Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Multiorbital character of the density wave in trilayer nickelate superconductors

Abhi Suthar1, Vignesh Sundaramurthy1, Matías Bejas2, Congcong Le3, Pascal Puphal1, Pablo Sosa-Lizama1, Armin Schulz1, Jürgen Nuss1, Masahiko Isobe1 et al.

Peter A. van Aken1, Y. Eren Suyolcu1, Matteo Minola1, Andreas P. Schnyder1, Xianxin Wu4, Bernhard Keimer1, Giniyat Khaliullin1, Andrés Greco2,*, and Matthias Hepting1,†

  • *Contact author: agreco@fceia.unr.edu.ar
  • †Contact author: hepting@fkf.mpg.de

Phys. Rev. B 114, 045132 – Published 30 July, 2026

DOI: https://doi.org/10.1103/znvc-8425

Abstract

Ruddlesden–Popper nickelates exhibit high-temperature superconductivity closely intertwined with charge and spin density waves. However, fundamental questions persist regarding the interplay between the associated density wave (DW) fluctuations and superconductivity, as well as the orbital character and symmetry underlying the DW instabilities. Here, we utilize polarized Raman scattering to investigate the phononic and electronic Raman responses of the trilayer nickelate La4Ni3O10 across its concomitant charge and spin density wave transitions. In addition to distinct phonon anomalies occurring below the transition temperature, we observe a depletion of continuum spectral weight up to 114 meV and a pronounced peak centered at this energy. By combining momentum-selective information from polarized electronic Raman scattering with Raman-response model calculations based on a multiorbital Raman vertex in a reconstructed two-orbital DW state involving both Ni−3dx2−y2 and Ni−3dz2 orbitals, we identify 114 meV as the energy scale 2ΔDW of the DW gap, characterized by incoherent opening and non-mean-field behavior. Furthermore, the model calculations reveal that the corresponding 2ΔDW peak has a multiorbital origin, requiring both orbital contributions and their mixing beyond single-orbital projections, thus shedding light on the nature of the DW instabilities in La4Ni3O10.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (73)

  1. D. J. Scalapino, A common thread: The pairing interaction for unconventional superconductors, Rev. Mod. Phys. 84, 1383 (2012).
  2. P. A. Lee, N. Nagaosa, and X.-G. Wen, Doping a Mott insulator: Physics of high-temperature superconductivity, Rev. Mod. Phys. 78, 17 (2006).
  3. R. M. Fernandes, A. I. Coldea, H. Ding, I. R. Fisher, P. J. Hirschfeld, and G. Kotliar, Iron pnictides and chalcogenides: A new paradigm for superconductivity, Nature (London) 601, 35 (2022).
  4. P. Gegenwart, Q. Si, and F. Steglich, Quantum criticality in heavy-fermion metals, Nat. Phys. 4, 186 (2008).
  5. J. A. N. Bruin, H. Sakai, R. S. Perry, and A. P. Mackenzie, Similarity of scattering rates in metals showing T-linear resistivity, Science 339, 804 (2013).
  6. T. Timusk and B. Statt, The pseudogap in high-temperature superconductors: An experimental survey, Rep. Prog. Phys. 62, 61 (1999).
  7. T. P. Devereaux and R. Hackl, Inelastic light scattering from correlated electrons, Rev. Mod. Phys. 79, 175 (2007).
  8. M. Opel, R. Nemetschek, C. Hoffmann, R. Philipp, P. F. Müller, R. Hackl, I. Tüttő, A. Erb, B. Revaz, E. Walker, H. Berger, and L. Forró, Carrier relaxation, pseudogap, and superconducting gap in high-Tc cuprates: A Raman scattering study, Phys. Rev. B 61, 9752 (2000).
