Phonon renormalization reflecting dynamic charge inhomogeneity in copper-oxide superconductors

Our inelastic neutron scattering measurements show that there is a strong anomaly in the Cu-O bond-stretching phonon in cuprate superconductors La$_{2-x}$Sr$_{x}$CuO$_{4}$ (x=0.07,0.15). This behavior also appears in superconducting YBa$_{2}$Cu$_{3}$O$_{6+x}$, however it is completely absent in undoped and overdoped LSCO.$^{ }$In La$_{1.875}$Ba$_{0.125}$CuO$_{4}$ and La$_{1.48}$Nd$_{0.4}$Sr$_{0.12}$CuO$_{4}$, compounds that exhibit spatially modulated charge and magnetic order, often called stripe order, the anomaly occurs at a wave vector corresponding to the charge order. The results suggest that this giant electron-phonon anomaly, which is absent in LDA calculations, is associated with charge inhomogeneity induced by strong electronic correlations. It follows that electron-phonon coupling may be important to understanding the superconductivity although its contribution to the mechanism is probably non-BCS-like.