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We report a direct observation of a sharp Kohn-like anomaly in the doublydegenerate 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 ofinelastic x-ray scattering. This anomaly is clearly seen when the inelasticsignal is analysed using a single mode but is also consistent with a two modehypothesis possibly due to a splitting of the degenerate modes due to symmetrybreaking stripes. Our observation shows that the effect persists at the stripepropagation vector in a superconducting system close to optimal doping.

Sharp optical phonon softening close to optimal doping in La$_{2-x}$Ba$_x$CuO$_{4+\delta}$