  9. M. Bakr, A. P. Schnyder, L. Klam, D. Manske, C. T. Lin, B. Keimer, M. Cardona, and C. Ulrich, Electronic and phononic Raman scattering in detwinned YBa2Cu3O6.95 and Y0.85Ca0.15Ba2Cu3O6.95: s-wave admixture to the dx2−y2-wave order parameter, Phys. Rev. B 80, 064505 (2009).
  10. Y. Gallais, R. M. Fernandes, I. Paul, L. Chauvière, Y.-X. Yang, M.-A. Méasson, M. Cazayous, A. Sacuto, D. Colson, and A. Forget, Observation of incipient charge nematicity in Ba(Fe1−XCoX)2As2, Phys. Rev. Lett. 111, 267001 (2013).
  11. F. Kretzschmar, T. Böhm, U. Karahasanović, B. Muschler, A. Baum, D. Jost, J. Schmalian, S. Caprara, M. Grilli, C. Di Castro, et al., Critical spin fluctuations and the origin of nematic order in Ba(Fe1−xCox)2As2, Nat. Phys. 12, 560 (2016).
  12. B. Loret, N. Auvray, Y. Gallais, M. Cazayous, A. Forget, D. Colson, M.-H. Julien, I. Paul, M. Civelli, and A. Sacuto, Intimate link between charge density wave, pseudogap and superconducting energy scales in cuprates, Nat. Phys. 15, 771 (2019).
  13. Y. Nomura and R. Arita, Superconductivity in infinite-layer nickelates, Rep. Prog. Phys. 85, 052501 (2022).
  14. M. Wang, H.-H. Wen, T. Wu, D.-X. Yao, and T. Xiang, Normal and superconducting properties of La3Ni2O7, Chin. Phys. Lett. 41, 077402 (2024).
  15. H. Sun, M. Huo, X. Hu, J. Li, Z. Liu, Y. Han, L. Tang, Z. Mao, P. Yang, B. Wang, et al., Signatures of superconductivity near 80 K in a nickelate under high pressure, Nature (London) 621, 493 (2023).
  16. Y. Zhu, D. Peng, E. Zhang, B. Pan, X. Chen, L. Chen, H. Ren, F. Liu, Y. Hao, N. Li, et al., Superconductivity in pressurized trilayer La4Ni3O10−δ single crystals, Nature (London) 631, 531 (2024).
  17. H. Sakakibara, M. Ochi, H. Nagata, Y. Ueki, H. Sakurai, R. Matsumoto, K. Terashima, K. Hirose, H. Ohta, M. Kato, Y. Takano, and K. Kuroki, Theoretical analysis on the possibility of superconductivity in the trilayer Ruddlesden-Popper nickelate La4Ni3O10 under pressure and its experimental examination: Comparison with La3Ni2O7, Phys. Rev. B 109, 144511 (2024).
  18. Q. Li, Y.-J. Zhang, Z.-N. Xiang, Y. Zhang, X. Zhu, and H.-H. Wen, Signature of superconductivity in pressurized La4Ni3O10, Chin. Phys. Lett. 41, 017401 (2024).
  19. M. Zhang, C. Pei, D. Peng, X. Du, W. Hu, Y. Cao, Q. Wang, J. Wu, Y. Li, H. Liu, C. Wen, J. Song, Y. Zhao, C. Li, W. Cao, S. Zhu, Q. Zhang, N. Yu, P. Cheng, L. Zhang, et al., Superconductivity in trilayer nickelate La4Ni3O10 under Pressure, Phys. Rev. X 15, 021005 (2025).
  20. J. Zhang, D. Phelan, A. S. Botana, Y.-S. Chen, H. Zheng, M. Krogstad, S. G. Wang, Y. Qiu, J. A. Rodriguez-Rivera, R. Osborn, et al., Intertwined density waves in a metallic nickelate, Nat. Commun. 11, 6003 (2020).
