Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Dispersive charge density wave excitations in Bi2Sr2CaCu2O8+δ

Abstract

Experimental evidence on high-Tc cuprates reveals ubiquitous charge density wave (CDW) modulations1,2,3,4,5,6,7,8,9,10, which coexist with superconductivity. Although the CDW had been predicted by theory11,12,13, important questions remain about the extent to which the CDW influences lattice and charge degrees of freedom and its characteristics as functions of doping and temperature. These questions are intimately connected to the origin of the CDW and its relation to the mysterious cuprate pseudogap10,14. Here, we use ultrahigh-resolution resonant inelastic X-ray scattering to reveal new CDW character in underdoped Bi2.2Sr1.8Ca0.8Dy0.2Cu2O8+δ. At low temperature, we observe dispersive excitations from an incommensurate CDW that induces anomalously enhanced phonon intensity, unseen using other techniques. Near the pseudogap temperature T, the CDW persists, but the associated excitations significantly weaken with an indication of CDW wavevector shift. The dispersive CDW excitations, phonon anomaly, and analysis of the CDW wavevector provide a comprehensive momentum-space picture of complex CDW behaviour and point to a closer relationship with the pseudogap state.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: RIXS process and a hint of lower-energy excitations near QCDW.
Figure 2: CDW and phonons at 20 K.
Figure 3: CDW excitations in Bi2212 and calculated RIXS intensity in a 1D model.
Figure 4: Temperature dependence of the CDW and the phonon anomaly.

Similar content being viewed by others

References

  1. 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).

    Article  ADS  Google Scholar 

  2. Howald, C., Eisaki, H., Kaneko, N. & Kapitulnik, A. Coexistence of periodic modulation of quasiparticle states and superconductivity in Bi2Sr2CaCu2O8+δ . Proc. Natl Acad. Sci. USA 100, 9705–9709 (2003).

    Article  ADS  Google Scholar 

  3. Abbamonte, P. et al. Spatially modulated ‘Mottness’ in La2−xBaxCuO4 . Nat. Phys. 1, 155–158 (2005).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. Chang, J. et al. Direct observation of competition between superconductivity and charge density wave order in YBa2Cu3O6.67 . Nat. Phys. 8, 871–876 (2012).

    Article  Google Scholar 

  6. Comin, R. et al. Charge order driven by Fermi-arc instability in Bi2Sr2−xLaxCuO6+δ . Science 343, 390–392 (2014).

    Article  ADS  Google Scholar 

  7. Hashimoto, M. et al. Direct observation of bulk charge modulations in optimally doped Bi1.5Pb0.6Sr1.54CaCu2O8+δ . Phys. Rev. B 89, 220511(R) (2014).

    Article  ADS  Google Scholar 

  8. da Silva Neto, E. H. et al. Ubiquitous interplay between charge ordering and high-temperature superconductivity in cuprates. Science 343, 393–396 (2014).

    Article  ADS  Google Scholar 

  9. Tabis, W. et al. Charge order and its connection with Fermi-liquid charge transport in a pristine high-Tc cuprate. Nat. Commun. 5, 5875 (2014).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  11. Zaanen, J. & Gunnarsson, O. Charged magnetic domain lines and the magnetism of high-Tc oxides. Phys. Rev. B 40, 7391(R) (1989).

    Article  ADS  Google Scholar 

  12. Poilblanc, D. & Rice, T. M. Charged solitons in the Hartree–Fock approximation to the large-U Hubbard model. Phys. Rev. B 39, 9749(R) (1989).

    Article  ADS  Google Scholar 

  13. Emery, V. J., Kivelson, S. A. & Lin, H. Q. Phase separation in the tJ model. Phys. Rev. Lett. 64, 475–478 (1990).

    Article  ADS  Google Scholar 

  14. Badoux, S. et al. Change of carrier density at the pseudogap critical point of a cuprate superconductor. Nature 531, 210–214 (2016).

    Article  ADS  Google Scholar 

  15. Ament, L. J. P., van Veenendaal, M., Devereaux, T. P., Hill, J. P. & van den Brink, J. Resonant inelastic X-ray scattering studies of elementary excitations. Rev. Mod. Phys. 83, 705–767 (2011).

    Article  ADS  Google Scholar 

  16. Braicovich, L. et al. Magnetic excitations and phase separation in the underdoped La2−xSrxCuO4 superconductor measured by resonant inelastic X-ray scattering. Phys. Rev. Lett. 104, 077002 (2010).

    Article  ADS  Google Scholar 

  17. Le Tacon, M. et al. Intense paramagnon excitations in a large family of high-temperature superconductors. Nat. Phys. 7, 725–730 (2011).

    Article  Google Scholar 

  18. Schlappa, J. et al. Spin–orbital separation in the quasi-one-dimensional Mott insulator Sr2CuO3 . Nature 485, 82–85 (2012).

    Article  ADS  Google Scholar 

  19. Dean, M. P. M. et al. Persistence of magnetic excitations in La2−xSrxCuO4 from the undoped insulator to the heavily overdoped non-superconducting metal. Nat. Mater. 12, 1019–1023 (2013).

    Article  ADS  Google Scholar 

  20. Peng, Y. Y. et al. Magnetic excitations and phonons simultaneously studied by resonant inelastic X-ray scattering in optimally doped Bi1.5Pb0.55Sr1.6La0.4CuO6+δ . Phys. Rev. B 92, 064517 (2015).

