pith. sign in

arxiv: 2605.17520 · v2 · pith:E5AWUIQPnew · submitted 2026-05-17 · ❄️ cond-mat.supr-con · cond-mat.str-el

Enhanced s^pm-wave superconductivity in electron-doped La₃Ni₂O₇

Xun Liu , Chao Deng , Wenfeng Wu , Liang Si , Mi Jiang This is my paper

Pith reviewed 2026-05-21 08:05 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.str-el
keywords nickelate superconductorselectron dopings±-wave superconductivityLa3Ni2O7heterostructurebilayer modelinter-orbital pairingquantum Monte Carlo
0
0 comments X

The pith

Electron doping enhances s±-wave superconductivity in La3Ni2O7 bilayers and heterostructures.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper investigates electron doping in Ruddlesden-Popper nickelates, a strategy less explored than hole doping despite its success in cuprates. Using first-principles calculations and large-scale dynamical cluster quantum Monte Carlo simulations on a two-orbital bilayer model, the authors study bulk La3Ni2O7 at ambient pressure and 15 GPa plus a heterostructure with La3Al2O7. They find that electron doping generically raises the superconducting transition temperature for s±-wave pairing in all three systems. The heterostructure achieves the highest Tc specifically in the underdoped regime. An inter-orbital cooperative mechanism, in which pairing on the dz2 orbital induces pairing on the dx2-y2 orbital, drives the enhancement.

Core claim

In the two-orbital bilayer model for bulk La3Ni2O7 at ambient pressure and 15 GPa and for the La3Ni2O7:La3Al2O7 heterostructure, electron doping generically enhances s±-wave pairing superconductivity, with the heterostructure showing the highest Tc in the underdoped regime. The pairing arises from an inter-orbital cooperative mechanism in which the pairing on the dz2 orbital induces that on the dx2-y2 orbital.

What carries the argument

Two-orbital bilayer model simulated via dynamical cluster quantum Monte Carlo, with an inter-orbital cooperative mechanism linking dz2 and dx2-y2 orbital pairings.

If this is right

  • s±-wave pairing becomes the favored superconducting channel under electron doping across the studied systems.
  • The heterostructure provides a feasible experimental route to higher Tc without requiring extreme pressures.
  • Inter-orbital cooperation between dz2 and dx2-y2 orbitals stabilizes the enhanced superconductivity.
  • Electron doping may serve as a complementary strategy to hole doping in Ruddlesden-Popper nickelates.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If confirmed, experimental synthesis should target electron-doped heterostructures to verify elevated Tc values.
  • The contrast with cuprate behavior indicates that the preferred doping type for high Tc is material- and orbital-specific.
  • The model could be extended to predict optimal doping concentrations that maximize Tc in related nickelate compounds.

Load-bearing premise

The two-orbital bilayer model combined with dynamical cluster quantum Monte Carlo accurately captures the low-energy electronic structure and pairing interactions without significant finite-size or approximation errors that would alter the predicted Tc enhancement.

What would settle it

Experimental measurement of a lower or unchanged superconducting Tc upon electron doping in La3Ni2O7 or the heterostructure, or confirmation that the pairing symmetry is not s±-wave.

Figures

Figures reproduced from arXiv: 2605.17520 by Chao Deng, Liang Si, Mi Jiang, Wenfeng Wu, Xun Liu.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration of the bilayer two-orbital [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Extrapolated [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Characteristic BSE eigenvectors revealing stronger [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Temperature dependence of the inverse of [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Temperature dependence of the eigenvalue 1 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original abstract

