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Anomalous doping evolution of collective charge excitations in an n-type cuprate

Ke-Jun Xu1,2, Nathan Giles-Donovan1,2, Stefano Agrestini3, Jaewon Choi3,*, Mirian Garcia-Fernandez3, Kejin Zhou3,†, Junfeng He4,5,‡, Costel R. Rotundu4,5,§, Young S. Lee4,5,6 et al.

Thomas P. Devereaux4,5,7, Zhi-Xun Shen4,5,6,8, Dung-Hai Lee1,2,∥, Robert J. Birgeneau1,2,¶, and Wei-Sheng Lee4,**

  • *Present address: Department of Physics and Astronomy, Seoul National University, Seoul 08826, Republic of Korea.
  • †Present address: National Synchrotron Radiation Laboratory and School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230026, China.
  • ‡Present address: Department of Physics, University of Science and Technology of China, Hefei 230026, China.
  • §Present address: Charlotte, North Carolina, USA.
  • ∥Contact author: dunghai@berkeley.edu
  • Contact author: robertjb@berkeley.edu
  • **Contact author: leews@stanford.edu
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APS Open Sci. 1, 000200 – Published 3 November, 2026

DOI: https://doi.org/10.1103/nbry-mk8w

Abstract

Metallic systems with delocalized valence electrons host collective charge density oscillations known as plasmons. On the other hand, conventional insulators do not have free electrons and the low-energy charge degrees of freedom are pinned to the ions. The fate of the collective charge excitations in the intermediate regime is an outstanding question. This problem is especially important for strongly correlated systems such as the layered cuprates, where unconventional superconductivity and other emergent phenomena arise from valence electrons on the border between Mott localization and itinerancy. Using resonant inelastic xray scattering, we track this evolution in the prototypical electron-doped cuprate Nd2−xCexCuO4. We find a continuous transformation of the low-energy charge response: from an acoustic plasmon in the metallic regime, to a gapped mode with a dispersion anomaly at intermediate doping, and finally to a nearly dispersionless 139 meV excitation at half filling. The 139 meV excitation at zero doping has approximately twice the energy of the oxygen phonons responsible for the dispersion anomaly observed in angle-resolved photoemission spectroscopy. To explain this evolution, we introduce an inhomogeneous microscopic framework where plasmons in metallic regions couple with two-phonon excitations in insulating regions. These results establish a unified picture of collective charge excitations across the phase diagram of electron-doped cuprates and reveal a missing link in the charge dynamics of carrier doped Mott insulators.

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References (60)

