experimentally determined electron dispersion and dielectric function, we demonstrate the possibility of superconductivity with the order parameter of the $d_{k_{x}^{2}-k_{y}^{2}}$ symmetry and the transition temperature well in excess of 100K.