Anomalous dispersion of longitudinal optical phonons in oxygen-doped La2−xSrxCuO4+δ

Inelastic neutron scattering has been used to study the in-plane Cu-O bond-stretching mode in oxygen-doped ${\\mathrm{La}}_{1.94}{\\mathrm{Sr}}_{0.06}{\\mathrm{CuO}}_{4.035}$ $({T}_{c}=38\\phantom{\\rule{0.28em}{0ex}}\\text{K})$ and ${\\mathrm{La}}_{2}{\\mathrm{CuO}}_{4+\\ensuremath{\\delta}}$ $({T}_{c}=43\\phantom{\\rule{0.28em}{0ex}}\\text{K})$. Similar to results from optimally doped ${\\mathrm{La}}_{1.85}{\\mathrm{Sr}}_{0.15}{\\mathrm{CuO}}_{4}$ $({T}_{c}=35\\phantom{\\rule{0.28em}{0ex}}\\text{K})$, we observe anomalous features in the dispersion of this half-breathing mode in the form of a softening halfway through the Brillouin zone. Considering the differences in electronic structure and local environment between the oxygen- and strontium-doped compounds with similar ${T}_{\\text{c}}$, we rule out a connection between the phonon anomaly and structural instabilities related to the specific dopant type. We interpret the phonon anomaly as a signature of correlated charge fluctuations ubiquitous in optimally doped superconductors.