Scale-free structural organization of oxygen interstitials in La2CuO4+y

It is well known that the microstructures of the transition-metal oxides1, 2, 3, including the high-transition-temperature (high-Tc) copper oxide superconductors4, 5, 6, 7, are complex. This is particularly so when there are oxygen interstitials or vacancies8, which influence the bulk properties. For example, the oxygen interstitials in the spacer layers separating the superconducting CuO2 planes undergo ordering phenomena in Sr2O1+yCuO2 (ref. 9), YBa2Cu3O6+y (ref. 10) and La2CuO4+y (refs 11-15) that induce enhancements in the transition temperatures with no changes in hole concentrations. It is also known that complex systems often have a scale-invariant structural organization16, but hitherto none had been found in high-Tc materials. Here we report that the ordering of oxygen interstitials in the La2O2+y spacer layers of La2CuO4+y high-Tc superconductors is characterized by a fractal distribution up to a maximum limiting size of 400 ?m. Intriguingly, these fractal distributions of dopants seem to enhance superconductivity at high temperature.