pith. sign in

arxiv: 2606.24126 · v1 · pith:U6VKKMHEnew · submitted 2026-06-23 · ❄️ cond-mat.str-el · cond-mat.mtrl-sci

Fluctuation exchange study on the electron-hole asymmetry of the superconductivity across 1/3 filling in the trilayer Hubbard model

Yushi Yamada , Masataka Kakoi , Masayuki Ochi , Kazuhiko Kuroki This is my paper

Pith reviewed 2026-06-25 23:16 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.mtrl-sci
keywords trilayer Hubbard modelfluctuation exchange approximationelectron-hole asymmetrysuperconductivity1/3 fillingband renormalizationinterlayer hopping
0
0 comments X

The pith

In the trilayer Hubbard model, superconductivity near 1/3 filling becomes electron-hole asymmetric for large U, favoring the hole-doped side due to asymmetric band renormalization.

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

The paper applies the fluctuation exchange approximation to the trilayer Hubbard model with large interlayer hoppings, where the bonding, nonbonding, and antibonding bands have limited overlap. Near 1/3 filling the bonding and nonbonding bands together approach half filling. For small onsite repulsion U the superconducting tendency remains roughly symmetric between electron and hole doping, consistent with a two-band near-half-filled picture. For large U the symmetry breaks, with superconductivity strengthened when electrons are removed from 1/3 filling. The authors trace the asymmetry to unequal renormalization of the three bands under strong interactions.

Core claim

Within the fluctuation exchange approximation applied to the trilayer Hubbard model, superconductivity near 1/3 filling is electron-hole symmetric at small U but becomes asymmetric at large U, with the hole-doped side (electrons removed from 1/3 filling) showing stronger pairing; this arises from the asymmetric renormalization of the bonding, nonbonding, and antibonding bands.

What carries the argument

Asymmetric renormalization of the bonding, nonbonding, and antibonding bands under large onsite U within the fluctuation exchange approximation.

If this is right

  • Superconducting transition temperatures or pairing strengths become higher when doping removes electrons from 1/3 filling than when it adds electrons.
  • The effective bandwidths and fillings of the bonding and nonbonding bands diverge from each other as U grows.
  • The antibonding band plays a secondary role in the pairing asymmetry at large U.
  • Electron-hole symmetry holds only in the weak-coupling regime where band renormalization remains symmetric.

Where Pith is reading between the lines

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

  • If the asymmetry survives in more exact methods, it could guide the search for higher-Tc superconductivity in multilayer materials by choosing the doping direction.
  • Varying the interlayer hopping strength might tune the size of the asymmetry, providing a testable prediction for model extensions.

Load-bearing premise

The fluctuation exchange approximation remains quantitatively reliable for large values of U in this three-band system with the chosen interlayer hoppings.

What would settle it

A calculation or measurement that finds stronger superconductivity on the electron-doped side of 1/3 filling, or equal strength on both sides, for large U in a trilayer geometry with similar interlayer hoppings.

Figures

Figures reproduced from arXiv: 2606.24126 by Kazuhiko Kuroki, Masataka Kakoi, Masayuki Ochi, Yushi Yamada.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Real-space structure of the trilayer square lattice. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: shows the eigenvalue λ obtained by solving the linearized Eliashberg equation (9) for various U/t⊥ and the band filling n. Here, the band filling is defined as the number of electrons per site, by which n = 2/3 corre￾sponds to 1/3-filling. Interestingly, while λ is symmetric about n = 2/3 for U/t⊥ = 2, λ in the electron-doped region is strongly suppressed for U/t⊥ = 4 and 6. This situation is reminiscent o… view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Band representations of the gap function ∆( [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Spectral functions and partial density of states (DOS) for (a) [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Orbital representations of the gap function for (a) [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a)–(d)Imaginary part of the 1111 component of the [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
read the original abstract

We study within the fluctuation exchange approximation the trilayer Hubbard model where three layers of the Hubbard model are coupled by large interlayer hoppings so that the overlap of the bonding, nonbonding, and antibonding bands is relatively small. We pay special attention to the band fillings close to 1/3, for which the bonding and nonbonding bands as a whole are close to half filling. For relatively small values of the onsite $U$, superconductivity roughly exhibits electron-hole symmetric behavior, as expected for a nearly half-filled two-band system. By contrast, an asymmetry appears when $U$ becomes large, where superconductivity is more favored in the hole-doped regime, i.e., in the regime where electrons are removed from 1/3 filling. We attribute this asymmetry to the asymmetric renormalization of the bonding, nonbonding, and antibonding bands when $U$ is large.

