Electron-phonon coupling associated with charge-stripe order in cuprate superconductors

We have used inelastic neutron scattering to study the Cu-O bond-stretching phonon in La$_{1.875}$Ba$_{0.125}$CuO$_{4}$ and La$_{1.48}$Nd$_{0.4}$Sr$_{0.12}$CuO$_{4}$, two cuprate compounds that exhibit charge-stripe order. This is the phonon mode that one expects to be most sensitive to spatial inhomogeneity in the electronic structure of the CuO$_{2}$ planes. Besides the cosine-like downward dispersion of the mode from zone center to zone boundary, we observe a dip in the dispersion and a very large energy width ($>$ 10 meV) at \textbf{q} = \textbf{a}*/4. The dip and width gradually become smaller with increasing temperature. These evidences of a strong electron-phonon coupling (the dispersion dip and large energy width) have not been predicted by any conventional calculations. The nature of the connection with charge-stripe order will be discussed.