Low-q dispersion of transverse acoustic phonons in YBa${}_2$Cu${}_3$O${}_{7-\delta }$

Abstract

High-resolution ($\Delta E$=1.3 meV) inelastic X-ray scattering (IXS) in optimally doped untwinned YBa${}_2$Cu${}_3$O${}_{7-\delta }$ single crystals show that the dispersion of transverse acoustic phonons in the a-direction remains linear with no softening due to bending modes in the long wavelength limit, down to q=0.02. The sound velocity is found to be 2700 +/- 70 m s${}^{-1}$, in excellent agreement with ultrasound measurements, and unchanged upon cooling from room temperature to 98 K. These results rule out a strong coupling between bending dynamics of the CuO${}_2$ planes and charge carriers in cuprates.