  21. M. Kakoi, T. Oi, Y. Ohshita, M. Yashima, K. Kuroki, T. Kato, H. Takahashi, S. Ishiwata, Y. Adachi, N. Hatada, T. Uda, and H. Mukuda, Multiband metallic ground state in multilayered nickelates La3Ni2O7 and La4Ni3O10 probed by 139La-NMR at ambient pressure, J. Phys. Soc. Jpn. 93, 053702 (2024).
  22. M. Li, J. Gong, Y. Zhu, Z. Chen, J. Zhang, E. Zhang, Y. Li, R. Yin, S. Wang, J. Zhao, D.-L. Feng, Z. Du, and Y.-J. Yan, Direct visualization of an incommensurate unidirectional charge density wave in La4Ni3O10, Phys. Rev. B 112, 045132 (2025).
  23. R. Khasanov, V. Sazgari, T. J. Hicken, I. Plokhikh, M. Medarde, E. Pomjakushina, L. Keller, V. Pomjakushin, M. Bartkowiak, S. Królak, M. J. Winiarski, A. Steppke, J. A. Krieger, H. Luetkens, T. Klimczuk, C. W. Schneider, D. J. Gawryluk, and Z. Guguchia, Pressure and oxygen-isotope substitution on density-wave transitions in La4Ni3O10, Phys. Rev. Res. 8, 013249 (2026).
  24. T. Fukamachi, K. Oda, Y. Kobayashi, T. Miyashita, and M. Sato, Studies on successive electronic state changes in systems with NiO2 planes–La−NMR/NQR139–, J. Phys. Soc. Jpn. 70, 2757 (2001).
  25. R. Khasanov, T. J. Hicken, D. J. Gawryluk, V. Sazgari, I. Plokhikh, L. P. Sorel, M. Bartkowiak, S. Bötzel, F. Lechermann, I. M. Eremin, H. Luetkens, and Z. Guguchia, Pressure-enhanced splitting of density wave transitions in La3Ni2O7, Nat. Phys. 21, 430 (2025).
  26. C.-Q. Chen, Z. Luo, M. Wang, W. Wú, and D.-X. Yao, Trilayer multiorbital models of La4Ni3O10, Phys. Rev. B 110, 014503 (2024).
  27. Q.-G. Yang, K.-Y. Jiang, D. Wang, H.-Y. Lu, and Q.-H. Wang, Effective model and s±-wave superconductivity in trilayer nickelate La4Ni3O10, Phys. Rev. B 109, L220506 (2024).
  28. Y. Zhang, L.-F. Lin, A. Moreo, T. A. Maier, and E. Dagotto, Prediction of s±-wave superconductivity enhanced by electronic doping in trilayer nickelates La4Ni3O10 under pressure, Phys. Rev. Lett. 133, 136001 (2024).
  29. J. Huang and T. Zhou, Interlayer pairing-induced partially gapped Fermi surface in trilayer La4Ni3O10 superconductors, Phys. Rev. B 110, L060506 (2024).
  30. H. LaBollita, J. Kapeghian, M. R. Norman, and A. S. Botana, Electronic structure and magnetic tendencies of trilayer La4Ni3O10 under pressure: Structural transition, molecular orbitals, and layer differentiation, Phys. Rev. B 109, 195151 (2024).
  31. I. V. Leonov, Electronic structure and magnetic correlations in the trilayer nickelate superconductor La4Ni3O10 under pressure, Phys. Rev. B 109, 235123 (2024).
  32. P.-F. Tian, H.-T. Ma, X. Ming, X.-J. Zheng, and H. Li, Effective model and electron correlations in trilayer nickelate superconductor La4Ni3O10, J. Phys.: Condens. Matter 36, 355602 (2024).
  33. M. Zhang, H. Sun, Y.-B. Liu, Q. Liu, W.-Q. Chen, and F. Yang, s±-wave superconductivity in pressurized La4Ni3O10, Phys. Rev. B 110, L180501 (2024).
  34. M. Zhang, H. Sun, Y.-B. Liu, Q. Liu, W.-Q. Chen, and F. Yang, Spin-density wave and superconductivity in La4Ni3O10 under ambient pressure, Phys. Rev. B 111, 144502 (2025).
