revealed by inelastic X-ray scattering*

While charge modulations are ubiquitous in high-temperature superconducting cuprates, understanding their coupling to phonons can provide crucial insight into the role of electron-phonon interactions in high-temperature superconductivity. Here, we have used high-resolution inelastic X-ray scattering to study the doping dependence of the low-energy phonons in the monolayer cuprate (Bi,Pb)₂(Sr,La)₂CuO_6+d, from heavily underdoped (p=0.03) to overdoped (p=0.21) samples. We observe that the longitudinal acoustic phonon along the Cu-O bond direction exhibits a line-shape broadening near the wave vector ~ 0.25 rlu in underdoped samples even when charge order is suppressed, while no broadening occurs in the overdoped samples. Surprisingly, an additional low energy mode around 4 meV is observed in the underdoped samples and is absent in overdoped materials. The origin of the longitudinal phonon broadening and the new low energy mode will be discussed especially in relation to charge order.