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

2 major / 1 minor

Summary. The manuscript studies superconductivity in the trilayer Hubbard model (with large interlayer hoppings yielding separated bonding/nonbonding/antibonding bands) near 1/3 filling using the fluctuation exchange (FLEX) approximation. It reports roughly electron-hole symmetric Tc behavior at small U, but an asymmetry at large U that favors the hole-doped side; this is attributed to asymmetric renormalization of the three bands.

Significance. If the FLEX results hold, the work supplies a concrete illustration of how strong-coupling effects can generate doping asymmetry via differential band renormalizations in a multi-band Hubbard system. This is potentially relevant to layered correlated materials. The study employs a standard diagrammatic method on a standard model, but the absence of non-perturbative benchmarks limits the strength of the conclusions.

major comments (2)
  1. [Abstract] Abstract and main results: the headline asymmetry is reported only for large U, yet the manuscript provides no comparison of FLEX results to non-perturbative methods (DMFT, QMC, or exact diagonalization) at the same parameters. Because FLEX is a perturbative resummation whose controlled regime is weak-to-intermediate coupling, and because the effective interaction strength approaches the bandwidth at large U, the reported band renormalizations and resulting Tc asymmetry rest on an uncontrolled extrapolation.
  2. [Abstract] Abstract: the mechanism is stated as 'asymmetric renormalization of the bonding, nonbonding, and antibonding bands,' but no quantitative measure (e.g., extracted quasiparticle weights, band shifts, or widths versus filling) is supplied to demonstrate that the renormalization is in fact asymmetric in the manner required to produce the claimed Tc asymmetry.
minor comments (1)
  1. [Abstract] The abstract would be clearer if it specified the numerical ranges used for 'relatively small' and 'large' values of U.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We respond point-by-point to the major comments below.

read point-by-point responses

  1. Referee: [Abstract] Abstract and main results: the headline asymmetry is reported only for large U, yet the manuscript provides no comparison of FLEX results to non-perturbative methods (DMFT, QMC, or exact diagonalization) at the same parameters. Because FLEX is a perturbative resummation whose controlled regime is weak-to-intermediate coupling, and because the effective interaction strength approaches the bandwidth at large U, the reported band renormalizations and resulting Tc asymmetry rest on an uncontrolled extrapolation.

    Authors: We acknowledge that FLEX is a perturbative method whose validity at large U (where U approaches the bandwidth) is not rigorously controlled. The trilayer model with the chosen interlayer hoppings makes non-perturbative benchmarks (DMFT, QMC, or ED) computationally demanding at the required system sizes and parameter points, which is why we employed FLEX as a standard diagrammatic approach for multi-band Hubbard superconductivity. In the revision we will add an explicit discussion of the approximation's regime of applicability and emphasize the qualitative character of the reported asymmetry. revision: partial

  2. Referee: [Abstract] Abstract: the mechanism is stated as 'asymmetric renormalization of the bonding, nonbonding, and antibonding bands,' but no quantitative measure (e.g., extracted quasiparticle weights, band shifts, or widths versus filling) is supplied to demonstrate that the renormalization is in fact asymmetric in the manner required to produce the claimed Tc asymmetry.

    Authors: We agree that explicit quantitative measures would make the claimed mechanism more transparent. Although the main text discusses the band renormalizations, we will add figures (or tables) in the revised manuscript that extract and plot quasiparticle weights, effective band shifts, and widths as functions of filling for representative U values, directly illustrating the asymmetry between the bonding, nonbonding, and antibonding bands. revision: yes

Circularity Check

0 steps flagged

No circularity; asymmetry is computed output of FLEX on standard model

full rationale

The paper applies the fluctuation exchange approximation to the trilayer Hubbard model and reports an electron-hole asymmetry in superconductivity that emerges at large U, attributed to band renormalizations. No quoted step defines a quantity in terms of itself, renames a fitted parameter as a prediction, or reduces the central claim to a self-citation chain. The derivation chain consists of standard diagrammatic equations whose outputs (Tc values and band shifts) are independent of the target asymmetry; the result is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the applicability of the fluctuation exchange approximation to the trilayer Hubbard model at large U and on the modeling choice of large interlayer hoppings that produce small band overlap.

axioms (1)
  • domain assumption The fluctuation exchange approximation accurately captures the superconducting instability in the trilayer Hubbard model for the U values studied.
    The method is invoked to obtain all reported results.

pith-pipeline@v0.9.1-grok · 5705 in / 1127 out tokens · 30173 ms · 2026-06-25T23:16:11.423695+00:00 · methodology

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

64 extracted references · 1 linked inside Pith

  1. [1]

    Kuroki, T

    K. Kuroki, T. Kimura, and R. Arita, High-temperature superconductivity in dimer array systems, Phys. Rev. B 66, 184508 (2002)

