  High temperature superconductivity emerges in unique materials, like
cuprates, that belong to the class of heterostructures at atomic limit, made of
a superlattice of superconducting atomic layers intercalated by spacer layers.
The physical properties of a strongly correlated electronic system, emerge from
the competition between different phases with a resulting inhomogeneity from
nanoscale to micron scale. Here we focus on the spatial arrangements of two
types of structural defects in the cuprate La2CuO4+y : i) the local lattice
distortions in the CuO2 active layers and ii) the lattice distortions around
the charged chemical dopants in the spacer layers. We use a new advanced
microscopy method: scanning nano X-ray diffraction (nXRD). We show here that
local lattice distortions form incommensurate nanoscale ripples spatially
anticorrelated with puddles of self-organized chemical dopants in the spacer
layers.
