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Symmetry of charge order in cuprates

Nature Materials volume 14, pages 796–800 (2015)Cite this article

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Abstract

Charge-ordered ground states permeate the phenomenology of 3d-based transition metal oxides, and more generally represent a distinctive hallmark of strongly correlated states of matter. The recent discovery of charge order in various cuprate families has fuelled new interest into the role played by this incipient broken symmetry within the complex phase diagram of high-Tc superconductors. Here, we use resonant X-ray scattering to resolve the main characteristics of the charge-modulated state in two cuprate families: Bi2Sr2−xLaxCuO6+δ (Bi2201) and YBa2Cu3O6+y (YBCO). We detect no signatures of spatial modulations along the nodal direction in Bi2201, thus clarifying the inter-unit-cell momentum structure of charge order. We also resolve the intra-unit-cell symmetry of the charge-ordered state, which is revealed to be best represented by a bond order with modulated charges on the O-2p orbitals and a prominent d-wave character. These results provide insights into the origin and microscopic description of charge order in cuprates, and its interplay with superconductivity.

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Figure 1: Charge-ordering patterns and wavevectors.
Figure 2: Charge modulation symmetry components.
Figure 3: Azimuthal angle-dependent RXS measurements: geometry and experimental data.
Figure 4: Experimental and calculated CDW peak intensity versus azimuthal angle.

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References

  1. Yoshizawa, H., Kawano, H., Tomioka, Y. & Tokura, Y. Neutron-diffraction study of the magnetic-field-induced metal–insulator transition in Pr0.7Ca0.3MnO3 . Phys. Rev. B 52, R13145–R13148 (1995).

    Article  Google Scholar 

  2. Tranquada, J. M., Buttrey, D. J. & Sachan, V. Incommensurate stripe order in La2−xSrxNiO4 with x = 0.225. Phys. Rev. B 54, 12318–12323 (1996).

    Article  CAS  Google Scholar 

  3. Cwik, M. et al. Magnetic correlations in La2−xSrxCoO4 studied by neutron scattering: Possible evidence for stripe phases. Phys. Rev. Lett. 102, 057201 (2009).

    Article  CAS  Google Scholar 

  4. 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  Google Scholar 

  5. v. Zimmermann, M. et al. Hard X-ray diffraction study of charge stripe order in La1.48Nd0.4Sr0.12CuO4 . Europhys. Lett. 41, 629–634 (1998).

    Article  Google Scholar 

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

    CAS  Google Scholar 

  7. Fink, J. et al. Charge ordering in La1.8−xEu0.2SrxCuO4 studied by resonant soft x-ray diffraction. Phys. Rev. B 79, 100502 (2009).

    Article  Google Scholar 

  8. Poilblanc, D. & Rice, T. M. Charged solitons in the Hartree–Fock approximation to the large-U Hubbard model. Phys. Rev. B 39, 9749–9752 (1989).

    Article  CAS  Google Scholar 

  9. Zaanen, J. & Gunnarsson, O. Charged magnetic domain lines and the magnetism of high-Tc oxides. Phys. Rev. B 40, 7391–7394 (1989).

    Article  CAS  Google Scholar 

  10. Machida, K. Magnetism in La2CuO4 based compounds. Physica C 158, 192–196 (1989).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  12. Castellani, C., Di Castro, C. & Grilli, M. Singular quasiparticle scattering in the proximity of charge instabilities. Phys. Rev. Lett. 75, 4650–4653 (1995).

    Article  CAS  Google Scholar 

  13. 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).

    Article  CAS  Google Scholar 

  14. 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  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  17. Chang, J. et al. Direct observation of competition between superconductivity and charge density wave order in YBa2Cu3Oy . Nature Phys. 8, 871–876 (2012).

    Article  CAS  Google Scholar 

  18. Achkar, A. J. et al. Distinct charge orders in the planes and chains of ortho-III ordered YBa2Cu3O6+δ superconductors identified by resonant elastic X-ray scattering. Phys. Rev. Lett. 109, 167001 (2012).

    Article  CAS  Google Scholar 

  19. Blackburn, E. et al. X-ray diffraction observations of a charge-density-wave order in superconducting ortho-II Y Ba2Cu3O6.54 single crystals in zero magnetic field. Phys. Rev. Lett. 110, 137004 (2013).

