Letter | Published:

A ‘checkerboard’ electronic crystal state in lightly hole-doped Ca2-xNaxCuO2Cl2

Nature volume 430, pages 10011005 (26 August 2004) | Download Citation



The phase diagram of hole-doped copper oxides shows four different electronic phases existing at zero temperature. Familiar among these are the Mott insulator, high-transition-temperature superconductor and metallic phases. A fourth phase, of unknown identity, occurs at light doping along the zero-temperature bound of the ‘pseudogap’ regime1. This regime is rich in peculiar electronic phenomena1, prompting numerous proposals that it contains some form of hidden electronic order. Here we present low-temperature electronic structure imaging studies of a lightly hole-doped copper oxide: Ca2-xNaxCuO2Cl2. Tunnelling spectroscopy (at energies |E| > 100 meV) reveals electron extraction probabilities greatly exceeding those for injection, as anticipated for a doped Mott insulator. However, for |E| < 100 meV, the spectrum exhibits a V-shaped energy gap centred on E = 0. States within this gap undergo intense spatial modulations, with the spatial correlations of a four CuO2-unit-cell square ‘checkerboard’, independent of energy. Intricate atomic-scale electronic structure variations also exist within the checkerboard. These data are consistent with an unanticipated crystalline electronic state, possibly the hidden electronic order, existing in the zero-temperature pseudogap regime of Ca2-xNaxCuO2Cl2.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


  1. 1.

    & The pseudogap in high-temperature superconductors: an experimental survey. Rep. Prog. Phys. 62, 61–122 (1999)

  2. 2.

    et al. A four unit cell periodic pattern of quasi-particle states surrounding vortex cores in Bi2Sr2CaCu2O8+δ. Science 295, 466–469 (2002)

  3. 3.

    et al. Local ordering in the pseudogap state of the high-Tc superconductor Bi2Sr2CaCu2O8+δ. Science 303, 1995–1998 (2004)

  4. 4.

    McElroy, K. et al. Destruction of antinodal state coherence via ‘checkerboard’ charge ordering in strongly underdoped superconducting Bi2Sr2CaCu2O8+δ. Preprint at 〈〉 (2004).

  5. 5.

    , & Inherent inhomogeneities in tunneling spectra of Bi2Sr2CaCu2O8-x crystals in the superconducting state. Phys. Rev. B 64, 100504 (2001)

  6. 6.

    , , & Nanometer scale mapping of the density of states in an inhomogeneous superconductor. Europhys. Lett. 54, 84–90 (2001)

  7. 7.

    et al. Relating atomic-scale electronic phenomena to wave-like quasiparticle states in superconducting Bi2Sr2CaCu2O8+δ. Nature 422, 592–596 (2003)

  8. 8.

    et al. Photoemission evidence for a remnant Fermi surface and a d-wave-like dispersion in insulating Ca2CuO2Cl2. Science 282, 2067–2072 (1998)

  9. 9.

    et al. Evolution of a metal to insulator transition in Ca2-xNaxCuO2Cl2 as seen by angle-resolved photoemission. Phys. Rev. B 67, 165101 (2003)

  10. 10.

    , & Probable hole-doped superconductivity without apical oxygens in (Ca, Na)2CuO2Cl2. Nature 371, 139–141 (1994)

  11. 11.

    et al. Growth of Na-doped Ca2CuO2Cl2 single crystals under high pressures of several GPa. J. Am. Chem. Soc. 124, 12275–12278 (2002)

  12. 12.

    et al. Imaging nano-scale electronic inhomogeneity in lightly doped Mott insulator Ca2-xNaxCuO2Cl2. Phys. Rev. Lett. (2004) (in the press); preprint at 〈

  13. 13.

    et al. Quasiparticle tunneling spectra of the high-Tc mercury cuprates: Implications of the d-wave two-dimensional van Hove scenario. Phys. Rev. B 57, 3650–3662 (1998)

  14. 14.

    Fu, H. C., Davis, J. C. & Lee, D.-H. On the charge ordering observed by recent STM experiments. Preprint at 〈〉 (2004)

  15. 15.

    Non-Fermi-liquid states and pairing instability of a general model of copper oxide metals. Phys. Rev. B 55, 14554–14580 (1997)

  16. 16.

    , , & Hidden order in the cuprates. Phys. Rev. B 63, 094503 (2001)

  17. 17.

    Lee, P. A. Pseudogap and competing states in underdoped cuprates. Preprint at 〈〉 (2003).

  18. 18.

