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

  • Nature volume 466, pages 841844 (12 August 2010)
  • doi:10.1038/nature09260
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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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  1. 1.

    Complexity in strongly correlated electronic systems. Science 309, 257–262 (2005)

  2. 2.

    Critical features of colossal magnetoresistive manganites. Rep. Prog. Phys. 69, 797–851 (2006)

  3. 3.

    Smart Structures: Blurring the Distinction Between the Living and the Nonliving (Monogr. Phys. Chem. Mater. 65, Oxford Univ. Press, 2007)

  4. 4.

    HTC oxides: a collusion of spin, charge and lattice. J. Phys. Conf. Ser. 108, 012027 (2008)

  5. 5.

    in Superconductivity in Complex Systems (eds Müller, K. A. & Bussmann-Holder, A.) 1–11 (Structure and Bonding 114, Springer, 2005)

  6. 6.

    & Possible high Tc superconductivity in the Ba−La−Cu−O system. Z. Phys. B 64, 189–193 (1986)

  7. 7.

    Percolative theories of strongly disordered ceramic high temperature superconductors. Proc. Natl Acad. Sci. USA 107, 1307–1310 (2010)

  8. 8.

    & Oxygen ion conductors. Mater. Today 6, 30–37 (2003)

  9. 9.

    et al. Enhancement of the superconducting critical temperature of Sr2CuO3+δ up to 95 K by ordering dopant atoms. Phys. Rev. B 74, 100506(R) (2006)

  10. 10.

    et al. Dynamics of oxygen ordering in YBa2Cu3O6+x studied by neutron and high-energy synchrotron X-ray diffraction. Physica C 282–287, 1089–1090 (1997)

  11. 11.

    , , & An intrinsic tendency of electronic phase separation into two superconducting states in La2-xSrxCuO4+y. Phys. Rev. B 65, 144522 (2002)

  12. 12.

    , , & Thermal treatment effect of the oxidized LaCuO4: the access of continuous and discontinuous. Physica C 425, 37–43 (2005)

  13. 13.

    et al. Phase separation in superoxygenated La2−xSrxCuO4+y. Nature Mater. 5, 377–382 (2006)

  14. 14.

    et al. Transformation of strings into an inhomogeneous phase of stripes and itinerant carriers. Phys. Lett. A 275, 118–123 (2000)

  15. 15.

    et al. Neutron scattering study of the effects of dopant disorder on the superconductivity and magnetic order in stage-4 La2CuO4+y. Phys. Rev. B 69, 020502(R) (2004)

  16. 16.

    & Fractal Concepts in Surface Growth (Cambridge Univ. Press, 1995)

  17. 17.

    et al. Local mapping of strain at grain boundaries in colossal magnetoresistive films using X-ray microdiffraction. J. Appl. Phys. 91, 7742–7744 (2002)

  18. 18.

    , , , & X-ray microdiffraction images of antiferromagnetic domain evolution in chromium. Science 295, 1042–1045 (2002)

  19. 19.

    et al. Scanning X-ray microdiffraction of optically manipulated liposomes. Appl. Phys. Lett. 91, 234107 (2007)

  20. 20.

    Ten Lectures on Wavelets (CBMS-NSF Regional Conf. Ser. Appl. Math. 61, Society for Industrial and Applied Mathematics, 1992)

  21. 21.

    , & Misfit strain in superlattices controlling the electron-lattice interaction via microstrain in active layers. Adv. Condens. Matter Phys. 2010, 261849 (2010)

  22. 22.

    , , & The strain of CuO2 lattice: the second variable for the phase diagram of cuprate perovskites. J. Phys. Math. Gen. 36, 9133–9142 (2003)

  23. 23.

    et al. Localized holes in superconducting lanthanum cuprate. Phys. Rev. B 57, R712–R715 (1998)

  24. 24.

    et al. Muon spin relaxation studies of incommensurate magnetism and superconductivity in stage-4 La2CuO4.11 and La1.88Sr0.12CuO4. Phys. Rev. B 66, 014524 (2002)

  25. 25.

    , & Power-law distributions in empirical data. SIAM Rev. 51, 661–703 (2009)

  26. 26.

    et al. Feshbach resonance and mesoscopic phase separation near a quantum critical point in multiband FeAs-based superconductors. Superconduct. Sci. Technol. 22, 014004 (2009)

  27. 27.

    , & String theory, quantum phase transitions, and the emergent Fermi liquid. Science 325, 439–444 (2009)

  28. 28.

    Feshbach shape resonance in multiband superconductivity in heterostructures. J. Superconduct. Novel Magnet. 18, 25–36 (2005)

  29. 29.

    , , & Superconductivity of a striped phase at the atomic limit. Physica C 296, 269–280 (1998)

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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”.

Author information

Author notes

    • Michela Fratini

    Present address: Institute for Photonic and Nanotechnologies, CNR, Via Cineto Romano 42, 00156 Roma, Italy.


  1. Department of Physics, Sapienza University of Rome, Piazzale Aldo Moro 2, 00185 Roma, Italy

    • Michela Fratini
    • , Nicola Poccia
    • , Alessandro Ricci
    • , Gaetano Campi
    •  & Antonio Bianconi
  2. Institute of Crystallography, CNR, Via Salaria Km 29.300, Monterotondo Stazione, Roma, I-00016, Italy

    • Gaetano Campi
  3. European Synchrotron Radiation Facility, B.P. 220, F-38043 Grenoble Cedex, France

    • Manfred Burghammer
  4. London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, 17–19 Gordon Street, London WC1H 0AH, UK

    • Gabriel Aeppli


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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.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Antonio Bianconi.

Supplementary information

PDF files

  1. 1.

    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.


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