In cuprates, electron doping yields a much lower superconducting $T_c$ than hole doping. For recently discovered nickelate superconductors, the analogous doping strategies become more challenging. Consequently, while hole-doped Ruddlesden-Popper (RP) nickelates have been extensively studied, electron-doped RP nickelates remain rarely explored both experimentally and theoretically. Here we fill this gap by systematically investigating the two-orbital bilayer model for three representative systems: bulk La$_3$Ni$_2$O$_7$ at ambient pressure and 15\,GPa, and a heterostructure La$_3$Ni$_2$O$_7$:La$_3$Al$_2$O$_7$ that provides a feasible experimental route to electron doping. Using first-principle calculations and large-scale dynamical cluster quantum Monte Carlo simulations, we find that electron doping generically enhances $s^\pm$-wave pairing superconductivity (SC) in all three cases, with the heterostructure showing the highest $T_c$ in the underdoped regime. Furthermore, our results suggest an inter-orbital cooperative mechanism that the pairing on the $d_{x^2-y^2}$ orbital, induced by that on the $d_{z^2}$ orbital, plays a vital role in the SC. This work provides the theoretical prediction of enhanced SC in electron-doped RP nickelates and calls for future experimental verification.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript examines electron doping in three La3Ni2O7-based systems (ambient-pressure bulk, 15 GPa bulk, and a La3Ni2O7:La3Al2O7 heterostructure) via first-principles calculations and large-scale dynamical cluster quantum Monte Carlo (DQMC) simulations on a two-orbital bilayer model. It reports that electron doping generically enhances s±-wave pairing superconductivity, with the heterostructure yielding the highest Tc in the underdoped regime, and attributes this to an inter-orbital cooperative mechanism in which d_z2 pairing induces d_x2-y2 pairing.

Significance. If the reported Tc enhancement and heterostructure ranking survive scrutiny, the work supplies a concrete theoretical route to higher-Tc electron-doped nickelates, complementing the extensive literature on hole-doped RP nickelates and offering falsifiable predictions for future experiments. The use of first-principles parameters plus large-scale DQMC is a standard and reproducible approach for this class of materials.

major comments (1)
  1. The central claim that electron doping produces a robust increase in s± Tc (and that the heterostructure ranks highest) rests on DQMC results whose sensitivity to cluster size is not demonstrated. The DCA approximation on a finite cluster plus self-consistent bath can distort the momentum structure of sign-changing s± pairing, particularly in the underdoped regime where correlations are strong; without explicit cluster-size scaling or convergence checks for the relative Tc ordering, the reported enhancement and system ranking remain vulnerable to finite-size artifacts.
minor comments (2)
  1. The abstract states that the heterostructure shows the highest Tc but does not quantify the Tc values or doping levels at which the comparison is made; adding these numbers would improve clarity.
  2. Notation for the two orbitals (d_x2-y2 and d_z2) and the precise definition of the bilayer hopping parameters should be stated explicitly in the model section to allow direct reproduction.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the positive assessment of its significance. We address the single major comment below and have revised the manuscript to incorporate additional checks that strengthen the central claims.

read point-by-point responses

  1. Referee: The central claim that electron doping produces a robust increase in s± Tc (and that the heterostructure ranks highest) rests on DQMC results whose sensitivity to cluster size is not demonstrated. The DCA approximation on a finite cluster plus self-consistent bath can distort the momentum structure of sign-changing s± pairing, particularly in the underdoped regime where correlations are strong; without explicit cluster-size scaling or convergence checks for the relative Tc ordering, the reported enhancement and system ranking remain vulnerable to finite-size artifacts.

    Authors: We appreciate the referee's emphasis on the need for explicit cluster-size convergence in DCA calculations, particularly for sign-changing s± pairing under strong correlations. Our original calculations employed a standard large cluster for the two-orbital bilayer model that captures the essential momentum structure and inter-orbital physics. To directly address this concern, the revised manuscript now includes new supplementary calculations performed on a smaller cluster size for direct comparison across all three systems (ambient-pressure bulk, pressurized bulk, and heterostructure). These additional results demonstrate that the enhancement of s±-wave Tc with electron doping persists, the heterostructure continues to exhibit the highest Tc in the underdoped regime, and the relative ordering among the three systems remains unchanged. The inter-orbital cooperative mechanism (d_z2-induced d_x2-y2 pairing) is robust and not sensitive to the cluster size within the range explored. We have added a dedicated paragraph in the Methods section and a new supplementary figure documenting these checks, along with a brief discussion of why the qualitative trends are expected to hold. revision: yes

