Dispersion of the high-energy phonon modes in Nd$_{1.85}$Ce$_{0.15}$CuO$_4$

The dispersion of the high-energy phonon modes in the electron doped high-temperature superconductor Nd$_{1.85}$Ce$_{0.15}$CuO$_4$ has been studied by inelastic neutron scattering. The frequencies of phonon modes with Cu-O bond-stretching character drop abruptly when going from the Brillouin zone center along the [100]-direction; this dispersion is qualitatively similar to observations in the hole-doped cuprates. We also find a softening of the bond-stretching modes along the [110]-direction but which is weaker and exhibits a sinusoidal dispersion. The phonon anomalies are discussed in comparison to hole-doped cuprate superconductors and other metallic perovskites.