Abstract
Charge order is now accepted as an integral constituent of cuprate high-temperature superconductors, one that is intimately related to other electronic instabilities including antiferromagnetism and superconductivity1,2,3,4,5,6,7,8,9,10,11. Unlike conventional Peierls density waves, the charge correlations in cuprates have been predicted to display a rich momentum space topology depending on the underlying fermiology12,13,14,15,16,17,18. However, charge order has only been observed along the high-symmetry Cu–O bond directions. Here, using resonant soft X-ray scattering, we investigate the evolution of the full momentum space topology of charge correlations in T′-(Nd,Pr)2CuO4 as a function of electron doping. We report that, when the parent Mott insulator is doped, charge correlations first emerge with full rotational symmetry in momentum space, indicating glassy charge density modulation in real space possibly seeded by local defects. At higher doping levels, the orientation of charge correlations is locked to the Cu–O bond directions, restoring a more conventional long-ranged bidirectional charge order. Through charge susceptibility calculations, we reproduce the evolution in topology of charge correlations across the antiferromagnetic phase boundary and propose a revised phase diagram of T′-Ln2CuO4 with a superconducting region extending toward the Mott limit.
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The 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
28 May 2019
An amendment to this paper has been published and can be accessed via a link at the top of the paper.
References
Birgeneau, R. J. et al. Static and dynamic spin fluctuations in superconducting La2–xSrxCuO4. Phys. Rev. B 39, 2868–2871 (1989).
Hoffman, J. E. A four unit cell periodic pattern of quasi-particle states surrounding vortex cores in Bi2Sr2CaCu2O8+x. Science 295, 466–469 (2002).
Comin, R. Resonant X-ray scattering studies of charge order in cuprates. Annu. Rev. Condens. Matter Phys. 7, 369–405 (2016).
Vershinin, M. et al. Local ordering in the pseudogap state of the high-T c superconductor Bi2Sr2CaCu2O8+δ. Science 303, 1995–1998 (2004).
Ghiringhelli, G. et al. Long-range incommensurate charge fluctuations in (Y,Nd)Ba2Cu3O6+x. Science 337, 821–825 (2012).
Chang, J. et al. Direct observation of competition between superconductivity and charge density wave order in YBa2Cu3O6.67. Nat. Phys. 8, 871–876 (2012).
da Silva Neto, E. H. et al. Ubiquitous interplay between charge ordering and high temperature superconductivity in cuprates. Science 343, 393–396 (2014).
Comin, R. et al. Charge order driven by fermi-arc instability in Bi2Sr2−xLaxCuO6+δ. Science 343, 390–392 (2014).
Tabis, W. et al. Charge order and its connection with Fermi-liquid charge transport in a pristine high-T C cuprate. Nat. Commun. 5, 5875 (2014).
da silva Neto, E. H. et al. Charge ordering in electron doped superconductor Nd2–xCexCuO4. Science 347, 282–285 (2015).
da Silva Neto, E. H. et al. Doping dependent charge order correlations in electron-doped cuprates. Sci. Adv. 2, e1600782 (2016).
Sachdev, S. & La Placa, R. Bond order in two-dimensional metals with antiferromagnetic exchange interactions. Phys. Rev. Lett. 111, 027202 (2013).
Sau, J. D. & Sachdev, S. Mean-field theory of competing orders in metals with antiferromagnetic exchange interactions. Phys. Rev. B 89, 075129 (2014).
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, 35149 (2014).
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 (2017).
Atkinson, W. A., Kampf, A. P. & Bulut, S. Charge order in the pseudogap phase of cuprate superconductors. New J. Phys. 17, 013025 (2015).
Dalla Torre, E. G., He, Y., Benjamin, D. & Demler, E. Exploring quasiparticles in high-T c cuprates through photoemission, tunneling, and X-ray scattering experiments. New J. Phys. 17, 22001 (2015).
Duong, L. Q. & Das, T. Correlation between Fermi arc and charge order resulting from the momentum-dependent self-energy correction in cuprates. Phys. Rev. B 96, 125154 (2017).
Marshall, D. S. et al. Unconventional electronic structure evolution with hole doping in Bi2Sr2CaCu2O8+δ: angle-resolved photoemission results. Phys. Rev. Lett. 76, 4841 (1996).
Armitage, N. P. et al. Doping dependence of an n-type cuprate superconductor investigated by angle-resolved photoemission spectroscopy. Phys. Rev. Lett. 88, 257001 (2002).
Cai, P. et al. Visualizing the evolution from the Mott insulator to a charge ordered insulator in lightly doped cuprates. Nat. Phys. 12, 1047–1051 (2015).
Peng, Y. Y. et al. Re-entrant charge order in overdoped (Bi,Pb)2.12Sr1.88CuO6+δ outside the pseudogap regime. Nat. Mater. 17, 697–702 (2018).
Helm, T. et al. Evolution of the Fermi surface of the electron-doped high-temperature superconductor Nd2–xCexCuO4 revealed by Shubnikov–de Haas oscillations. Phys. Rev. Lett. 103, 157002 (2009).
