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  • Letter
  • Open Access

Orbital order and superconductivity in bilayer nickelate compounds

Giniyat Khaliullin1 and Jiří Chaloupka2

Phys. Rev. B 113, L041115 – Published 20 January, 2026

DOI: https://doi.org/10.1103/4qsd-ws9c

Abstract

We propose a theory for bilayer nickelate materials, where a large tetragonal field—intrinsic or induced by epitaxial strain—lifts the orbital degeneracy and localizes the 3z2−r2 orbital states. These states host local spins S=1/2 bound into singlets by strong interlayer coupling, and their dynamics is described by weakly dispersive singlet-triplet excitations (“triplons”). The charge carriers occupy the wide bands of x2−y2 symmetry, and their Cooper pairing is mediated by the high-energy triplon excitations. As the x2−y2 band filling increases, i.e., moving further away from the Ni3+ valence state, the indirect Ruderman-Kittel-Kasuya-Yosida interactions between local spins induce spin-density-wave order via triplon condensation. Implications of the model for compressively strained La3Ni2O7 films and electron-doped oxychloride Sr3Ni2O5Cl2 are discussed.

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References (42)

  1. M. Imada, A. Fujimori, and Y. Tokura, Metal-insulator transitions, Rev. Mod. Phys. 70, 1039 (1998).
  2. D. I. Khomskii, Transition Metal Compounds (Cambridge University Press, Cambridge, 2014).
  3. G. Khaliullin, Orbital order and fluctuations in Mott insulators, Prog. Theor. Phys. Suppl. 160, 155 (2005).
  4. D. Li, K. Lee, B. Y. Wang, M. Osada, S. Crossley, H. R. Lee, Y. Cui, Y. Hikita, and H. Y. Hwang, Superconductivity in an infinite-layer nickelate, Nature (London) 572, 624 (2019).
  5. H. Sun, M. Huo, X. Hu, J. Li, Z. Liu, Y. Han, L. Tang, Z. Mao, P. Yang, B. Wang, J. Cheng, D.-X. Yao, G.-M. Zhang, and M. Wang, Signatures of superconductivity near 80 K in a nickelate under high pressure, Nature (London) 621, 493 (2023).
  6. G. Wang, N. N. Wang, X. L. Shen, J. Hou, L. Ma, L. F. Shi, Z. A. Ren, Y. D. Gu, H. M. Ma, P. T. Yang, Z. Y. Liu, H. Z. Guo, J. P. Sun, G. M. Zhang, S. Calder, J.-Q. Yan, B. S. Wang, Y. Uwatoko, and J.-G. Cheng, Pressure-induced superconductivity in polycrystalline La3Ni2O7−δ, Phys. Rev. X 14, 011040 (2024).
  7. M. L. Medarde, Structural, magnetic, and electronic properties of RNiO3 perovskites (R = rare earth), J. Phys.: Condens. Matter 9, 1679 (1997).
  8. H. Sakakibara, N. Kitamine, M. Ochi, and K. Kuroki, Possible high-Tc superconductivity in La3Ni2O7 under high pressure through manifestation of a nearly half-filled bilayer Hubbard model, Phys. Rev. Lett. 132, 106002 (2024).
  9. Q.-G. Yang, D. Wang, and Q.-H. Wang, Possible s±-wave superconductivity in La3Ni2O7, Phys. Rev. B 108, L140505 (2023).
  10. Z. Liao, L. Chen, G. Duan, Y. Wang, C. Liu, R. Yu, and Q. Si, Electron correlations and superconductivity in La3Ni2O7 under pressure tuning, Phys. Rev. B 108, 214522 (2023).
  11. Y.-F. Yang, G.-M. Zhang, and F.-C. Zhang, Interlayer valence bonds and two-component theory for high-Tc superconductivity of La3Ni2O7 under pressure, Phys. Rev. B 108, L201108 (2023).