    Article  ADS  Google Scholar 

  21. Schmidt, A. R. et al. Electronic structure of the cuprate superconducting and pseudogap phases from spectroscopic imaging STM. New J. Phys. 13, 065014 (2011).

    Article  ADS  Google Scholar 

  22. Hashimoto, M., Vishik, I. M., He, R. H., Devereaux, T. P. & Shen, Z. X. Energy gaps in high-transition-temperature cuprate superconductors. Nat. Phys. 10, 483–495 (2014).

    Article  Google Scholar 

  23. Graf, J. et al. Bond stretching phonon softening and kinks in the angle-resolved photoemission spectra of optimally doped Bi2Sr1.6La0.4Cu2O6+δ superconductors. Phys. Rev. Lett. 100, 227002 (2008).

    Article  ADS  Google Scholar 

  24. Reznik, D. et al. Electron–phonon coupling reflecting dynamic charge inhomogeneity in copper oxide superconductors. Nature 440, 1170–1173 (2006).

    Article  ADS  Google Scholar 

  25. Le Tacon, M. et al. Inelastic X-ray scattering in YBa2Cu3O6.6 reveals giant phonon anomalies and elastic central peak due to charge-density-wave formation. Nat. Phys. 10, 52–58 (2014).

    Article  Google Scholar 

  26. Ament, L. J. P., van Veenendaal, M. & van den Brink, J. Determining the electron-phonon coupling strength from resonant inelastic X-ray scattering at transition metal L-edges. Euro. Phys. Lett. 95, 27008 (2011).

    Article  ADS  Google Scholar 

  27. Lee, W. S. et al. Role of lattice coupling in establishing electronic and magnetic properties in quasi-one-dimensional cuprates. Phys. Rev. Lett. 110, 265502 (2013).

    Article  ADS  Google Scholar 

  28. Devereaux, T. P. et al. Directly characterizing the relative strength and momentum dependence of electron-phonon coupling using resonant inelastic X-ray scattering. Phys. Rev. X 6, 041019 (2016).

    Google Scholar 

  29. Kaneshita, E., Ichioka, M. & Machida, K. Spin and charge excitations in incommensurate spin density wave. J. Phys. Soc. Jpn 70, 866–876 (2001).

    Article  ADS  Google Scholar 

  30. Kajimoto, R. et al. Hole concentration dependence of the ordering process of the stripe order in La2−xSrxNiO4 . Phys. Rev. B 64, 144432 (2001).

    Article  ADS  Google Scholar 

  31. Mesaros, A. et al. Commensurate 4a0-period charge density modulations throughout the Bi2Sr2CaCu2O8+x pseudogap regime. Proc. Natl Acad. Sci. USA 113, 12661–12666 (2016).

    Article  Google Scholar 

  32. Ghiringhelli, G. et al. SAXES, a high resolution spectrometer for resonant X-ray emission in the 400–1600 eV energy range. Rev. Sci. Instrum. 77, 113108 (2006).

    Article  ADS  Google Scholar 

  33. Strocov, V. N. et al. High-resolution soft X-ray beamline ADRESS at the Swiss Light Source for resonant inelastic X-ray scattering and angle-resolved photoelectron spectroscopies. J. Synchrotron Radiat. 17, 631–643 (2010).

    Article  Google Scholar 

  34. Minola, M. et al. Collective nature of spin excitations in superconducting cuprates probed by resonant inelastic x-ray scattering. Phys. Rev. Lett. 114, 217003 (2015).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank S. A. Kivelson for discussions. 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. L.C. acknowledges the support from Department of Energy, SLAC Laboratory Directed Research and Development funder contract under DE-AC02-76SF00515. The data in Fig. 1b were taken partly at the Advanced Resonant Spectroscopies (ADRESS) beam line of the Swiss Light Source, using the Super Advanced X-ray Emission Spectrometer (SAXES) instrument jointly built by Paul Scherrer Institut (Villigen, Switzerland), Politecnico di Milano (Italy), and École Polytechnique Fédérale de Lausanne (Switzerland); all other RIXS data were taken at the ID32 of the ESRF (Grenoble, France) using the ERIXS spectrometer designed jointly by the ESRF and Politecnico di Milano. ARPES data were taken at Stanford Synchrotron Radiation Lightsource, operated by the US Department of Energy, Office of Science, Office of Basic Energy Sciences.

Author information

Authors and Affiliations

Authors

Contributions

W.-S.L., G.G., L.B., T.P.D. and Z.-X.S. conceived the experiment. L.C., W.-S.L., G.G., Y.Y.P., M.H., L.B., K.K. and N.B.B. conducted the experiment at ESRF. L.C., W.-S.L., G.G., Y.Y.P., L.B. and M.H. analysed the data. T.P.D. and B.M. performed the theoretical calculations. Y.H., S.C., S.I., Y.Y., H.E. and M.S. synthesized and prepared samples for the experiments. L.C. and W.-S.L. wrote the manuscript with input from all the authors.

Corresponding authors

Correspondence to Z.-X. Shen, T. P. Devereaux or W.-S. Lee.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 2554 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chaix, L., Ghiringhelli, G., Peng, Y. et al. Dispersive charge density wave excitations in Bi2Sr2CaCu2O8+δ. Nature Phys 13, 952–956 (2017). https://doi.org/10.1038/nphys4157

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue date:

  • DOI: https://doi.org/10.1038/nphys4157

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing