Sharp optical-phonon softening near optimal doping inLa2−xBaxCuO4+δobserved via inelastic x-ray scattering

We report a direct observation of a sharp Kohn-type anomaly in the doubly degenerate copper-oxygen bond-stretching phonon mode occurring at $\mathbf{q}=(0.3,0,0)$ in ${\text{La}}_{2\ensuremath{-}x}{\text{Ba}}_{x}{\text{CuO}}_{4+\ensuremath{\delta}}$, with $x=0.14\ifmmode\pm\else\textpm\fi{}0.01$, thanks to the high $\mathbf{Q}$ resolution of inelastic x-ray scattering. This anomaly is clearly seen when the inelastic signal is analyzed 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.