  12. Y.-B. Liu, J.-W. Mei, F. Ye, W.-Q. Chen, and F. Yang, s±-Wave pairing and the destructive role of apical-oxygen deficiencies in La3Ni2O7 under pressure, Phys. Rev. Lett. 131, 236002 (2023).
  13. 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).
  14. H. Oh and Y.-H. Zhang, Type-II t−J model and shared superexchange coupling from Hund's rule in superconducting La3Ni2O7, Phys. Rev. B 108, 174511 (2023).
  15. J. Chen, F. Yang, and W. Li, Orbital-selective superconductivity in the pressurized bilayer nickelate La3Ni2O7: An infinite projected entangled-pair state study, Phys. Rev. B 110, L041111 (2024).
  16. C. Lu, Z. Pan, F. Yang, and C. Wu, Interplay of two Eg orbitals in superconducting La3Ni2O7 under pressure, Phys. Rev. B 110, 094509 (2024).
  17. L. Liu, J. Guo, D. Hu, G. Yan, Y. Chen, L. Yu, M. Wang, X.-D. Liu, and X. Huang, Evidence for the Meissner effect in the nickelate superconductor La3Ni2O7−δ single crystal using diamond quantum sensors, Phys. Rev. Lett. 135, 096001 (2025).
  18. S. V. Mandyam, E. Wang, Z. Wang, B. Chen, N. C. Jayarama, A. Gupta, E. A. Riesel, V. I. Levitas, C. R. Laumann, and N. Y. Yao, Uncovering origins of heterogeneous superconductivity in La3Ni2O7 using quantum sensors, arXiv:2510.02429.
  19. E. K. Ko, Y. Yu, Y. Liu, L. Bhatt, J. Li, V. Thampy, C.-T. Kuo, B. Y. Wang, Y. Lee, K. Lee, J.-S. Lee, B. H. Goodge, D. A. Muller, and H. Y. Hwang, Signatures of ambient pressure superconductivity in thin film La3Ni2O7, Nature (London) 638, 935 (2025).
  20. G. Zhou, W. Lv, H. Wang, Z. Nie, Y. Chen, Y. Li, H. Huang, W.-Q. Chen, Y.-J. Sun, Q.-K. Xue, and Z. Chen, Ambient-pressure superconductivity onset above 40 K in (La,Pr)3Ni2O7 films, Nature (London) 640, 641 (2025).
  21. Y. Liu, E. K. Ko, Y. Tarn, L. Bhatt, J. Li, V. Thampy, B. H. Goodge, D. A. Muller, S. Raghu, Y. Yu, and H. Y. Hwang, Superconductivity and normal-state transport in compressively strained La2PrNi2O7 thin films, Nat. Mater. 24, 1221 (2025).
  22. B. Hao, M. Wang, W. Sun, Y. Yang, Z. Mao, S. Yan, H. Sun, H. Zhang, L. Han, Z. Gu, J. Zhou, D. Ji, and Y. Nie, Superconductivity and phase diagram in Sr-doped La3−xSrxNi2O7 thin films, arXiv:2505.12603.
  23. Y.-T. Hsu, Y. Liu, Y. Kohama, T. Kotte, V. Sharma, Y. Tarn, Y. Yu, and H. Y. Hwang, Fermi-liquid transport beyond the upper critical field in superconducting La2PrNi2O7 thin films, arXiv:2505.19011.
  24. M. Osada, C. Terakura, A. Kikkawa, M. Nakajima, H.-Y. Chen, Y. Nomura, Y. Tokura, and A. Tsukazaki, Strain-tuning for superconductivity in La3Ni2O7 thin films, Commun. Phys. 8, 251 (2025).
  25. In La3Ni2O7 films, the superconducting transition is broader and Tc∼40K is lower than in the bulk, which can be attributed to the observed local inhomogeneities in lattice structure and oxygen stoichiometry [26].
  26. L. Bhatt, A. Y. Jiang, E. K. Ko, N. Schnitzer, G. A. Pan, D. F. Segedin, Y. Liu, Y. Yu, Y.-F. Zhao, E. A. Morales, C. M. Brooks, A. S. Botana, H. Y. Hwang, J. A. Mundy, D. A. Muller, and B. H. Goodge, Resolving structural origins for superconductivity in strain-engineered La3Ni2O7 thin films, arXiv:2501.08204.
  27. Y. Tsujimoto, J. Sugiyama, M. Ochi, K. Kuroki, P. Manuel, D. D. Khalyavin, I. Umegaki, M. Månsson, D. Andreica, S. Hara, T. Sakurai, S. Okubo, H. Ohta, A. T. Boothroyd, and K. Yamaura, Impact of mixed anion ordered state on the magnetic ground states of S=1/2 square-lattice quantum spin antiferromagnets, Sr2NiO3Cl and Sr2NiO3F, Phys. Rev. Mater. 6, 114404 (2022).
