Inelastic X-ray scattering study of the bond stretching phonon mode in Bi$_2$Sr$_{2x}$Cu$_2$O$_{6+\delta}$

The phonon dispersions of the single layer high temperature superconductor Bi$_2$Sr$_{2-x}$Cu$_2$O$_{6+\delta}$ along the [$\xi$ 0 0] direction have been determined by inelastic x-ray scattering. The two highest longitudinal phonon branches, associated with the Cu-O bond stretching and out-of-plane oxygen vibration, are clearly resolved for the first time. The comparison with La$_{2}$Sr$_x$Cu$_2$O$_{0}$ will be discussed.