  35. H. Li, X. Zhou, T. Nummy, J. Zhang, V. Pardo, W. E. Pickett, J. F. Mitchell, and D. S. Dessau, Fermiology and electron dynamics of trilayer nickelate La4Ni3O10, Nat. Commun. 8, 704 (2017).
  36. X. Du, Y. L. Wang, Y. D. Li, Y. T. Cao, M. X. Zhang, C. Y. Pei, J. M. Yang, W. X. Zhao, K. Y. Zhai, Z. K. Liu, Z. W. Li, J. K. Zhao, Z. T. Liu, D. W. Shen, Z. Li, Y. He, Y. L. Chen, Y. P. Qi, H. J. Guo, and L. X. Yang, Dichotomy in low- and high-energy band renormalizations in trilayer nickelate La4Ni3O10: A comparison with cuprates, Phys. Rev. Lett. 135, 146506 (2025).
  37. Y. Li, Y. Cao, L. Liu, P. Peng, H. Lin, C. Pei, M. Zhang, H. Wu, X. Du, W. Zhao, et al., Distinct ultrafast dynamics of bilayer and trilayer nickelate superconductors regarding the density-wave-like transitions, Sci. Bull. 70, 180 (2025).
  38. S. Xu, C.-Q. Chen, M. Huo, D. Hu, H. Wang, Q. Wu, R. Li, D. Wu, M. Wang, D.-X. Yao, T. Dong, and N. Wang, Origin of the density wave instability in trilayer nickelate La4Ni3O10 revealed by optical and ultrafast spectroscopy, Phys. Rev. B 111, 075140 (2025).
  39. S. Xu, H. Wang, M. Huo, D. Hu, Q. Wu, L. Yue, D. Wu, M. Wang, T. Dong, and N. Wang, Collapse of density wave and emergence of superconductivity in pressurized-La4Ni3O10 evidenced by ultrafast spectroscopy, Nat. Commun. 16, 7039 (2025).
  40. D.-H. Gim, C. H. Park, and K. H. Kim, Orbital-selective quasiparticle depletion across the density wave transition in trilayer nickelate La4Ni3O10, Phys. Rev. Lett. 135, 136505 (2025).
  41. J. Shu, J. Shen, X. Zhou, Y. Zhu, Q. Wang, D. Wang, W. He, J. Yuan, K. Jin, D. Shen, C. Le, J. Zhao, Z. Du, G. He, and D. Feng, Contrasting momentum-selective spin-density-wave gaps in bilayer and trilayer nickelates, arXiv:2602.02174.
  42. G. He, J. Shen, S. Xie, H. Zhang, M. Huo, J. Shu, D. Hu, X. Zhou, Y. Zhang, L. Qin, et al., Anisotropic electronic correlations in the spin density wave state of La3Ni2O7, Nat. Commun. 17, 72810 (2026).
  43. G. Blesio, S. Beck, O. Gingras, A. Georges, and J. Mravlje, Signatures of Hund metal and finite-frequency nesting in Sr2RuO4 revealed by electronic Raman scattering, Phys. Rev. Res. 6, 023124 (2024).
  44. C. Lu, Z. Pan, F. Yang, and C. Wu, Superconductivity in La4Ni3O10 under pressure, Phys. Rev. B 111, 134515 (2025).
  45. Y. Zhang, L.-F. Lin, A. Moreo, S. Okamoto, T. A. Maier, and E. Dagotto, General trends of superconducting pairing and magnetic correlations in the Ruddlesden-Popper nickelate m-layered superconductors Lam+1NimO3m+1, Phys. Rev. B 112, 094517 (2025).
  46. Y. Gu, C. Le, Z. Yang, X. Wu, and J. Hu, Effective model and pairing tendency in the bilayer Ni-based superconductor La3Ni2O7, Phys. Rev. B 111, 174506 (2025).
  47. Z. Luo, X. Hu, M. Wang, W. Wú, and D.-X. Yao, Bilayer two-orbital model of La3Ni2O7 under pressure, Phys. Rev. Lett. 131, 126001 (2023).
  48. C. Le, J. Zhan, X. Wu, and J. Hu, Landscape of correlated orders in strained bilayer nickelate thin films, arXiv:2501.14665.
  49. F. Lechermann, J. Gondolf, S. Bötzel, and I. M. Eremin, Electronic correlations and superconducting instability in La3Ni2O7 under high pressure, Phys. Rev. B 108, L201121 (2023).
  50. Y. Cao and Y.-F. Yang, Flat bands promoted by Hund's rule coupling in the candidate double-layer high-temperature superconductor La3Ni2O7 under high pressure, Phys. Rev. B 109, L081105 (2024).
  51. S. Ryee, N. Witt, G. Sangiovanni, and T. O. Wehling, Optimal superconductivity near a Lifshitz transition in strained (La,Pr)3Ni2O7, Phys. Rev. Lett. 135, 236003 (2025).
  52. X. Jia, Y. Shen, H. LaBollita, X. Chen, J. Zhang, Y. Li, H. Zhao, M. G. Kanatzidis, M. Krogstad, H. Zheng, A. H. Said, A. Alatas, S. Rosenkranz, D. Phelan, M. P. M. Dean, M. R. Norman, J. F. Mitchell, A. S. Botana, and Y. Cao, Lattice-charge coupling in a trilayer nickelate with intertwined density wave order, Phys. Rev. X 16, 011013 (2026).
  53. See Supplemental Material at http://link.aps.org/supplemental/10.1103/znvc-8425 for additional information on sample synthesis and characterization, phonon calculations, and the two-orbital model calculations.
  54. M. Hepting, M. Minola, A. Frano, G. Cristiani, G. Logvenov, E. Schierle, M. Wu, M. Bluschke, E. Weschke, H.-U. Habermeier, E. Benckiser, M. Le Tacon, and B. Keimer, Tunable charge and spin order in PrNiO3 thin films and superlattices, Phys. Rev. Lett. 113, 227206 (2014).
  55. H. L. Liu, S. Yoon, S. L. Cooper, G. Cao, and J. E. Crow, Raman-scattering study of the charge and spin dynamics of the layered ruthenium oxide Ca3Ru2O7, Phys. Rev. B 60, R6980 (1999).
  56. S. Kumar, Ø. Fjellvåg, A. O. Sjåstad, and H. Fjellvåg, Physical properties of Ruddlesden-Popper (n = 3) nickelate: La4Ni3O10, J. Magn. Magn. Mater. 496, 165915 (2020).
  57. D. Rout, S. R. Mudi, M. Hoffmann, S. Spachmann, R. Klingeler, and S. Singh, Structural and physical properties of trilayer nickelates R4Ni3O10 (R=La, Pr, and Nd), Phys. Rev. B 102, 195144 (2020).
  58. C. Falter and F. Schnetgöke, Influence of ionic charge and dipole fluctuations on the lattice dynamics, dielectric properties, and infrared response of La2CuO4, Phys. Rev. B 65, 054510 (2002).
  59. S. Deswal, D. Kumar, D. Rout, S. Singh, and P. Kumar, Dynamics of electron–electron correlation and electron–phonon coupled phase progression in trilayer nickelate La4Ni3O10, Appl. Phys. Lett. 127, 071903 (2025).
  60. X. Chen, J. Zhang, A. S. Thind, S. Sharma, H. LaBollita, G. Peterson, H. Zheng, D. P. Phelan, A. S. Botana, R. F. Klie, and J. F. Mitchell, Polymorphism in the Ruddlesden–Popper Nickelate La3Ni2O7: Discovery of a Hidden Phase with Distinctive Layer Stacking, J. Am. Chem. Soc. 146, 3640 (2024).
