  It is well known that the microstructures of the transition-metal oxides
(refs 1-3), including the high-transition-temperature (high-Tc) copper oxide
superconductors (refs 4-7), are complex. This is particularly so when there are
oxygen interstitials or vacancies (ref.8), which influence the bulk properties.
For example, the oxygen interstitials in the spacer layers separating the
superconducting CuO2 planes undergo ordering phenomena in Sr(2)O(1+y)CuO(2)
(ref. 9), YBa(2)Cu(3)O(6+y) (ref. 10) and La(2)CuO(4+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 La(2)O(2+y) spacer layers of La(2)CuO(4+y) high-Tc superconductors is
characterized by a fractal distribution up to a maximum limiting size of 400
microns. Intriguingly, these fractal distributions of dopants seem to enhance
superconductivity at high temperature.