Circularity Check

0 steps flagged

No circularity: simulation outputs are independent of inputs

full rationale

The paper constructs a two-orbital bilayer Hamiltonian from first-principles calculations for three systems (bulk La3Ni2O7 at ambient pressure and 15 GPa, plus the heterostructure), then applies dynamical cluster quantum Monte Carlo to compute pairing susceptibilities and Tc values as functions of electron doping. The reported generic enhancement of s±-wave superconductivity, the inter-orbital cooperative mechanism, and the heterostructure ranking are direct numerical outputs from solving the model; they are not presupposed by definition, obtained by fitting parameters to the target quantities, or reduced via load-bearing self-citations. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the two-orbital bilayer model for the three systems and the reliability of DQMC for extracting pairing instabilities; no new entities are postulated.

axioms (1)
  • domain assumption The two-orbital bilayer model sufficiently describes the low-energy physics of electron-doped La3Ni2O7.
    Invoked to model bulk at ambient pressure, 15 GPa, and the heterostructure.

pith-pipeline@v0.9.0 · 5796 in / 1322 out tokens · 41328 ms · 2026-05-21T08:05:19.473038+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

67 extracted references · 67 canonical work pages · 1 internal anchor

  1. [1]

    J. G. Bednorz and K. A. M¨ uller, Possible high T c superconductivity in the Ba-La-Cu-O system, Zeitschrift f¨ ur Physik B Condensed Matter64, 189 (1986)

    work page 1986

  2. [2]

    C. C. Tsuei and J. R. Kirtley, Pairing symmetry in cuprate superconductors, Rev. Mod. Phys.72, 969 (2000)

    work page 2000

  3. [3]

    Damascelli, Z

    A. Damascelli, Z. Hussain, and Z.-X. Shen, Angle- resolved photoemission studies of the cuprate superconductors, Rev. Mod. Phys.75, 473 (2003)

    work page 2003

  4. [4]

    L. Deng, T. Habamahoro, A. Safezoddeh, B. Karki, S. Kazibwe, D. J. Schulze, Z. Wu, M. Julian, R. P. Prasankumar, H. Zhou, J. S. Smith, P. R. Hosur, and C.-W. Chu, Ambient-pressure 151 K superconductivity in HgBa2Ca2Cu3O8+δ via pressure quench, Proceedings of the National Academy of Sciences123(2026)

    work page 2026

  5. [5]

    J. M, G. A Conde, G. C Falcony, and S. V, Tl-based superconductors for high-current, high-field applications, Superconductor Science and Technology9, 427 (1996)

    work page 1996

  6. [6]

    Schilling, M

    A. Schilling, M. Cantoni, J. D. Guo, and H. R. Ott, Superconductivity above 130 K in the Hg–Ba–Ca–Cu–O system, Nature363, 1476 (1993)

    work page 1993

  7. [7]

    Kawashima, Y

    T. Kawashima, Y. Matsui, and M. E. Takayama, New oxycarbonate superconductors (Cu0.5C0.5)Ba2Can−1CunO2n+3 (n= 3,4) prepared at high pressure, Physica C: Superconductivity224, 69 (1994)

    work page 1994

  8. [9]

    P. W. Anderson, The resonating valence bond state in 6 la2cuo4 and superconductivity, science235, 1196 (1987)

    work page 1987

  9. [10]

    Attfield, A

    J. Attfield, A. Kharlanov, and J. McAllister, Cation effects in doped la2cuo4 superconductors, Nature394, 157 (1998)

    work page 1998

  10. [11]

    Takagi, S

    H. Takagi, S. Uchida, and Y. Tokura, Superconductivity produced by electron doping in CuO 2-layered compounds, Phys. Rev. Lett.62, 1197 (1989)

    work page 1989

  11. [12]

    Smith, A

    M. Smith, A. Manthiram, J. Zhou, J. Goodenough, and J. Markert, Electron-doped superconductivity at 40 k in the infinite-layer compound sr1–yndycu02, nature351, 549 (1991)

    work page 1991

  12. [13]

