Intimate link between charge density wave, pseudogap and superconducting energy scales in cuprates

Article metrics


The cuprate high-temperature superconductors develop spontaneous charge density wave (CDW) order below a temperature TCDW and over a wide range of hole doping (p). An outstanding challenge in the field is to understand whether this modulated phase is related to the more exhaustively studied pseudogap and superconducting phases1,2. To address this issue, it is important to extract the energy scale ΔCDW associated with the CDW order, and to compare it with the pseudogap ΔPG and with the superconducting gap ΔSC. However, while TCDW is well characterized from earlier work3, little is currently known about ΔCDW. Here, we report the extraction of ΔCDW for several cuprates using electronic Raman spectroscopy. We find that on approaching the parent Mott state by lowering p, ΔCDW increases in a manner similar to the doping dependence of ΔPG and ΔSC. This reveals that these three phases have a common microscopic origin. In addition, we find that ΔCDW ≈ ΔSC over a substantial doping range, which suggests that CDW and superconducting phases are intimately related; for example, they may be intertwined or connected by an emergent symmetry1,4,5,6,7,8,9.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Nodal Raman responses (B2g) of several cuprates.
Fig. 2: Temperature dependence of the CDW Raman signal.
Fig. 3: Doping and temperature dependence of the CDW Raman signal.
Fig. 4: Energy scales of CDW, superconducting and pseudogap orders.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


  1. 1.

    Fradkin, E., Kivelson, S. A. & Tranquada, J. M. Colloquium: theory of intertwined orders in high temperature superconductors. Rev. Mod. Phys. 87, 457–482 (2015).

  2. 2.

    Keimer, B., Kivelson, S. A., Norman, M. R., Uchida, S. & Zaanen, J. From quantum matter to high-temperature superconductivity in copper oxides. Nature 518, 179–186 (2015).

  3. 3.

    Comin, R. & Damascelli, A. Resonant x-ray scattering studies of charge order in cuprates. Annu. Rev. Condens. Matter Phys. 7, 369–405 (2016).

  4. 4.

    Efetov, K. B., Meier, H. & Pépin, C. Pseudogap state near a quantum critical point. Nat. Phys. 9, 442–446 (2013).

  5. 5.

    Sachdev, S. & La Placa, R. Bond order in two-dimensional metals with antiferromagnetic exchange interactions. Phys. Rev. Lett. 111, 027202 (2013).

  6. 6.

    Davis, J. C. S. & Lee, D.-H. Concepts relating magnetic interactions, intertwined electronic orders, and strongly correlated superconductivity. Proc. Natl Acad. Sci. USA 110, 17623–17630 (2013).

  7. 7.

    Allais, A., Chowdhury, D. & Sachdev, S. Connecting high-field quantum oscillations to zero-field electron spectral functions in the underdoped cuprates. Nat. Commun. 5, 5771 (2014).

  8. 8.

    Wang, Y., Agterberg, D. F. & Chubukov, A. Coexistence of charge-density-wave and pair-density-wave orders in underdoped cuprates. Phys. Rev. Lett. 114, 197001 (2015).

  9. 9.

    Wang, X., Wang, Y., Schattner, Y., Berg, E. & Fernandes, R. M. Fragility of charge order near an antiferromagnetic quantum critical point. Phys. Rev. Lett. 120, 247002 (2018).

  10. 10.

    Tranquada, J. M., Sternlieb, B. J., Axe, J. D., Nakamura, Y. & Uchida, S. Evidence for stripe correlations of spins and holes in copper oxide superconductors. Nature 375, 561–563 (1995).

  11. 11.

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

  12. 12.

    Wu, T. et al. Magnetic-field-induced charge-stripe order in the high-temperature superconductor YBa2Cu3Oy. Nature 477, 191–194 (2011).

  13. 13.

    Ghiringhelli, G. et al. Long-range incommensurate charge fluctuations in (Y,Nd)Ba2Cu3O6+x. Science 337, 821–825 (2012).

  14. 14.

    Hücker, M. et al. Competing charge, spin, and superconducting orders in underdoped YBa2Cu3Oy. Phys. Rev. B 90, 054514 (2014).

  15. 15.

    LeBoeuf, D. et al. Thermodynamic phase diagram of static charge order in underdoped YBa2Cu3Oy. Nat. Phys. 9, 79–83 (2013).

  16. 16.

    Cyr-Choinière, O. et al. Sensitivity of T c to pressure and magnetic field in the cuprate superconductor YBa2Cu3Oy: evidence of charge order suppression by pressure. Phys. Rev. B 98, 064513 (2018).

  17. 17.

    Ralević, U. et al. Charge density wave modulation and gap measurements in CeTe3. Phys. Rev. B 94, 165132 (2016).

  18. 18.