  1. D. Pines and D. Bohm, A collective description of electron interactions: II. Collective vs individual particle aspects of the interactions, Phys. Rev. 85, 338 (1952).
  2. S. Martin, A. T. Fiory, R. M. Fleming, L. F. Schneemeyer, and J. V. Waszczak, Normal-state transport properties of Bi2+xSr2−yCuO6+δ crystals, Phys. Rev. B 41, 846(R) (1990).
  3. S.-D. Chen, M. Hashimoto, Y. He, D. Song, K.-J. Xu, J.-F. He, T. P. Devereaux, H. Eisaki, D.-H. Lu, J. Zaanen, and Z.-X. Shen, Incoherent strange metal sharply bounded by a critical doping in Bi2212, Science 366, 1099 (2019).
  4. R. L. Greene, P. R. Mandal, N. R. Poniatowski, and T. Sarkar, The strange metal state of the electron-doped cuprates, Ann. Rev. Mod. Phys 11, 213 (2020).
  5. M. Mitrano, A. A. Husain, S. Vig, A. Kogar, M. S. Rak, S. I. Rubeck, J. Schmalian, B. Uchoa, J. Schneeloch, R. Zhong, G. D. Gu, and P. Abbamonte, Anomalous density fluctuations in a strange metal, Proc. Natl. Acad. Sci. USA 115, 5392 (2018).
  6. J. G. Bednorz and K. A. Möller, Possible high-Tc superconductivity in the Ba-La-Cu-O system, Z. Phys. B 64, 189 (1986).
  7. B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida, and J. Zaanen, From quantum matter to high-temperature superconductivity in copper oxides, Nature (London) 518, 179 (2015).
  8. S. Sachdev, Colloquium: Order and quantum phase transitions in the cuprate superconductors, Rev. Mod. Phys. 75, 913 (2003).
  9. P. A. Lee, N. Nagaosa, and X.-G. Wen, Doping a Mott insulator: Physics of high-temperature superconductivity, Rev. Mod. Phys. 78, 17 (2006).
  10. Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori, and P. Jarillo-Herrero, Correlated insulator behaviour at half-filling in magic-angle graphene superlattices, Nature (London) 556, 80 (2018).
  11. B. Vignolle, A. Carrington, R. A. Cooper, M. M. J. French, A. P. Mackenzie, C. Jaudet, D. Vignolles, C. Proust, and N. E. Hussey, Quantum oscillations in an overdoped high-Tc superconductor, Nature (London) 455, 952 (2008).
  12. M. Platé, J. D. F. Mottershead, I. S. Elfimov, D. C. Peets, R. Liang, D. A. Bonn, W. N. Hardy, S. Chiuzbaian, M. Falub, M. Shi, L. Patthey, and A. Damascelli, Fermi surface and quasiparticle excitations of overdoped Tl2Ba2CuO6+δ, Phys. Rev. Lett. 95, 077001 (2005).
  13. A. Damascelli, Z. Hussain, and Z.-X. Shen, Angle-resolved photoemission studies of the cuprate superconductors, Rev. Mod. Phys. 75, 473 (2003).
  14. M. Hepting, L. Chaix, E. W. Huang, R. Fumagalli, Y. Y. Peng, B. Moritz, K. Kummer, N. B. Brookes, W. C. Lee, M. Hashimoto, T. Sarkar, J.-F. He, C. R. Rotundu, Y. S. Lee, R. L. Greene, L. Braicovich, G. Ghiringhelli, Z. X. Shen, T. P. Devereaux, and W. S. Lee, Three-dimensional collective charge excitations in electron-doped copper oxide superconductors, Nature (London) 563, 374 (2018).
  15. M. Hepting, M. Bejas, A. Nag, H. Yamase, N. Coppola, D. Betto, C. Falter, M. García-Fernández, S. Agrestini, K.-J. Zhou, M. Minola, C. Sacco, L. Maritato, P. Orgiani, H. Wei, K. Shen, D. Schlom, A. Galdi, A. Greco, and B. Keimer, Gapped collective charge excitations and interlayer hopping in cuprate superconductors, Phys. Rev. Lett. 129, 047001 (2022).