    Ikeda, Y

    A. Ikeda, Y. Krockenberger, and H. Yamamoto, Molecular beam epitaxy of electron-doped infinite-layer ca1−xRxcuo2 thin films, Phys. Rev. Mater.3, 064803 (2019)

    work page 2019

  13. [14]

    S.I, (2) non-interacting band structures and density distribution in Section

    See Supplementary Material athttp://link....for: (1) further details on the methodology in Section. S.I, (2) non-interacting band structures and density distribution in Section. S.II, and (3) a more detailed analysis of the temperature evolution of the eigenvectors forN c = 1×2 in Section. S.III

    work page

  14. [15]

    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, Natrue 572, 624 (2019)

    work page 2019

  15. [16]

    S. Zeng, C. Li, L. E. Chow, Y. Cao, Z. Zhang, C. S. Tang, X. Yin, Z. S. Lim, J. Hu, P. Yang, and A. Ariando, Superconductivity in infinite-layer nickelate la1−xca xnio2 thin films, Science Advances8, eabl9927 (2022)

    work page 2022

  16. [17]

    Wenjie, J

    S. Wenjie, J. Zhicheng, X. Chengliang, H. Bo, Y. Shengjun, W. Maosen, L. Yueying, L. Hongquan, D. Jianyang, L. Jiayu, L. Zhengtai, L. Jishan, C. Hanghui, S. Dawei, and N. Yuefeng, Electronic structure of superconducting infinite-layer lanthanum nickelates, Science Advances11, eadr5116 (2025)

    work page 2025

  17. [18]

    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, Natrue621, 493 (2023)

    work page 2023

  18. [19]

    Zhang, D

    Y. Zhang, D. Su, Y. Huang, Z. Shan, H. Sun, M. Huo, K. Ye, J. Zhang, Z. Yang, Y. Xu, Y. Su, R. Li, M. Smidman, M. Wang, L. Jiao, and H. Yuan, High- temperature superconductivity with zero resistance and strange-metal behaviour in La 3Ni2O7−δ, Natrue Physics 20, 1269 (2024)

    work page 2024

  19. [20]

    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. X14, 011040 (2024)

    work page 2024

  20. [21]

    Zhang, C

    M. Zhang, C. Pei, Q. Wang, Y. Zhao, C. Li, W. Cao, S. Zhu, J. Wu, and Y. Qi, Effects of pressure and doping on Ruddlesden-Popper phases La n+1NinO3n+1, Journal of Materials Science and Technology185, 147 (2024)

    work page 2024

  21. [22]

    N. Wang, G. Wang, X. Shen, J. Hou, J. Luo, X. Ma, H. Yang, L. Shi, J. Dou, J. Feng, J. Yang, Y. Shi, Z. Ren, H. Ma, P. Yang, Z. Liu, Y. Liu, H. Zhang, X. Dong, Y. Wang, K. Jiang, J. Hu, S. Nagasaki, K. Kitagawa, S. Calder, J. Yan, J. Sun, B. Wang, R. Zhou, Y. Uwatoko, and J. Cheng, Bulk high-temperature superconductivity in pressurized tetragonal La 2PrNi...

    work page 2024

  22. [23]

    Y. Zhu, D. Peng, E. Zhang, B. Pan, X. Chen, L. Chen, H. Ren, F. Liu, Y. Hao, N. Li, Z. Xing, F. Lan, J. Han, J. Wang, D. Jia, H. Wo, Y. Gu, Y. Gu, L. Ji, W. Wang, H. Gou, Y. Shen, T. Ying, X. Chen, W. Yang, H. Cao, C. Zheng, Q. Zeng, J.-g. Guo, and J. Zhao, Superconductivity in pressurized trilayer La 4Ni3O10−δ single crystals, Natrue631, 521 (2024)

    work page 2024

  23. [24]

    Zhang, C

    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, Z. Li, J. Zhao, Y. Chen, C. Jin, H. Guo, C. Wu, F. Yang, Q. Zeng, S. Yan, L. Yang, and Y. Qi, Superconductivity in Trilayer Nickelate La4Ni3O10 under Pressure, Phys. Rev. X15, 021005 (2025)

    work page 2025

  24. [25]

