Electronic inhomogeneities in superconducting YBa$_{2}$Cu$_{3}$O$_{6+x}$

There has been an increasing amount of experimental evidence for the presence of local electronic inhomogeneities in superconducting cuprates. Inelastic pulsed neutron scattering measurements on YBa$_{2}$Cu$_{3}$O$_{6+x }$single crystals with different oxygen concentrations show that the zone boundary softening of the in-plane LO Cu-O bond stretching mode is the same for all doping levels. In addition, the spectral weight of the softened mode increases with increasing doping. This indicates that there is a microscopic electronic phase separation in superconducting YBa$_{2}$Cu$_{3}$O$_{6+x}$. Furthermore, triple axis inelastic neutron scattering measurements on the underdoped YBa$_{2}$Cu$_{3}$O$_{6.6}$ performed at different temperatures revealed that a new local mode appears at 65 meV at higher temperatures (200 K and above). It might indicate the presence of polarons.