  16. A. Nag, M. Zhu, M. Bejas, J. Li, H. C. Robarts, H. Yamase, A. N. Petsch, D. Song, H. Eisaki, A. C. Walters, M. García-Fernández, A. Greco, S. M. Hayden, and K.-J. Zhou, Detection of acoustic plasmons in hole-doped lanthanum and bismuth cuprate superconductors using resonant inelastic x-ray scattering, Phys. Rev. Lett. 125, 257002 (2020).
  17. A. Nag, L. Zinni, J. Choi, J. Li, S. Tu, A. C. Walters, S. Agrestini, S. M. Hayden, M. Bejas, Z. Lin, H. Yamase, K. Jin, M. García-Fernández, J. Fink, A. Greco, and K.-J. Zhou, Impact of electron correlations on two-particle charge response in electron- and hole-doped cuprates, Phys. Rev. Res. 6, 043184 (2024).
  18. V. Z. Kresin and H. Morawitz, Layer plasmons and high-Tc superconductivity, Phys. Rev. B 37, 7854 (1988).
  19. Y. Ishii and J. Ruvalds, Acoustic plasmons and cuprate superconductivity, Phys. Rev. B 48, 3455 (1993).
  20. A. Bill, H. Morawitz, and V. Z. Kresin, Electronic collective modes and superconductivity in layered conductors, Phys. Rev. B 68, 144519 (2003).
  21. V. J. Emery and S. A. Kivelson, Importance of phase fluctuations in superconductors with small superfluid density, Nature (London) 374, 434 (1995).
  22. J. Lin, J. Yuan, K. Jin, Z. Yin, G. Li, K.-J. Zhou, X. Lu, M. Dantz, T. Schmitt, H. Ding, H. Guo, M. P. M. Dean, and X. Liu, Doping evolution of the charge excitations and electron correlations in electron-doped superconducting La2−xCexCuO4, npj Quantum Mater. 5, 4 (2020).
  23. M. Naito, S. Karimoto, and A. Tsukada, Epitaxy-stabilized n-type superconducting cuprates, Supercond. Sci. Technol. 15, 1663 (2002).
  24. M. Hepting, T. D. Boyko, V. Zimmermann, M. Bejas, Y. E. Suyolcu, P. Puphal, R. J. Green, L. Zinni, J. Kim, D. Casa, et al., Evolution of plasmon excitations across the phase diagram of the cuprate superconductor La2−xSrxCuO4, Phys. Rev. B 107, 214516 (2023).
  25. Y. Krockenberger, J. Kurian, A. Winkler, A. Tsukada, M. Naito, and L. Alff, Superconductivity phase diagrams for the electron-doped cuprates R2−xCexCuO4 (R=La, Pr, Nd, Sm, and Eu), Phys. Rev. B 77, 060505(R) (2008).
  26. N. P. Armitage, P. Fournier, and R. L. Greene, Progress and perspectives on electron-doped cuprates, Rev. Mod. Phys. 82, 2421 (2010).
  27. K.-J. Xu, Q. Guo, M. Hashimoto, Z.-X. Li, S.-D. Chen, J. He, Y. He, C. Li, M. H. Berntsen, C. R. Rotundu, Y. S. Lee, T. P. Devereaux, A. Rydh, D.-H. Lu, D.-H. Lee, O. Tjernberg, and Z.-X. Shen, Bogoliubov quasiparticle on the gossamer Fermi surface in electron-doped cuprates, Nat. Phys. 19, 1834 (2023).
  28. K.-J. Xu, J. He, S.-D. Chen, Y. He, S. N. Abadi, C. R. Rotundu, Y. S. Lee, D.-H. Lu, Q. Guo, O. Tjernberg, T. P. Devereaux, D.-H. Lee, M. Hashimoto, and Z.-X. Shen, Anomalous normal-state gap in an electron-doped cuprate, Science 385, 796 (2024).
  29. See Supplemental Material at http://link.aps.org/supplemental/10.1103/nbry-mk8w for details on the materials and methods, which includes Ref. [59].
