Abstract
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.
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Acknowledgements
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.
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Supplementary information
Supplementary Figure 1
Doping dependence of the spectra from x = 0.08 to 0.12. (PDF 84 kb)
Supplementary Figure 2
Topography and associated Fourier transform showing the existence of 1/4 and 3/4 signal in topographic signal. (PDF 282 kb)
Supplementary Figure 3
Raw spectra and averages from the white and red points of Fig. 3b from the main text. (PDF 100 kb)
Supplementary Figure 4
Doping dependence of the low temperature resistivity from x = 0.06 to 0.10. (PDF 101 kb)
Supplementary Figure 5
Low energy spectra along a line cut showing heterogeneous features possibly related to superconductivity in x = 0.12 sample. (PDF 278 kb)
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Hanaguri, T., Lupien, C., Kohsaka, Y. et al. A ‘checkerboard’ electronic crystal state in lightly hole-doped Ca2-xNaxCuO2Cl2. Nature 430, 1001–1005 (2004). https://doi.org/10.1038/nature02861
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DOI: https://doi.org/10.1038/nature02861
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