Transverse displacement modulation of the 1D metallic chains in optimally doped yttrium barium copper oxide superconductor*

We report on comprehensive quantitative analyses of x-ray diffuse scattering studies of nanoscale inhomogeneities in the optimally doped YBCO superconductor. In addition to previously studied ${\bf q}_0=\left(\frac{1}{4},0,0\right)$ superstructure due to oxygen vacancy ordered ORTHO-IV phase and Huang diffuse scattering due to coherent long-range strain, we present a clear x-ray scattering observation of a transverse displacement modulation of the 1D CuO metallic chains. This modulation co-exists within the well-formed ORTHO-IV patches and persists at temperatures well below $T_c$. Interestingly, the periodicity of this modulation is close to that of $\frac{1}{2k_F}$ according to electronic band calculations. The significance of these modulation and their role in the formation of the electronic inhomogeneities on a nano-meter length scales will be discussed.