  30. W. S. Lee, J. J. Lee, E. A. Nowadnick, S. Gerber, W. Tabis, S. W. Huang, V. N. Strocov, E. M. Motoyama, G. Yu, B. Moritz, H. Y. Huang, R. P. Wang, Y. B. Huang, W. B. Wu, C. T. Chen, D. J. Huang, M. Greven, T. Schmitt, Z. X. Shen, and T. P. Devereaux, Asymmetry of collective excitations in electron- and hole-doped cuprate superconductors, Nat. Phys. 10, 883 (2014).
  31. S. Das Sarma and E. H. Hwang, Collective modes of the massless Dirac plasma, Phys. Rev. Lett. 102, 206412 (2009).
  32. Y. Dagan, M. M. Qazilbash, C. P. Hill, V. N. Kulkarni, and R. L. Greene, Evidence for a quantum phase transition in Pr2−xCexCuO4−δ from transport measurements, Phys. Rev. Lett. 92, 167001 (2004).
  33. E. M. Motoyama, G. Yu, I. M. Vishik, O. P. Vajk, P. K. Mang, and M. Greven, Spin correlations in the electron-doped high-transition-temperature superconductor Nd2−xCexCuO4±δ, Nature (London) 445, 186 (2007).
  34. M. Hofmann, D. Strauch, U. Schroder, and E. Rampf, Lattice dynamics and inelastic neutron and synchrotron scattering cross-sections in Nd2CuO4, J. Phys.: Condens. Matter 6, 3669 (1994).
  35. Y. Onose, Y. Taguchi, K. Ishizaka, and Y. Tokura, Charge dynamics in underdoped Nd2−xCexCuO4: Pseudogap and related phenomena, Phys. Rev. B 69, 024504 (2004).
  36. S. Sugai, T. Kobayashi, and J. Akimitsu, Magnons and phonons in Nd2CuO4, Phys. Rev. B 40, 2686(R) (1989).
  37. B. Moritz, S. Johnston, T. P. Devereaux, B. Muschler, W. Prestel, R. Hackl, M. Lambacher, A. Erb, S. Komiya, and Y. Ando, Investigation of particle-hole asymmetry in the cuprates via electronic Raman scattering, Phys. Rev. B 84, 235114 (2011).
  38. M. H. Cohen and J. Ruvalds, Two-phonon bound states, Phys. Rev. Lett. 23, 1378 (1969).
  39. N. Chelwani, A. Baum, T. Böhm, M. Opel, F. Venturini, L. Tassini, A. Erb, H. Berger, L. Forró, and R. Hackl, Magnetic excitations and amplitude fluctuations in insulating cuprates, Phys. Rev. B 97, 024407 (2018).
  40. R. S. Markiewicz, S. Sahrakorpi, M. Lindroos, H. Lin, and A. Bansil, One-band tight-binding model parametrization of the high-Tc cuprates including the effect of kz dispersion, Phys. Rev. B 72, 054519 (2005).
  41. M. Horio, K. Hauser, Y. Sassa, Z. Mingazheva, D. Sutter, K. Kramer, A. Cook, E. Nocerino, O. K. Forslund, O. Tjernberg, et al., Three-dimensional Fermi surface of overdoped La-based cuprates, Phys. Rev. Lett. 121, 077004 (2018).
  42. M. Horio, K. P. Kramer, Q. Wang, A. Zaidan, K. von Arx, D. Sutter, C. E. Matt, Y. Sassa, N. C. Plumb, M. Shi, et al., Oxide Fermi liquid universality revealed by electron spectroscopy, Phys. Rev. B 102, 245153 (2020).
  43. S. L. Cooper, G. A. Thomas, A. J. Millis, P. E. Sulewski, J. Orenstein, D. H. Rapkine, S.-W. Cheong, and P. L. Trevor, Optical studies of gap, exchange, and hopping energies in the insulating cuprates, Phys. Rev. B 42, 10785(R) (1990).
  44. K. M. Shen, F. Ronning, D. H. Lu, W. S. Lee, N. J. C. Ingle, W. Meevasana, F. Baumberger, A. Damascelli, N. P. Armitage, L. L. Miller, Y. Kohsaka, M. Azuma, M. Takano, H. Takagi, and Z.-X. Shen, Missing quasiparticles and the chemical potential puzzle in the doping evolution of the cuprate superconductors, Phys. Rev. Lett. 93, 267002 (2004).
  45. P. W. Anderson, Absence of diffusion in certain random lattices, Phys. Rev. 109, 1492 (1958).
