Observation of low energy dispersive modes in un- derdoped (La, Nd) 2--x Sr x CuO 4

We find excitations lower in energy than known phonon modes in underdoped La$_{2-x}$Sr$_x$CuO$_{4+delta}$ (x=0.08), with both inelastic X-Ray scattering (IXS) and inelastic neutron scattering (INS). A non dispersive excitation at 9 meV is identified and is also seen by INS in (La,Nd)$_{2-x}$Sr$_x$CuO$_{4+delta}$, with 40$%$ Nd substitution. INS also identifies a still lower energy dispersive mode at low q in the Nd free sample. These modes are clearly distinct from the longitudinal acoustic phonon and correspond in energy to the Zone Centre modes measured by optical spectroscopy and associated with stripe dynamics.

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 $mathrm{x=0.14pm0.01}$, 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.