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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 μm. Intriguingly, these fractal distributions of dopants seem to enhance superconductivity at high temperature.

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Figure 1: Mixed real- and reciprocal-space images of dopant ordering.
Figure 2: Scale-free fractal distribution and power-law statistical analysis of ordered i-O domains.
Figure 3: Nucleation and growth of i-O superstructures.


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We are grateful to the ID13 beamline staff at ESRF, R. Davies, S. Agrestini, V. Palmisano, E. J. Sarria, L. Simonelli and A. Vittorini Orgeas for help in the early stage of this research project. We thank J. Zaanen and G. Bianconi for suggestions, comments and help with the data analysis. This experimental work has been carried out with the financial support of the European STREP project 517039 “Controlling Mesoscopic Phase Separation” (COMEPHS) (2005–2008) and Sapienza University of Rome, research project “Stripes and High-Tc Superconductivity”.

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Authors and Affiliations



A.B. and M.F. designed the experiment; M.B. provided the X-ray beamline; N.P., A.R. and M.F. performed the data analysis. All authors contributed to providing experimental support, interpreting data and writing the manuscript.

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Correspondence to Antonio Bianconi.

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The authors declare no competing financial interests.

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Supplementary Information

This file contains Supplementary Information comprising Micro X-ray diffraction experimental set up; Surface resistivity method; The spatial correlation function and Supplementary Figures 1-2 with legends. (PDF 183 kb)

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Fratini, M., Poccia, N., Ricci, A. et al. Scale-free structural organization of oxygen interstitials in La2CuO4+y. Nature 466, 841–844 (2010).

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