    Li, Y.-J

    Q. Li, Y.-J. Zhang, Z.-N. Xiang, Y. Zhang, X. Zhu, and H.-H. Wen, Signature of Superconductivity in Pressurized La 4Ni3O10, Chinese Physics Letters41, 017401 (2024)

    work page 2024

  25. [26]

    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 in Sr-doped La 3Ni2O7 thin films, Nature Materials24, 1756 (2025)

    work page 2025

  26. [27]

    Y. Wang, K. Jiang, J. Ying, T. Wu, J. Cheng, J. Hu, and X. Chen, Recent progress in nickelate superconductors, National Science Review12, nwaf373 (2025)

    work page 2025

  27. [28]

    Y. Liu, B. Y. Wang, J. Li, Y. Tarn, L. Bhatt, M. Colletta, Y.-M. Wu, C.-T. Kuo, J.-S. Lee, B. H. Goodge, D. A. Muller, Z.-X. Shen, S. Raghu, H. Y. Hwang, and Y. Yu, A superconducting half-dome in bilayer nickelates, arXiv:2603.12196

    work page arXiv

  28. [29]

    Nomura, M

    Y. Nomura, M. Hirayama, T. Tadano, Y. Yoshimoto, K. Nakamura, and R. Arita, Formation of a two- dimensional single-component correlated electron system and band engineering in the nickelate superconductor ndnio2, Phys. Rev. B100, 205138 (2019)

    work page 2019

  29. [30]

    Y. Gu, S. Zhu, X. Wang, J. Hu, and H. Chen, A substantial hybridization between correlated ni-d orbital and itinerant electrons in infinite-layer nickelates, Communications Physics3, 84 (2020)

    work page 2020

  30. [31]

    You, Interstitialsstates and chemical pressure as key drivers of enhanced electron-phonon coupling in infinite-layer nickelates, Phys

    J.-Y. You, Interstitialsstates and chemical pressure as key drivers of enhanced electron-phonon coupling in infinite-layer nickelates, Phys. Rev. B113, 064510 (2026)

    work page 2026

  31. [32]

    C. Deng, M. Kitatani, G. Jiang, S. Guo, N. Witt, A. Zhang, W. Wu, M. Jiang, K. Held, and L. Si, Heterostructuring as gateway to electron doping of nickelate superconductors (2026), under preparation

    work page 2026

  32. [38]

    Blaha, K

    P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, and J. Luitz, Wien2k: An augmented plane wave plus local 7 orbitals program for calculating crystal properties (2001)

    work page 2001

  33. [47]

    J.-H. Ji, C. Lu, Z.-Y. Shao, Z. Pan, F. Yang, and C. Wu, Strong-coupling study of the pairing mechanism in pressurized La 3Ni2O7, Phys. Rev. B112, 214515 (2025)

    work page 2025

  34. [48]

    A Unified Understanding of the Experimental Controlling of the T$_\text{c}$ of La$_3$Ni$_2$O$_7$

    Z. Chen, J.-H. Ji, Y.-B. Liu, M. Zhang, and F. Yang, A Unified Understanding of the Experimental Controlling of the T c of La3Ni2O7, arXiv:2603.14519

    work page internal anchor Pith review Pith/arXiv arXiv

  35. [49]

    T. A. Maier, M. Jarrell, T. C. Schulthess, P. R. C. Kent, and J. B. White, Systematic Study ofd-Wave Superconductivity in the 2D Repulsive Hubbard Model, Phys. Rev. Lett.95, 237001 (2005)

    work page 2005

  36. [50]

    Yang, G.-M

    Y.-F. Yang, G.-M. Zhang, and F.-C. Zhang, Interlayer valence bonds and two-component theory for high-T c superconductivity of La 3Ni2O7 under pressure, Phys. Rev. B108, L201108 (2023)

    work page 2023

  37. [51]

    C. Lu, Z. Pan, F. Yang, and C. Wu, Interlayer- Coupling-Driven High-Temperature Superconductivity in La 3Ni2O7 under Pressure, Phys. Rev. Lett.132, 146002 (2024)

    work page 2024

  38. [52]

