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


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.

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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.

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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.


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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.

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Authors and Affiliations



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.

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Correspondence to A. Sacuto.

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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.

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

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Loret, B., Auvray, N., Gallais, Y. et al. Intimate link between charge density wave, pseudogap and superconducting energy scales in cuprates. Nat. Phys. 15, 771–775 (2019).

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