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Spectroscopic fingerprint of charge order melting driven by quantum fluctuations in a cuprate

An Author Correction to this article was published on 09 October 2020

This article has been updated


Copper oxide high-TC superconductors possess a number of exotic orders that coexist with or are proximal to superconductivity. Quantum fluctuations associated with these orders may account for the unusual characteristics of the normal state, and possibly affect the superconductivity1,2,3,4. Yet, spectroscopic evidence for such quantum fluctuations remains elusive. Here, we use resonant inelastic X-ray scattering to reveal spectroscopic evidence of fluctuations associated with a charge order5,6,7,8,9,10,11,12,13,14 in nearly optimally doped Bi2Sr2CaCu2O8+δ. In the superconducting state, while the quasielastic charge order signal decreases with temperature, the interplay between charge order fluctuations and bond-stretching phonons in the form of a Fano-like interference increases, an observation that is incompatible with expectations for competing orders. Invoking general principles, we argue that this behaviour reflects the properties of a dissipative system near an order–disorder quantum critical point, where the dissipation varies with the opening of the pseudogap and superconducting gap at low temperatures, leading to the proliferation of quantum critical fluctuations, which melt charge order.

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Fig. 1: Temperature dependence of the CO in the quasielastic region.
Fig. 2: The temperature dependence of RIXS phonon spectra.
Fig. 3: Dissipation and QCP.
Fig. 4: Modelling the Fano interference between CO excitations and bond-stretching phonons.

Data availability

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

Change history

  • 09 October 2020

    An amendment to this paper has been published and can be accessed via a link at the top of the paper.


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This work is supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under contract DE-AC02-76SF00515. We acknowledge the Diamond Light Source for providing the science commissioning time at the I21 RIXS beamline under Proposal SP18462.

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Authors and Affiliations



W.S.L. conceived the experiment. W.S.L., K.-J.Z., M. Hepting, J.L., A.N., A.C.W., M.G.-F. and H.R. conducted the experiment at the Diamond Light Source. J.L., A.N. and K.-J.Z. performed the data processing from the detector. W.S.L., M. Hepting and H.L. analysed the data. W.S.L., B.M., J.Z. and T.P.D. performed the theoretical calculations. K.-J.Z., A.C.W. and M.G.-F. constructed and commissioned the ID21 RIXS beamline and spectrometer at the Diamond Light Source. M. Hashimoto, D.S. and H.E. synthesized and prepared samples for the experiments. W.S.L., Z.X.S., B.M., J.Z. and T.P.D. wrote the manuscript with input from all authors.

Corresponding authors

Correspondence to W. S. Lee, Ke-Jin Zhou or T. P. Devereaux.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks José Lorenzana 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.

Extended data

Extended Data Fig. 1 RIXS experiment and scattering geometry.

a, A representative RIXS spectral taking at Cu L3-edge. In this work, we discuss the inelastic scattering signal below 0.1 eV. The inset shows a typical x-ray absorption curve across the Cu L3-edge, taken by measuring total florescent yield. b, A sketch of the scattering geometry. The crystal axes are denoted as a, b and c. ki and kf represent the incident and scattering photon momentum. 2θ is the scattering angle. The yellow arrow represents the polarization of the incident x-ray. All the data shown in this manuscript were taken using incident beam with sigma polarization.

Extended Data Fig. 2 Raw RIXS spectra and Fitting.

a, An example of the spectra fitting. The fit function consists of a Gaussian function for the elastic peak (blue), an anti-Lorentzian function for the RIXS phonon (red), and a smooth background from high energy (black dashed line). The fit function is convoluted with a Gaussian function with a FWHM corresponding to the energy resolution of the RIXS instrument and fit to the data. b, All Raw RIXS spectra discussed in this work. The red curves are the fits, showing good agreements with the experimental data.

Extended Data Fig. 3 CO excitations continuum used in the model.

a, Intensity map of Im[χλ(q,ω)] with for modeling 15 K data. b, Energy distribution curves at QCO (the vertical black dashed lines in a) with different values of the damping Γ that are used to model the temperature dependence behavior shown in Fig. 4c. c, Momentum distribution curve at 0.06 eV (the horizontal black dashed lines in a), approximately at the bond-stretching phonon energy.

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Lee, W.S., Zhou, KJ., Hepting, M. et al. Spectroscopic fingerprint of charge order melting driven by quantum fluctuations in a cuprate. Nat. Phys. 17, 53–57 (2021).

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