    Sebastian, S. E. & Proust, C. Quantum oscillations in hole-doped cuprates. Annu. Rev. Condens. Matter Phys. 6, 411–430 (2015).

  19. 19.

    Loret, B. et al. Crystal growth and characterization of HgBa2Ca2Cu3O8+δ superconductors with the highest critical temperature at ambient pressure. Inorg. Chem. 56, 9396–9399 (2017).

  20. 20.

    Julien, M.-H. et al. Spin gap in HgBa2Ca2Cu3O8+δ single crystals from 63Cu NMR. Phys. Rev. Lett. 76, 4238–4241 (1996).

  21. 21.

    Mukuda, H., Shimizu, S., Iyo, A. & Kitaoka, Y. High-T c superconductivity and antiferromagnetism in multilayered copper oxides –a new paradigm of superconducting mechanism–. J. Phys. Soc. Jpn 81, 011008 (2012).

  22. 22.

    Das, T. Q = 0 collective modes originating from the low-lying Hg–O band in superconducting HgBa2CuO4+δ. Phys. Rev. B 86, 054518 (2012).

  23. 23.

    Grilli, M., Seibold, G., Di Ciolo, A. & Lorenzana, J. Fermi surface dichotomy in systems with fluctuating order. Phys. Rev. B 79, 125111 (2009).

  24. 24.

    Lyons, K. B., Fleury, P. A., Schneemeyer, L. F. & Waszczak, J. V. Spin fluctuations and superconductivity in Ba2YCu3O6. Phys. Rev. Lett. 60, 732–735 (1988).

  25. 25.

    Tabis, W. et al. Synchrotron x-ray scattering study of charge-density-wave order in HgBa2CuO4+δ. Phys. Rev. B 96, 134510 (2017).

  26. 26.

    Blanco-Canosa, S. et al. Resonant x-ray scattering study of charge-density wave correlations in YBa2Cu3O6+x. Phys. Rev. B 90, 054513 (2014).

  27. 27.

    Hinton, J. P. et al. The rate of quasiparticle recombination probes the onset of coherence in cuprate superconductors. Sci. Rep. 6, 23610 (2016).

  28. 28.

    Chatterjee, U. et al. Emergence of coherence in the charge-density wave state of 2H-BbSe2. Nat. Commun. 6, 6313 (2015).

  29. 29.

    Le Tacon, M. et al. Two energy scales and two distinct quasiparticle dynamics in the superconducting state of underdoped cuprates. Nat. Phys. 2, 537–543 (2006).

  30. 30.

    Sacuto, A. et al. New insights into the phase diagram of the copper oxide superconductors from electronic Raman scattering. Rep. Prog. Phys. 76, 022502 (2013).

  31. 31.

    Loret, B. et al. Unconventional high-energy-state contribution to the Cooper pairing in the underdoped copper-oxide superconductor HgBa2Ca2Cu3O8+δ. Phys. Rev. Lett. 116, 197001 (2016).

  32. 32.

    McElroy, K. et al. Coincidence of checkerboard charge order and antinodal state decoherence in strongly underdoped superconducting Bi2Sr2CaCu2O8+δ. Phys. Rev. Lett. 94, 197005 (2005).

  33. 33.

    Arpaia, R. et al. Dynamical charge density fluctuations pervading the phase diagram of a Cu-based high-T c superconductor. Preprint at (2018).

  34. 34.

    Vishik, I. M. et al. Angle-resolved photoemission spectroscopy study of HgBa2CuO4+δ. Phys. Rev. B 89, 195141 (2014).

  35. 35.

    Wu, T. et al. Incipient charge order observed by NMR in the normal state of YBa2Cu3Oy. Nat. Commun. 6, 6438 (2015).

Download references


We are grateful to V. Brouet, A. Carrington, J. C. S. Davis, R. M. Fernandes, E. Fradkin, G. Ghiringhelli, M. Le Tacon, A. Mesaros, C. Pépin, C. Proust, Y. Sidis and L. Taillefer for useful discussions. B.L. was supported by the DIM OxyMORE, Ile de France. We thank the Collège de France and the Canadian Institute for Advanced Research (CIFAR) for their hospitality.

Author information

B.L. and N.A. performed the Raman measurements with assistance from Y.G., M.Cazayous and A.S. at the University Paris Diderot. M.Civelli and I.P. performed the calculations on the Raman responses. B.L. and A.F. prepared the single crystals and D.C. supervised the crystal growth and the crystal characterization at CEA Saclay. B.L., Y.G., M.-H.J., I.P., M.Civelli and A.S. wrote the manuscript in consultation with all authors. A.S. supervised the project.

Correspondence to A. Sacuto.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Journal peer review information: Nature Physics thanks Riccardo Comin and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figures 1–7 and Supplementary references 1–35.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Further reading