Origin of phonon anomalies inLa2CuO4

The experimentally observed softening of the oxygen breathing mode at the X point, ${\mathrm{O}}_{\mathrm{X}}^{\mathrm{B}}$, and of a second CuO bond stretching mode of ${\mathrm{\Delta }}_1$ symmetry at the wave vector q=(0.5,0,0) in the doped metallic phase of La-Cu-O is investigated and shown to be driven by long-range, nonlocal electron-phonon interaction effects of monopole charge-redistribution type. The amplification of softening for both modes by about 1 THz, recently found in inelastic neutron scattering for an optimally doped ${\mathrm{La}}_{1.85}$ ${\mathrm{Sr}}_{0.15}$ ${\mathrm{CuO}}_4$ probe as compared with an underdoped ${\mathrm{La}}_{1.9}$ ${\mathrm{Sr}}_{0.1}$ ${\mathrm{CuO}}_4$ crystal is explained by the growing importance of the more extended orbitals in the charge response in particular at the Cu ion. Such an enlarged contribution of the more extended orbitals leads to a reduction of the dominant self-interaction, U, of the electrons mainly at the Cu and allows for an enhancement of the monopole charge redistributions whose magnitude determines the softening of the phonon modes. The existence of a specific mixture of localized and more extended states at the Fermi energy is crucial for the appearance of the strong nonlocal electron-phonon coupling of ionic origin and for the reinforcement of the phonon mediated part of pairing in the high-temperature superconductors.