    Z.-Y. Shao, C. Lu, M. Liu, Y.-B. Liu, Z. Pan, C. Wu, and F. Yang, Pairing withoutγ-Pocket in the La 3Ni2O7 Thin Film, arXiv:2507.20287

    work page arXiv

  39. [59]

    Shi-cong, Y

    M. Shi-cong, Y. yuan. Zheng, and W. W´ u, Intertwined Electron Pairing in the Bilayer Two-orbital Kanamori-Hubbard Model: a Unified Picture of Two Superconductivities in La 3Ni2O7, arXiv:2508.04554

    work page arXiv

  40. [60]

    N. P. Armitage, P. Fournier, and R. L. Greene, Progress and perspectives on electron-doped cuprates, Rev. Mod. Phys.82, 2421 (2010)

    work page 2010

  41. [61]

    Kitatani, L

    M. Kitatani, L. Si, O. Janson, R. Arita, Z. Zhong, and K. Held, Nickelate superconductors—a renaissance of the one-band hubbard model, npj Quantum Materials5, 59 (2020)

    work page 2020

  42. [62]

    Kitatani, L

    M. Kitatani, L. Si, P. Worm, J. M. Tomczak, R. Arita, and K. Held, Optimizing superconductivity: From cuprates via nickelates to palladates, Phys. Rev. Lett. 130, 166002 (2023)

    work page 2023

  43. [63]

    L. Si, E. Jacob, W. Wu, A. Hausoel, J. Krsnik, P. Worm, S. Di Cataldo, O. Janson, and K. Held, Closing in on possible scenarios for infinite-layer nickelates: Comparison of dynamical mean-field theory with angular-resolved photoemission spectroscopy, Phys. Rev. Res.6, 043104 (2024)

    work page 2024

  44. [64]

    Y. Gao, W. Wu, Z. Liu, K. Held, and L. Si, Topotactical hydrogen induced single-bandd-wave superconductivity in la2nio4, Phys. Rev. Lett.135, 026002 (2025). Supplementary material: Enhanceds ±-wave superconductivity in electron-doped La 3Ni2O7 Xun Liu ,1 Chao Deng ,2 Wenfeng Wu ,2 Liang Si ,2, 3, 4, 5 and Mi Jiang 1, 6 1Institute for Quantum Science, Scho...

    work page 2025

  45. [65]

    S1 used in this work are derived from first-principles calculations based on density functional theory (DFT) [1–4]

    Parameters from DFT calculations The tight-binding parameters shown in Table. S1 used in this work are derived from first-principles calculations based on density functional theory (DFT) [1–4]. DFT- level structural relaxations and electronic structure calculations were performed using the PAW [5] method implemented in VASP and the FP-(L)APW method implem...

    work page

  46. [66]

    As a celebrated many-body numerical approach, DCA accesses the thermodynamic limit observables by self-consistently embedding a finite cluster in a mean-field bath [9, 10]

    Dynamical cluster approximation (DCA) The bilayer two-orbital model is solved numerically using the dynamical cluster approximation (DCA) in combination with the continuous-time auxiliary- field (CT-AUX) quantum Monte Carlo (QMC) cluster solver [9–12]. As a celebrated many-body numerical approach, DCA accesses the thermodynamic limit observables by self-c...

    work page

  47. [67]

    Bethe-Salpeter equation (BSE) The superconducting properties can be studied by solving the Bethe-Salpeter equation (BSE) in its 2 eigenvalue form in the particle-particle channel [13, 14] − T Nc X K′ Γpp(K, K′)¯χpp 0 (K ′)ϕα(K ′) =λ α(T)ϕ α(K) (1) where Γ pp(K, K′) denotes the irreducible particle- particle vertex of the effective cluster problem, with K=...

    work page

  48. [68]

    Hohenberg and W

    P. Hohenberg and W. Kohn, Inhomogeneous Electron Gas, Phys. Rev.136, B864 (1964)

    work page 1964

  49. [69]

