Sharp optical phonon softening close to optimal doping in   La$_{2-x}$Ba$_x$CuO$_{4+\delta}$
  We report a direct observation of a sharp Kohn-like anomaly in the doubly degenerate copper-oxygen bond-stretching phonon mode occurring at $\mathbf{q}\mathrm{=(0.3, 0,0)}$ in La$_{2-x}$Ba$_x$CuO$_{4+\delta}$ with $\mathrm{x=0.14\pm0.01}$, thanks to the high $\mathbf{Q}$ resolution of inelastic x-ray scattering. This anomaly is clearly seen when the inelastic signal is analysed using a single mode but is also consistent with a two mode hypothesis possibly due to a splitting of the degenerate modes due to symmetry breaking stripes. Our observation shows that the effect persists at the stripe propagation vector in a superconducting system close to optimal doping. 
Matteo D'Astuto (IMPMC), Guy Dhalenne (CHIMSOL), Jeff Graf, Moritz   Hoesch (ESRF), Paola Giura (IMPMC), Michael Krisch (ESR...