  28. H. C. R. B. Bhatta, X. Zhang, Y. Zhong, and C. Jia, Structural and electronic evolution of bilayer nickelates under biaxial strain, arXiv:2502.01624.
  29. X.-W. Yi, W. Li, J.-Y. You, B. Gu, and G. Su, Unifying strain- and pressure-driven superconductivity in La3Ni2O7: Suppressed charge and spin density waves and enhanced interlayer coupling, Phys. Rev. B 112, L140504 (2025).
  30. M. Ochi, H. Sakakibara, H. Usui, and K. Kuroki, Theoretical study of the crystal structure of the bilayer nickel oxychloride Sr3Ni2O5Cl2 and analysis of possible unconventional superconductivity, Phys. Rev. B 111, 064511 (2025).
  31. For simplicity, the Slater-Koster rules [32] are used; corrections due to non-cubic symmetry can be readily included, but they are not essential here.
  32. J. C. Slater and G. F. Koster, Simplified LCAO method for the periodic potential problem, Phys. Rev. 94, 1498 (1954).
  33. A. M. Oleś, G. Khaliullin, P. Horsch, and L. F. Feiner, Fingerprints of spin-orbital physics in cubic Mott insulators: Magnetic exchange interactions and optical spectral weights, Phys. Rev. B 72, 214431 (2005).
  34. S. Sachdev and R. N. Bhatt, Bond-operator representation of quantum spins: Mean-field theory of frustrated quantum Heisenberg antiferromagnets, Phys. Rev. B 41, 9323 (1990).
  35. T. Sommer, M. Vojta, and K. W. Becker, Magnetic properties and spin waves of bilayer magnets in a uniform field, Eur. Phys. J. B 23, 329 (2001).
  36. See Supplemental Material at http://link.aps.org/supplemental/10.1103/4qsd-ws9c for the long-range hopping effects on the band dispersions and Fermi surface shapes, which includes Refs. [40, 41, 42].
  37. S. Doniach, The Kondo lattice and weak antiferromagnetism, Physica B+C 91, 231 (1977); See also P. Coleman, Introduction to Many-Body Physics (Cambridge University Press, Cambridge, 2015), Chap. 17.
  38. K. Yamane, Y. Matsushita, S. Adachi, T. Hiroto, R. Matsumoto, K. Terashima, H. Sakurai, and Y. Takano, High-pressure synthesis of bilayer nickelate Sr3Ni2O5Cl2 with a tetragonal crystal structure, Acta Cryst. C 81, 259 (2025).
  39. G. Khaliullin and J. Chaloupka, Supporting data for manuscript “Orbital order and superconductivity in bilayer nickelate compounds” [Data set], Zenodo (2026), doi: 10.5281/zenodo.18155533.
  40. E. Pavarini, I. Dasgupta, T. Saha-Dasgupta, O. Jepsen, and O. K. Andersen, Band-structure trend in hole-doped cuprates and correlation with Tcmax, Phys. Rev. Lett. 87, 047003 (2001).
  41. B. Y. Wang, Y. Zhong, S. Abadi, Y. Liu, Y. Yu, X. Zhang, Y.-M. Wu, R. Wang, J. Li, Y. Tarn, E. K. Ko, V. Thampy, M. Hashimoto, D. Lu, Y. S. Lee, T. P. Devereaux, C. Jia, H. Y. Hwang, and Z.-X. Shen, Electronic structure of compressively strained thin film La2PrNi2O7, arXiv:2504.16372.
  42. W. Sun, Z. Jiang, B. Hao, S. Yan, H. Zhang, M. Wang, Y. Yang, H. Sun, Z. Liu, D. Ji, Z. Gu, J. Zhou, D. Shen, D. Feng, and Y. Nie, Observation of superconductivity-induced leading-edge gap in Sr-doped La3Ni2O7 thin films, arXiv:2507.07409.

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