  The attempt to understand cuprate superconductors is complicated by the
presence of multiple strong interactions. While many believe that
antiferromagnetism is important for the superconductivity, there has been
revived interest in the role of electron-lattice coupling. The recently studied
conventional superconductor MgB2 has a very strong electron-lattice coupling,
involving a particular vibrational mode (phonon), that was predicted by
standard theory and confirmed quantitatively by experiment. Here we present
inelastic scattering measurements that show a similarly strong anomaly in the
Cu-O bond-stretching phonon in the cuprate superconductors La2-xSrxCuO4 (with
x=0.07, 0.15). This is in contrast to conventional theory, which does not
predict such behavior. The anomaly is strongest in La1.875Ba0.125CuO4 and
La1.48Nd0.4Sr0.12CuO4, compounds that exhibit spatially modulated charge and
magnetic order, often called stripe order. It occurs at a wave vector
corresponding to the charge order. These results suggest that this giant
electron-phonon anomaly, which is absent in undoped and over-doped
non-superconductors, is associated with charge inhomogeneity. It follows that
electron-phonon coupling may be important to our understanding of
superconductivity, although its contribution to the mechanism is likely to be
indirect.
