Competing striped structures in La2CuO4+y

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.