Multiscale distribution of oxygen puddles in 1/8 doped YBa2Cu3O6.67YBa_{2}Cu_{3}O_{6.67}

Despite intensive research a physical explanation of high Tc superconductors remains elusive. One reason for this is that these materials have generally a very complex structure making useless theoretical models for a homogeneous system. Little is known on the control of the critical temperature by the space disposition of defects because of lack of suitable experimental probes. X-ray diffraction and neutron scattering experiments used to investigate y oxygen dopants in YBa2Cu3O 6+y lack of spatial resolution. Here we report the spatial imaging of dopants distribution in-homogeneity in YBa2Cu3O6.67 using scanning nano X-ray diffraction. By changing the X-ray beam size from 1 micron to 300 nm of diameter, the lattice inhomogeneity increases. The ordered oxygen puddles size distribution vary between 6-8 nm using 1x1 {\mu}m2 beam, while it is between 5-12 nm with a fat tail using the 300x300 nm2 beam. The increased inhomogeneity at the nanoscale points toward an intrinsic granular complexity.Comment: letter, 4 figure