Fractal Structure Favoring Superconductivity at High Temperatures in a Stack of Membranes Near a Strain Quantum Critical Point

The statistical physics of the 3D ordered oxygen interstitials has been measured in La₂CuO_4+y using an advanced tool, scanning x-ray diffraction with focused synchrotron radiation. The observed fractal scale invariant distribution is found in a cuprate in the proximity to a stripes critical point in the 3D Aeppli-Bianconi phase diagram of cuprates, where T _c is function of both hole doping and superlattice misfit strain. Therefore high-temperature superconductivity is favored by complex fractal systems while on the contrary standard low temperature superconductivity is favored in simple periodic crystals. This work shows that the fractal structural distribution in a stack of membranes favors the macroscopic quantum coherent condensate at high temperature. This result opens new perspectives for the understanding the relationship between emergent scale-free distribution in living matter and possible quantum coherent phenomena able to resist to the attacks of temperature decoherence effects.