  61. P. Puphal, P. Reiss, N. Enderlein, Y.-M. Wu, G. Khaliullin, V. Sundaramurthy, T. Priessnitz, M. Knauft, A. Suthar, L. Richter, M. Isobe, P. A. van Aken, H. Takagi, B. Keimer, Y. E. Suyolcu, B. Wehinger, P. Hansmann, and M. Hepting, Unconventional crystal structure of the high-pressure superconductor La3Ni2O7, Phys. Rev. Lett. 133, 146002 (2024).
  62. J. Zhang, H. Zheng, Y.-S. Chen, Y. Ren, M. Yonemura, A. Huq, and J. F. Mitchell, High oxygen pressure floating zone growth and crystal structure of the metallic nickelates R4Ni3O10 (R=La,Pr), Phys. Rev. Mater. 4, 083402 (2020).
  63. N. Yuan, A. Elghandour, J. Arneth, K. Dey, and R. Klingeler, High-pressure crystal growth and investigation of the metal-to-metal transition of Ruddlesden–Popper trilayer nickelates La4Ni3O10, J. Cryst. Growth 627, 127511 (2024).
  64. M. Shi, Y. Li, Y. Wang, D. Peng, S. Yang, H. Li, K. Fan, K. Jiang, J. He, Q. Zeng, et al., Absence of superconductivity and density-wave transition in ambient-pressure tetragonal La4Ni3O10, Nat. Commun. 16, 2887 (2025).
  65. J.-P. Pouget and E. Canadell, Structural approach to charge density waves in low-dimensional systems: Electronic instability and chemical bonding, Rep. Prog. Phys. 87, 026501 (2024).
  66. J. Zhan, Y. Gu, X. Wu, and J. Hu, Cooperation between electron-phonon coupling and electronic interaction in bilayer nickelates La3Ni2O7, Phys. Rev. Lett. 134, 136002 (2025).
  67. C. Zhu, B. Li, Y. Fan, C. Yin, J. Zhai, J. Cheng, S. Liu, and Z. Shi, Magnetic phases and electron–phonon coupling in La3Ni2O7 under pressure, Comput. Mater. Sci. 250, 113676 (2025).
  68. Z. Ouyang, M. Gao, and Z.-Y. Lu, Absence of electron-phonon coupling superconductivity in the bilayer phase of La3Ni2O7 under pressure, npj Quantum Mater. 9, 80 (2024).
  69. Z. Liu, M. Huo, J. Li, Q. Li, Y. Liu, Y. Dai, X. Zhou, J. Hao, Y. Lu, M. Wang, and H.-H. Wen, Electronic correlations and partial gap in the bilayer nickelate La3Ni2O7, Nat. Commun. 15, 7570 (2024).
  70. B. Keimer, S. Kivelson, M. Norman, S. Uchida, and J. Zaanen, From quantum matter to high-temperature superconductivity in copper oxides, Nature (London) 518, 179 (2015).
  71. M. Uchida, K. Ishizaka, P. Hansmann, Y. Kaneko, Y. Ishida, X. Yang, R. Kumai, A. Toschi, Y. Onose, R. Arita, K. Held, O. K. Andersen, S. Shin, and Y. Tokura, Pseudogap of metallic layered nickelate R2−xSrxNiO4 (R=Nd,Eu) crystals measured using angle-resolved photoemission spectroscopy, Phys. Rev. Lett. 106, 027001 (2011).
  72. M. R. Norman, Landau theory of the density wave transition in trilayer Ruddlesden-Popper nickelates, Phys. Rev. B 112, 075149 (2025).
  73. S. Fan, M. Ou, M. Scholten, Q. Li, Z. Shang, Y. Wang, J. Xu, H. Yang, I. M. Eremin, and H.-H. Wen, Single-particle tunneling spectrum with a robust superconducting gap in La2PrNi2O7 thin films at ambient pressure, Sci.  Adv. 12, eaeg2429 (2026).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation