Visualization of the emergence of the pseudogap state and the evolution to superconductivity in a lightly hole-doped Mott insulator

Journal name:
Nature Physics
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Published online

Superconductivity emerges from the cuprate antiferromagnetic Mott state with hole doping. The resulting electronic structure1 is not understood, although changes in the state of oxygen atoms seem paramount2, 3, 4, 5. Hole doping first destroys the Mott state, yielding a weak insulator6, 7 where electrons localize only at low temperatures without a full energy gap. At higher doping levels, the ‘pseudogap’, a weakly conducting state with an anisotropic energy gap and intra-unit-cell breaking of 90° rotational (C4v) symmetry, appears3, 4, 8, 9, 10. However, a direct visualization of the emergence of these phenomena with increasing hole density has never been achieved. Here we report atomic-scale imaging of electronic structure evolution from the weak insulator through the emergence of the pseudogap to the superconducting state in Ca2− xNa xCuO2Cl2. The spectral signature of the pseudogap emerges at the lowest doping level from a weakly insulating but C4v-symmetric matrix exhibiting a distinct spectral shape. At slightly higher hole density, nanoscale regions exhibiting pseudogap spectra and 180° rotational (C2v) symmetry form unidirectional clusters within the C4v-symmetric matrix. Thus, hole doping proceeds by the appearance of nanoscale clusters of localized holes within which the broken-symmetry pseudogap state is stabilized. A fundamentally two-component electronic structure11 then exists in Ca2− xNa xCuO2Cl2 until the C2v-symmetric clusters touch at higher doping levels, and the long-range superconductivity appears.

At a glance


  1. Spectral features unique to the insulating samples.
    Figure 1: Spectral features unique to the insulating samples.

    a,b, 20×20nm2 square constant-current topographic images of x=0.06 and x=0.08, respectively. Scanning parameters are 0.1nA at −0.4V for a and 0.1nA at −0.3V for b. The markers with numbers indicate locations where spectra shown in e and f were taken. c,d, Differential conductance maps taken at −0.28V and −0.22V in the same field of view as in a and b, respectively. Scanning parameters are 0.2nA at −0.4V for c, and 0.15nA at −0.3V for d. The wavy, bright, arcs caused by the tip-induced impurity charging guarantee that these surfaces are insulating. e,f, Examples of differential conductance spectra taken in the insulating samples. Numbers denote locations where these spectra were taken in a and b. Peaks found in the spectra of f are caused by the tip-induced impurity charging. The set-up conditions of spectra in e and f are 0.2nA at −0.4V and 0.15nA at −0.3V, respectively.

  2. Spatial variations and doping evolution of the pseudogap.
    Figure 2: Spatial variations and doping evolution of the pseudogap.

    Examples of differential conductance spectra taken at various locations of multiple samples of 0.06≤x≤0.12. Each spectrum is shifted vertically for clarity and colour-coded on the basis of the values of Δ with the colour scale the same as used in b and c. The horizontal markers indicate zero of each curve. The black curves superimposed on the spectra are the results of fits described in the text. The vertical markers denote extracted Δ and the numbers denote α. be, 20×20nm2 square Δ-maps and α-maps of x=0.06 and x=0.08. The original 256×256 spectra were taken in the same fields of view as in Fig. 1a and b, respectively. Note that colour scales are common to b and c, and d and e. The white dotted square in c shows the area of Fig. 3a.

  3. Atomic and nanoscale short-range order of the pseudogap state found in
[Delta]-maps and
    Figure 3: Atomic and nanoscale short-range order of the pseudogap state found in Δ-maps and R-maps.

    a,b, 12×12nm2 square Δ-maps of x=0.08 and x=0.12, respectively. a was taken in the area shown by the white dotted square in Fig. 2c. b was taken in the same area of the same sample used in ref.  3. The colour scale is the same as used in Fig. 2b,c. The black arrows indicate directions of Cu–O bonds. The solid lines in b are trajectories along which spectra shown in c were taken. c, Differential conductance spectra of Ca1.88Na0.12CuO2Cl2 taken along lines 1 and 2 shown in b, demonstrating Δ is actually modulated at the atomic scale. Each observed black spectrum is shifted vertically for clarity. Results of the fit, blue and orange in colour, are superimposed on the observed spectra. The markers denote extracted Δ. dΔ extracted from fits to the spectra shown in c. The inset depicts the location of the trajectories where the spectra shown in c were taken, relative to the CuO2 plane. Δ is modulated along the trajectories in the same manner at the atomic scale, leading to the formation of bond-like objects on Cu–O–Cu complexes. e,f, 12×12nm2 square R-maps taken in the same areas as a and b, respectively. The integration voltages are 252meV for e and 150meV for f. The white arrows indicate directions of Cu–O bonds. The dashed ovals and rectangles are guides to the eye indicating an area with no clear pseudogap, a clear pseudogap and the nanometre-scale unidirectional clusters consisting of the bond-like objects, respectively.

  4. Quantitative analysis of local symmetry corroborating that the pseudogap state accompanies local C2 symmetry.
    Figure 4: Quantitative analysis of local symmetry corroborating that the pseudogap state accompanies local C2 symmetry.

    The values of Qxx and Qxy at each copper site indicated by the grey dots are expressed by the short bars. The length of the bars denotes the magnitude of Qxx and Qxy. The colour of the bars carries the same information as the length does for clarity. The direction of each bar corresponds to the sign of Qxx and Qxy. The left (a,b,e,f) and the right (c,d,g,h) four panels are computed for the Δ- and R-maps, respectively. The upper (ad) and lower (eh) panels are computed for x=0.08 and x=0.12, respectively. The ovals in ad and the rectangles in a,c,e and g are drawn at the same location as those in Fig. 3. The first and third columns (a,c,e,g) and second and fourth columns (b,f,d,h) are Qxx and Qxy, respectively. The original Δ- and R-maps are shown in Fig. 3. The inset of h depicts the locations of rCu, rO(i) and rO’(i) used in the definition of Qxx and Qxy described in the text.


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Author information


  1. Inorganic Complex Electron Systems Research Team, RIKEN Advanced Science Institute, Wako, Saitama 351-0198, Japan

    • Y. Kohsaka &
    • H. Takagi
  2. Magnetic Materials Laboratory, RIKEN Advanced Science Institute, Wako, Saitama 351-0198, Japan

    • T. Hanaguri &
    • H. Takagi
  3. Materials and Structures Lab., Tokyo Institute of Technology, Yokohama, Kanagawa 226-8503, Japan

    • M. Azuma
  4. Institute for Integrated Cell-Material Sciences, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan

    • M. Takano
  5. LASSP, Department of Physics, Cornell University, Ithaca, New York 14853, USA

    • J. C. Davis
  6. CMPMS Department, Brookhaven National Laboratory, Upton, New York 11973, USA

    • J. C. Davis
  7. School of Physics and Astronomy, University of St Andrews, St Andrews KY16 9SS, UK

    • J. C. Davis
  8. Kavli Institute at Cornell for Nanoscale Science, Cornell University, Ithaca, New York 14853, USA

    • J. C. Davis
  9. Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033, Japan

    • H. Takagi


Y.K., M.A. and M.T. grew single crystals. Y.K. and T.H. performed STM measurements. Y.K. analysed data. Y.K. and J.C.D. wrote the manuscript. J.C.D. and H.T. supervised the project.

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