Naito, M., Krockenberger, Y., Ikeda, A. & Yamamoto, H. Reassessment of the electronic state, magnetism, and superconductivity in high-T c cuprates with the Nd2CuO4structure. Physica C 523, 28–54 (2016).
Weber, C., Haule, K. & Kotliar, G. Strength of correlations in electron- and hole-doped cuprates. Nat. Phys. 6, 574–578 (2010).
Wei, H. I. et al. Electron doping of the parent cuprate La2CuO4 without cation substitution. Phys. Rev. Lett. 117, 147002 (2016).
Horio, M. et al. Electronic structure of Ce-doped and -undoped Nd2CuO4 superconducting thin films studied by hard X-ray photoemission and soft X-ray absorption spectroscopy. Phys. Rev. Lett. 120, 257001 (2018).
Horio, M. et al. Angle-resolved photoemission spectroscopy of the low-energy electronic structure of superconducting Pr2CuO4 driven by oxygen nonstoichiometry. Phys. Rev. B 98, 020505 (2018).
Lindhard, J. On the properties of a gas of charged particles. Kgl. Danske Videnskab. Selskab Mat.-fys. Medd. 28, 1–57 (1954).
Abbamonte, P., Demler, E., Seamus Davis, J. C. & Campuzano, J. C. Resonant soft X-ray scattering, stripe order, and the electron spectral function in cuprates. Physica C 481, 15–22 (2012).
Dalla Torre, E. G., Benjamin, D., He, Y., Dentelski, D. & Demler, E. Friedel oscillations as a probe of fermionic quasiparticles. Phys. Rev. B 93, 205117 (2016).
Das, T., Markiewicz, R. S. & Bansil, A. Intermediate coupling model of the cuprates. Adv. Phys. 63, 151–266 (2014).
Song, D. et al. Electron number-based phase diagram of Pr1–xLaCexCuO4–δ and possible absence of disparity between electron- and hole-doped cuprate phase diagrams. Phys. Rev. Lett. 118, 137001 (2017).
Motoyama, E. M. et al. Spin correlations in the electron-doped high-transition-temperature superconductor Nd2–xCexCuO4±δ. Nature 445, 186–189 (2007).
Krockenberger, Y. et al. Emerging superconductivity hidden beneath charge-transfer insulators. Sci. Rep. 3, 2235 (2013).
Krockenberger, Y., Yamamoto, H., Tsukada, A., Mitsuhashi, M. & Naito, M. Unconventional transport and superconducting properties in electron-doped cuprates. Phys. Rev. B 85, 184502 (2012).
Fine, B. V. Comment on ‘Broken translational and rotational symmetry via charge stripe order in underdoped YBa2Cu3O6+y’. Science 351, 235 (2016).
Acknowledgements
The authors are grateful to S. Kivelson, B. Fine, K. M. Shen and D. Hawthorn for insightful discussions. The authors thank L. Ye for support with resistivity measurements. This material is based on work supported by the National Science Foundation under Grant No. 1751739. The authors acknowledge the Berlin Electron Storage Ring (BESSY II), the Canadian Light Source and the Advanced Light Source for provision of synchrotron radiation beamtime. Research performed in the Canadian Light Source is funded by the Canada Foundation Innovation, the Natural Sciences and Engineering Research Council of Canada, the University of Saskatchewan, the Government of Saskatchewan, Western Economic Diversification Canada, the National Research Council Canada and the Canada Institutes of Health Research. This research used resources of the Advanced Light Source, which is a DOE Office of Science User Facility under contract no. DE-AC02-05CH11231. M.K. acknowledges a Samsung Scholarship from the Samsung Foundation of Culture. J.P. is financially supported by the Swiss National Science Foundation Early Postdoc Mobility fellowship project no. P2FRP2_171824 and Postdoc Mobility fellowship project no. P400P2_180744. Work by N.B. and J.A. is supported by the Gordon and Betty Moore Foundation’s EPiQS Initiative through Grant GBMF4374. T.D. acknowledges financial support from the Infosys Science foundation under Young investigator Award.
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M.K., J.P., E.S., A.F. and N.B. conducted the RXS experiments and analysed the data with help from M.C., K.Z., A.R., Z.H., S.L. and J.A. E.W., R.S., F.H., P.S. and E.A. maintained the X-ray beamlines and supported RXS experiments. T.D. performed the calculations. Y.K. and H.Y. grew the thin films, performed the transport measurements and analysed the data. R.C. conceived the experiment and directed the project. M.K. and R.C. wrote the manuscript with input from all other co-authors.
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Kang, M., Pelliciari, J., Frano, A. et al. Evolution of charge order topology across a magnetic phase transition in cuprate superconductors. Nat. Phys. 15, 335–340 (2019). https://doi.org/10.1038/s41567-018-0401-8
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DOI: https://doi.org/10.1038/s41567-018-0401-8