    & Charged magnetic domain lines and the magnetism of high-Tc oxides. Phys. Rev. B 40, 7391–7394 (1989)

  19. 19.

    Magnetism in La2CuO4 based compounds. Physica C 158, 192–196 (1989)

  20. 20.

    & Phase separation and stripe formation in the two-dimensional t-J model: A comparison of numerical results. Phys. Rev. B 61, 6320–6326 (2000)

  21. 21.

    , & Stripe phases in high-temperature superconductors. Proc. Natl Acad. Sci. USA 96, 8814–8817 (1999)

  22. 22.

    Quantum criticality: Competing ground states in low dimensions. Science 288, 475–480 (2000)

  23. 23.

    , & Shifting Bragg peaks of cuprate stripes as possible indications for fractionally charged kinks. Phys. Rev. B 63, 092501 (2001)

  24. 24.

    , & Electronic liquid-crystal phases of a doped Mott insulator. Nature 393, 550–553 (1998)

  25. 25.

    Superconducting charge-ordered states in cuprates. Phys. Rev. B 66, 104505 (2002)

  26. 26.

    , , & Translational symmetry breaking in the superconducting state of the cuprates: Analysis of the quasiparticle density of states. Phys. Rev. B 67, 094514 (2003)

  27. 27.

    Chen, H.-D., Vafek, O., Yazdani, A. & Zhang, S.-C. Pair density wave in the pseudogap state of high temperature superconductors. Preprint at 〈〉 (2004).

  28. 28.

    , , , & Antiferromagnetism and hole pair checkerboard in the vortex state of high Tc superconductors. Phys. Rev. Lett. 89, 137004 (2002)

  29. 29.

    Tešanović, Z. Charge modulation, spin response, and dual Hofstadter butterfly in high-Tc cuprates. Preprint at 〈〉 (2004).

  30. 30.

    Anderson, P. W. A suggested 4 × 4 structure in underdoped cuprate superconductors: a Wigner supersolid. Preprint at 〈〉 (2004).

Download references


We acknowledge and thank P. Coleman, E. Demler, M. Franz, J. E. Hoffman, P. A. Lee, K. Machida, K. McElroy, D. Pines, S. Sachdev, T. Senthil, T. Timusk, M. Vojta and J. Zaanen for discussions and communications. This work was supported by the ONR, NSF, MEXT, JST and NEDO. C.L. acknowledges support from a NSERC Postdoctoral Fellowship and Y.K. from a JPSJ Research Fellowship for Young Scientists.

Author information


  1. Magnetic Materials Laboratory, RIKEN (Institute of Physical and Chemical Research), Wako 351-0198, Japan

    • T. Hanaguri
    •  & H. Takagi
  2. Japan Science and Technology Agency, Kawaguchi 332-0012, Japan

    • T. Hanaguri
    • , M. Azuma
    •  & H. Takagi
  3. LASSP, Department of Physics, Cornell University, Ithaca, New York 14853 USA

    • C. Lupien
    •  & J. C. Davis
  4. Department of Advanced Materials Science, University of Tokyo, Kashiwa 277-8651, Japan

    • Y. Kohsaka
    •  & H. Takagi
  5. Department of Physics, University of California, and

    • D.-H. Lee
  6. Material Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

    • D.-H. Lee
  7. Institute for Chemical Research, Kyoto University, Uji 601-0011, Japan

    • M. Azuma
    •  & M. Takano


  1. Search for T. Hanaguri in:

  2. Search for C. Lupien in:

  3. Search for Y. Kohsaka in:

  4. Search for D.-H. Lee in:

  5. Search for M. Azuma in:

  6. Search for M. Takano in:

  7. Search for H. Takagi in:

  8. Search for J. C. Davis in:

Competing interests

The authors declare that they have no competing financial interests.

Corresponding authors

Correspondence to T. Hanaguri or J. C. Davis.

Supplementary information

PDF files

  1. 1.

    Supplementary Figure 1

    Doping dependence of the spectra from x = 0.08 to 0.12.

  2. 2.

    Supplementary Figure 2

    Topography and associated Fourier transform showing the existence of 1/4 and 3/4 signal in topographic signal.

  3. 3.

    Supplementary Figure 3

    Raw spectra and averages from the white and red points of Fig. 3b from the main text.

  4. 4.

    Supplementary Figure 4

    Doping dependence of the low temperature resistivity from x = 0.06 to 0.10.

  5. 5.

    Supplementary Figure 5

    Low energy spectra along a line cut showing heterogeneous features possibly related to superconductivity in x = 0.12 sample.

About this article

Publication history






Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.