Vibronic mechanism of high-T_c superconductivity

The dispersion of the in-plane Cu-O bond-stretching longitudinal optical 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 an overscreening of the intersite 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_kx²-ky² symmetry and the transition temperature well in excess of 100 K.