    Article  CAS  Google Scholar 

  20. Blanco-Canosa, S. et al. Momentum-dependent charge correlations in Y Ba2Cu3O6+δ superconductors probed by resonant X-ray scattering: Evidence for three competing phases. Phys. Rev. Lett. 110, 187001 (2013).

    Article  CAS  Google Scholar 

  21. Le Tacon, M. et al. Giant phonon anomalies and central peak due to charge density wave formation in YBa2Cu2O6.6 . Nature Phys. 10, 52–58 (2014).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  24. da Silva Neto, E. H. et al. Charge ordering in the electron-doped superconductor Nd2−xCexCuO4 . Science 347, 282–285 (2015).

    Article  CAS  Google Scholar 

  25. Kivelson, S. A. et al. How to detect fluctuating stripes in the high-temperature superconductors. Rev. Mod. Phys. 75, 1201–1241 (2003).

    Article  CAS  Google Scholar 

  26. Seibold, G., Grilli, M. & Lorenzana, J. Stripes in cuprate superconductors: Excitations and dynamic dichotomy. Physica C 481, 132–145 (2012).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  29. 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).

    Article  CAS  Google Scholar 

  30. Meier, H., Einenkel, M., Pépin, C. & Efetov, K. B. Effect of magnetic field on the competition between superconductivity and charge order below the pseudogap state. Phys. Rev. B 88, 020506 (2013).

    Article  Google Scholar 

  31. He, Y., Scherpelz, P. & Levin, K. Theory of fluctuating charge ordering in the pseudogap phase of cuprates via a preformed pair approach. Phys. Rev. B 88, 064516 (2013).

    Article  Google Scholar 

  32. Bulut, S., Atkinson, W. A. & Kampf, A. P. Spatially modulated electronic nematicity in the three-band model of cuprate superconductors. Phys. Rev. B 88, 155132 (2013).

    Article  Google Scholar 

  33. Nie, L., Tarjus, G. & Kivelson, S. A. Quenched disorder and vestigial nematicity in the pseudogap regime of the cuprates. Proc. Natl Acad. Sci. USA 111, 7980–7985 (2014).

    Article  CAS  Google Scholar 

  34. Dalla Torre, E. G., He, Y., Benjamin, D. & Demler, E. Exploring quasiparticles in high-Tc cuprates through photoemission, tunneling, and X-ray scattering experiments. New J. Phys. 111, 022001 (2015).

    Article  Google Scholar 

  35. Lee, P. A. Amperean pairing and the pseudogap phase of cuprate superconductors. Phys. Rev. X 4, 031017 (2014).

    Google Scholar 

  36. Wang, Y. & Chubukov, A. Charge-density-wave order with momentum (2q, 0) and (0,2q) within the spin-fermion model: Continuous and discrete symmetry breaking, preemptive composite order, and relation to pseudogap in hole-doped cuprates. Phys. Rev. B 90, 035149 (2014).

    Article  Google Scholar 

  37. Melikyan, A. & Norman, M. R. Symmetry of the charge density wave in cuprates. Phys. Rev. B 89, 024507 (2014).

    Article  Google Scholar 

  38. Fujita, K. et al. Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates. Proc. Natl Acad. Sci. USA 111, E3026–E3032 (2014).

    Article  CAS  Google Scholar 

  39. Achkar, A. J. et al. Orbital symmetry of charge density wave order in La1.875Ba0.125CuO4 and YBa2Cu3O6.67. Preprint at http://arXiv:1409.6787 (2014).

  40. Achkar, A. J. et al. Resonant X-ray scattering measurements of a spatial modulation of the Cu 3d and O 2p energies in stripe-ordered cuprate superconductors. Phys. Rev. Lett. 110, 017001 (2013).

    Article  CAS  Google Scholar 

  41. Metlitski, M. A. & Sachdev, S. Quantum phase transitions of metals in two spatial dimensions. II. Spin density wave order. Phys. Rev. B 82, 075128 (2010).

    Article  Google Scholar 

  42. Schüßler-Langeheine, C. et al. Spectroscopy of stripe order in La1.8Sr0.2NiO4 using resonant soft X-ray diffraction. Phys. Rev. Lett. 95, 156402 (2005).

    Article  Google Scholar 

  43. Matteo, S. D. Resonant x-ray diffraction: Multipole interpretation. J. Phys. D: Appl. Phys. 45, 163001 (2012).

    Article  Google Scholar 

  44. Vojta, M. & Rösch, O. Superconducting d-wave stripes in cuprates: Valence bond order coexisting with nodal quasiparticles. Phys. Rev. B 77, 094504 (2008).

