Letter | Published:

Detection of a Cooper-pair density wave in Bi2Sr2CaCu2O8+x

Nature volume 532, pages 343347 (21 April 2016) | Download Citation


The quantum condensate of Cooper pairs forming a superconductor was originally conceived as being translationally invariant. In theory, however, pairs can exist with finite momentum Q, thus generating a state with a spatially modulated Cooper-pair density1,2. Such a state has been created in ultracold 6Li gas3 but never observed directly in any superconductor. It is now widely hypothesized that the pseudogap phase4 of the copper oxide superconductors contains such a ‘pair density wave’ state5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21. Here we report the use of nanometre-resolution scanned Josephson tunnelling microscopy22,23,24 to image Cooper pair tunnelling from a d-wave superconducting microscope tip to the condensate of the superconductor Bi2Sr2CaCu2O8+x. We demonstrate condensate visualization capabilities directly by using the Cooper-pair density variations surrounding zinc impurity atoms25 and at the Bi2Sr2CaCu2O8+x crystal supermodulation26. Then, by using Fourier analysis of scanned Josephson tunnelling images, we discover the direct signature of a Cooper-pair density modulation at wavevectors QP ≈ (0.25, 0)2π/a0 and (0, 0.25)2π/a0 in Bi2Sr2CaCu2O8+x. The amplitude of these modulations is about five per cent of the background condensate density and their form factor exhibits primarily s or s′ symmetry. This phenomenology is consistent with Ginzburg–Landau theory5,13,14 when a charge density wave5,27 with d-symmetry form factor28,29,30 and wavevector QC = QP coexists with a d-symmetry superconductor; it is also predicted by several contemporary microscopic theories for the pseudogap phase18,19,20,21.

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We acknowledge and thank D. Agterberg, A. V. Balatsky, D. Chowdhury, A. Chubukov, E. Fradkin, R. Hulet, S. A. Kivelson, P. A. Lee, M. Norman, J. W. Orenstein, C. Pepin, S. Sachdev, J. Tranquada and Y. Wang for discussions and advice. The development and operation of HTS SJTM technology and M.H.H. and A.K. were funded by the Moore Foundation’s EPiQS Initiative through grant number GBMF4544. S.D.E. acknowledges studentship funding from the EPSRC under grant number EP/G03673X/1. J.C.S.D. and A.P.M. acknowledge research support from the EPSRC through the grant programme ‘Topological Protection and Non-Equilibrium States in Correlated Electron Systems’. S.U. and H.E. acknowledge support from a Grant-in-Aid for Scientific Research from the Ministry of Science and Education (Japan). S.H.J. and J.L. acknowledge support from the Institute for Basic Science, Korea under grant number IBS-R009-D1. J.C.S.D. and K.F. acknowledge salary support from the US Department of Energy, Office of Basic Energy Sciences, under contract number DEAC02-98CH10886. E.-A.K. acknowledges support from the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering under award DE-SC0010313.

Author information

Author notes

    • M. H. Hamidian
    • , S. D. Edkins
    •  & Sang Hyun Joo

    These authors contributed equally to this work.


  1. Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

    • M. H. Hamidian
  2. Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, New York 14853, USA

    • S. D. Edkins
    • , A. Kostin
    • , M. J. Lawler
    • , E.-A. Kim
    •  & J. C. Séamus Davis
  3. School of Physics and Astronomy, University of St Andrews, Fife KY16 9SS, UK

    • S. D. Edkins
    • , A. P. Mackenzie
    •  & J. C. Séamus Davis
  4. Institute of Applied Physics, Department of Physics and Astronomy, Seoul National University, Seoul 151-747, South Korea

    • Sang Hyun Joo
    •  & Jinho Lee
  5. Center for Correlated Electron Systems, Institute of Basic Science, Seoul 151-742, South Korea

    • Sang Hyun Joo
    •  & Jinho Lee
  6. Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japan

    • H. Eisaki
    •  & S. Uchida
  7. Department of Physics, University of Tokyo, Bunkyo, Tokyo 113-0011, Japan

    • S. Uchida
  8. Department of Physics, Binghamton University, Binghamton, New York 13902-6000, USA

    • M. J. Lawler
  9. Max Planck Institute for Chemical Physics of Solids, D-01187 Dresden, Germany

    • A. P. Mackenzie
  10. Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA

    • K. Fujita
    •  & J. C. Séamus Davis
  11. Kavli Institute at Cornell for Nanoscale Science, Cornell University, Ithaca, New York 14853, USA

    • J. C. Séamus Davis


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M.H.H., S.D.E., A.K., and J.L. developed the SJTM techniques and carried out the experiments. K.F., H.E. and S.U. synthesized and characterized the samples. M.H.H., S.D.E., A.K., S.H.J. and K.F. developed and carried out analyses. E.-A.K. and M.J.L. provided theoretical guidance. A.P.M., J.L. and J.C.S.D. supervised the project and wrote the paper with key contributions from M.H.H., S.D.E. and K.F. The manuscript reflects the contributions and ideas of all authors.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Jinho Lee or J. C. Séamus Davis.

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