    Kohn and L

    W. Kohn and L. J. Sham, Self-Consistent Equations Including Exchange and Correlation Effects, Phys. Rev. 140, A1133 (1965)

    work page 1965

  50. [70]

    Kresse and J

    G. Kresse and J. Furthm¨ uller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Computational Materials Science 6, 15 (1996)

    work page 1996

  51. [71]

    Kresse and J

    G. Kresse and J. Furthm¨ uller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B54, 11169 (1996)

    work page 1996

  52. [72]

    P. E. Bl¨ ochl, Projector augmented-wave method, Phys. Rev. B50, 17953 (1994)

    work page 1994

  53. [73]

    Blaha, K

    P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, and J. Luitz, Wien2k: An augmented plane wave plus local orbitals program for calculating crystal properties (2001)

    work page 2001

  54. [74]

    Schwarz, P

    K. Schwarz, P. Blaha, and G. Madsen, Electronic structure calculations of solids using the WIEN2k package for material sciences, Computer Physics Communications147, 71 (2002), proceedings of the Europhysics Conference on Computational Physics Computational Modeling and Simulation of Complex Systems

    work page 2002

  55. [75]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77, 3865 (1996)

    work page 1996

  56. [76]

    M. H. Hettler, A. N. Tahvildar-Zadeh, M. Jarrell, T. Pruschke, and H. R. Krishnamurthy, Nonlocal dynamical correlations of strongly interacting electron systems, Phys. Rev. B58, R7475 (1998)

    work page 1998

  57. [77]

    Maier, M

    T. Maier, M. Jarrell, T. Pruschke, and M. H. Hettler, Quantum cluster theories, Rev. Mod. Phys.77, 1027 (2005)

    work page 2005

  58. [78]

    U. R. H¨ ahner, G. Alvarez, T. A. Maier, R. Solc` a, P. Staar, M. S. Summers, and T. C. Schulthess, DCA++: A software framework to solve correlated electron problems with modern quantum cluster methods, Computer Physics Communications246, 106709 (2020)

    work page 2020

  59. [79]

    E. Gull, P. Werner, O. Parcollet, and M. Troyer, Continuous-time auxiliary-field monte carlo for quantum impurity models, Europhysics Letters82, 57003 (2008)

    work page 2008

  60. [80]

    T. A. Maier, M. S. Jarrell, and D. J. Scalapino, Structure of the pairing interaction in the two-dimensional Hubbard model, Phys. Rev. Lett.96, 047005 (2006)

    work page 2006

  61. [81]

    D. J. Scalapino,Handbook of High-Temperature Superconductivity: Theory and Experiment(Springer, New York, NY, 2007) pp. 495–526

    work page 2007

  62. [82]

    T. A. Maier and D. J. Scalapino, Pairfield fluctuations of a 2D Hubbard model, npj Quantum Materials4, 1 (2019)

    work page 2019

  63. [83]

    D. J. Scalapino, Pair Tunneling as a Probe of Fluctuations in Superconductors, Phys. Rev. Lett.24, 1052 (1970)

    work page 1970

  64. [84]

    Wu and A.-M.-S

    W. Wu and A.-M.-S. Tremblay,d-wave superconductivity in the frustrated two-dimensional periodic Anderson model, Phys. Rev. X5, 011019 (2015)

    work page 2015

  65. [85]

    Zheng and W

    Y.-Y. Zheng and W. W´ u,s ±-wave superconductivity in the bilayer two-orbital Hubbard model, Phys. Rev. B 111, 035108 (2025)

    work page 2025

  66. [86]

    T. A. Maier, P. Doak, L.-F. Lin, Y. Zhang, A. Moreo, and E. Dagotto, Interlayer pairing in bilayer nickelates , npj Quantum Materials11, 19 (2026)

    work page 2026

  67. [87]

    Jarrell, T

    M. Jarrell, T. Maier, C. Huscroft, and S. Moukouri, Quantum Monte Carlo algorithm for nonlocal corrections to the dynamical mean-field approximation, Phys. Rev. B64, 195130 (2001)

    work page 2001