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Letters to Nature

Nature 430, 1001-1005 (26 August 2004) | doi:10.1038/nature02861; Received 24 February 2004; Accepted 13 July 2004

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

T. Hanaguri1,2, C. Lupien3, Y. Kohsaka4, D.-H. Lee5,6, M. Azuma2,7, M. Takano7, H. Takagi1,2,4 & J. C. Davis3

  1. Magnetic Materials Laboratory, RIKEN (Institute of Physical and Chemical Research), Wako 351-0198, Japan
  2. Japan Science and Technology Agency, Kawaguchi 332-0012, Japan
  3. LASSP, Department of Physics, Cornell University, Ithaca, New York 14853 USA
  4. Department of Advanced Materials Science, University of Tokyo, Kashiwa 277-8651, Japan
  5. Department of Physics, University of California, and
  6. Material Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
  7. Institute for Chemical Research, Kyoto University, Uji 601-0011, Japan

Correspondence to: T. Hanaguri1,2J. C. Davis3 Email: jcdavis@ccmr.cornell.edu
Email: hanaguri@riken.jp

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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.