  46. Y. Onose, Y. Taguchi, K. Ishizaka, and Y. Tokura, Doping dependence of pseudogap and related charge dynamics in Nd2−xCexCuO4, Phys. Rev. Lett. 87, 217001 (2001).
  47. O. Fischer, M. Kugler, I. Maggio-Aprile, C. Berthod, and C. Renner, Scanning tunneling spectroscopy of high-temperature superconductors, Rev. Mod. Phys. 79, 353 (2007).
  48. F. C. Niestemski, S. Kunwar, S. Zhou, S. Li, H. Ding, Z. Wang, P. Dai, and V. Madhavan, A distinct bosonic mode in an electron-doped high-transition-temperature superconductor, Nature (London) 450, 1058 (2007).
  49. R. J. Koch, T. Seyller, and J. A. Schaefer, Strong phonon-plasmon coupled modes in the graphene/silicon carbide heterosystem, Phys. Rev. B 82, 201413(R) (2010).
  50. T. Bauer and C. Falter, Impact of dynamical screening on the phonon dynamics of metallic La2CuO4, Phys. Rev. B 80, 094525 (2009).
  51. C. Falter and M. Klenner, Nonadiabatic and nonlocal electron-phonon interaction and phonon-plasmon mixing in the high-temperature superconductors, Phys. Rev. B 50, 9426 (1994).
  52. C. Falter, M. Klenner, and G. A. Hoffmann, Phonon renormalization and c-axis phonon-plasmon mixing in La2CuO4, Phys. Rev. B 52, 3702 (1995).
  53. A. Lanzara, P. V. Bogdanov, X. J. Zhou, S. A. Kellar, D. L. Feng, E. D. Lu, T. Yoshida, H. Eisaki, A. Fujimori, K. Kishio, J.-I. Shimoyama, T. Noda, S. Uchida, Z. Hussain, and Z.-X. Shen, Evidence for ubiquitous strong electron–phonon coupling in high-temperature superconductors, Nature (London) 412, 510 (2001).
  54. S. R. Park, D. J. Song, C. S. Leem, C. Kim, C. Kim, B. J. Kim, and H. Eisaki, Angle-resolved photoemission spectroscopy of electron-doped cuprate superconductors: Isotropic electron-phonon coupling, Phys. Rev. Lett. 101, 117006 (2008).
  55. Y. He, M. Hashimoto, D. Song, S.-D. Chen, J. He, I. M. Vishik, B. Moritz, D.-H. Lee, N. Nagaosa, J. Zaanen, T. P. Devereaux, Y. Yoshida, H. Eisaki, D. H. Lu, and Z.-X. Shen, Rapid change of superconductivity and electron-phonon coupling through critical doping in Bi-2212, Science 362, 62 (2018).
  56. C. Honerkamp, H. C. Fu, and D.-H. Lee, Phonons and d-wave pairing in the two-dimensional Hubbard model, Phys. Rev. B 75, 014503 (2007).
  57. T. Cuk, F. Baumberger, D. H. Lu, N. Ingle, X. J. Zhou, H. Eisaki, N. Kaneko, Z. Hussain, T. P. Devereaux, N. Nagaosa, and Z.-X. Shen, Coupling of the B1g phonon to the antinodal electronic states of Bi2Sr2Ca0.92Y0.08Cu2O8+δ, Phys. Rev. Lett. 93, 117003 (2004).
  58. T. P. Devereaux, T. Cuk, Z.-X. Shen, and N. Nagaosa, Anisotropic electron-phonon interaction in the cuprates, Phys. Rev. Lett. 93, 117004 (2004).
  59. O. Matsumoto, A. Tsukada, H. Yamamoto, T. Manabe, and M. Naito, Generic phase diagram of Nd2−xCexCuO4, Physica C 470, S101 (2010).
  60. K.-J. Xu, Data for “Anomalous doping evolution of collective charge excitations in an n-type cuprate”, Dryad Repository, 2026, https://doi.org/10.5061/dryad.n02v6wxbm.

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APS Open Sci. 1, 000200– Published 3 November, 2026
Vol. 1
  • Received 20 May 2026
  • Accepted 14 October 2026
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