    Article  Google Scholar 

  45. Zaanen, J., Sawatzky, G. A. & Allen, J. W. Band gaps and electronic structure of transition-metal compounds. Phys. Rev. Lett. 55, 418–421 (1985).

    Article  CAS  Google Scholar 

  46. Emery, V. J. & Reiter, G. Reply to “Validity of the t–J model”. Phys. Rev. B 41, 7247–7249 (1990).

    Article  CAS  Google Scholar 

  47. Kohsaka, Y. et al. An intrinsic bond-centered electronic glass with unidirectional domains in underdoped cuprates. Science 315, 1380–1385 (2007).

    Article  CAS  Google Scholar 

  48. Lawler, M. J. et al. Intra-unit-cell electronic nematicity of the high-TC copper-oxide pseudogap states. Nature 466, 347–351 (2010).

    Article  CAS  Google Scholar 

  49. Liang, R., Bonn, D. A. & Hardy, W. N. Evaluation of CuO2 plane hole doping in YBa2Cu3O6+x single crystals. Phys. Rev. B 73, 180505 (2006).

    Article  Google Scholar 

  50. Ando, Y. et al. Carrier concentrations in Bi2Sr2−zLazCuO6+δ single crystals and their relation to the Hall coefficient and thermopower. Phys. Rev. B 61, R14956–R14959 (2000).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We are grateful to J. E. Hoffman, Y. He and M. Yee for sharing their STM data and for fruitful discussions. We also acknowledge M. Le Tacon, S. Sachdev, M. Norman, S. Kivelson, C. Pepin, E. D. Torre and E. Demler for insightful discussions. This work was supported by the Max Planck—UBC Centre for Quantum Materials, the Killam, A. P. Sloan, A. von Humboldt, and NSERC’s Steacie Memorial Fellowships (A.D.), the Canada Research Chairs Program (A.D., G.A.S.), NSERC, CFI and CIFAR Quantum Materials. Part of the research described in this paper was performed at the Canadian Light Source, which is funded by the CFI, NSERC, NRC, CIHR, the Government of Saskatchewan, WD Canada and the University of Saskatchewan. R.C. acknowledges the receipt of support from the CLS Graduate Student Travel Support Program. E.H.d.S.N. acknowledges support from the CIFAR Global Academy.

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada

    R. Comin, E. H. da Silva Neto, L. Chauviere, R. Liang, W. N. Hardy, D. A. Bonn, G. A. Sawatzky & A. Damascelli

  2. Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada

    R. Comin, E. H. da Silva Neto, L. Chauviere, R. Liang, W. N. Hardy, D. A. Bonn, G. A. Sawatzky & A. Damascelli

  3. Canadian Light Source, Saskatoon, Saskatchewan S7N 2V3, Canada

    R. Sutarto & F. He

  4. Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany,

    E. H. da Silva Neto, L. Chauviere, A. Fraño & B. Keimer

  5. Quantum Materials Program, Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada

    E. H. da Silva Neto

  6. Helmholtz-Zentrum Berlin für Materialien und Energie, Albert-Einstein Straße 15, 12489 Berlin, Germany

    A. Fraño

  7. National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba 305-8568, Japan

    Y. Yoshida & H. Eisaki

  8. Department of Physics and Astronomy, University of Waterloo, Waterloo N2L 3G1, Canada

    A. J. Achkar & D. G. Hawthorn

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  1. R. Comin
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Contributions

R.C., B.K., G.A.S. and A.D. conceived this investigation. R.C. performed RXS measurements at the Canadian Light Source with the assistance of R.S., F.H., E.H.d.S.N. and L.C. R.C. developed the theoretical model and performed related calculations. R.C., A.F., A.J.A., D.G.H., B.K., G.A.S. and A.D. are responsible for data analysis and interpretation. R.L., W.N.H. and D.A.B. provided the YBCO samples. Y.Y. and H.E. provided the Bi2201 samples. All of the authors discussed the underlying physics and contributed to the manuscript. R.C. and A.D. wrote the manuscript. A.D. is responsible for overall project direction, planning and management.

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Correspondence to R. Comin or A. Damascelli.

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Comin, R., Sutarto, R., He, F. et al. Symmetry of charge order in cuprates. Nature Mater 14, 796–800 (2015). https://doi.org/10.1038/nmat4295

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