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Novel nanoscale probes are opening new venues for understanding unconventional electronic and magnetic functionalities driven by multiscale lattice complexity in doped high-temperature superconducting perovskites. In this work, we focus on the multiscale texture at supramolecular level of oxygen interstitial (O-i) atomic stripes in HgBa2CuO4+y at optimal doping for the highest superconducting critical temperature (TC) of 94 K. We report compelling evidence for the nematic phase of oxygen interstitial O-i atomic wires with fractal-like spatial distribution over multiple scales using scanning micro- and nano-X-ray diffraction. The scale-free distribution of O-i atomic wires at optimum doping extending from the micron down to the nanoscale has been associated with the intricate filamentary network of hole-rich metallic wires in the CuO2 plane. The observed critical opalescence provides evidence for the proximity to a critical point that controls the emergence of high-temperature superconductivity at optimum doping.

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