    2002

  2. [2]

    T. A. Maier and D. J. Scalapino, Pair structure and the pairing interaction in a bilayer Hubbard model for un- conventional superconductivity, Phys. Rev. B84, 180513 (2011)

    2011

  3. [3]

    Nakata, D

    M. Nakata, D. Ogura, H. Usui, and K. Kuroki, Finite- energy spin fluctuations as a pairing glue in systems with coexisting electron and hole bands, Phys. Rev. B95, 214509 (2017)

    2017

  4. [4]

    Nomura, M

    Y. Nomura, M. Kitatani, S. Sakai, and R. Arita, Strong- coupling high-T c superconductivity in doped correlated band insulators, Phys. Rev. B112, L020504 (2025)

    2025

  5. [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 superconductiv- ity near 80 K in a nickelate under high pressure, Nature (London)621, 493 (2023)

    2023

  6. [6]

    Hou, P.-T

    J. Hou, P.-T. Yang, Z.-Y. Liu, J.-Y. Li, P.-F. Shan, L. Ma, G. Wang, N.-N. Wang, H.-Z. Guo, J.-P. Sun, Y. Uwatoko, M. Wang, G.-M. Zhang, B.-S. Wang, and J.-G. Cheng, Emergence of High-Temperature Supercon- ducting Phase in Pressurized La 3Ni2O7 Crystals, Chin. Phys. Lett.40, 117302 (2023)

    2023

  7. [7]

    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 Polycrys- talline La3Ni2O7−δ, Phys. Rev. X14, 011040 (2024)

    2024

  8. [8]

    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. Smid- man, M. Wang, L. Jiao, and H. Yuan, High-temperature superconductivity with zero resistance and strange-metal behaviour in La 3Ni2O7−δ, Nat. Phys.20, 1269 (2024)

    2024

  9. [9]

    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...

    2024

  10. [10]

    F. Li, Z. Xing, D. Peng, J. Dou, N. Guo, L. Ma, Y. Zhang, L. Wang, J. Luo, J. Yang, J. Zhang, T. Chang, Y.-S. Chen, W. Cai, J. Cheng, Y. Wang, Y. Liu, T. Luo, N. Hi- rao, T. Matsuoka, H. Kadobayashi, Z. Zeng, Q. Zheng, R. Zhou, Q. Zeng, X. Tao, and J. Zhang, Bulk super- conductivity up to 96 K in pressurized nickelate single crystals, Nature (London)649, ...

    2026

  11. [11]

    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, Signa- tures of ambient pressure superconductivity in thin film La3Ni2O7, Nature (London)638, 935 (2025)

    2025

  12. [12]

    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 on- set above 40 K in (La,Pr)3Ni2O7 films, Nature (London) 640, 641 (2025)

    2025

  13. [13]

    G. Zhou, H. Wang, H. Huang, Y. Chen, F. Peng, W. Lv, Z. Nie, W. Wang, J.-F. Jia, Q.-K. Xue, and Z. Chen, Superconductivity onset above 60 K in ambient-pressure nickelate films, Natl. Sci. Rev.13, nwag151 (2026)

    2026

  14. [14]

    Z. Luo, X. Hu, M. Wang, W. W´ u, and D.-X. Yao, Bilayer Two-Orbital Model of La 3Ni2O7 under Pressure, Phys. Rev. Lett.131, 126001 (2023)

    2023

  15. [15]

    Q.-G. Yang, D. Wang, and Q.-H. Wang, Possibles ±- wave superconductivity in La3Ni2O7, Phys. Rev. B108, L140505 (2023)

    2023

  16. [16]

    Sakakibara, N

    H. Sakakibara, N. Kitamine, M. Ochi, and K. Kuroki, Possible HighT c Superconductivity in La 3Ni2O7 under High Pressure through Manifestation of a Nearly Half- Filled Bilayer Hubbard Model, Phys. Rev. Lett.132, 106002 (2024)

    2024

  17. [17]

    Christiansson, F

    V. Christiansson, F. Petocchi, and P. Werner, Correlated Electronic Structure of La 3Ni2O7 under Pressure, Phys. Rev. Lett.131, 206501 (2023)

    2023

  18. [18]

    Lechermann, J

    F. Lechermann, J. Gondolf, S. B¨ otzel, and I. M. Eremin, Electronic correlations and superconducting instability in La 3Ni2O7 under high pressure, Phys. Rev. B108, L201121 (2023)

    2023

  19. [19]

    Y. Shen, M. Qin, and G.-M. Zhang, Effective Bi-Layer Model Hamiltonian and Density-Matrix Renormaliza- tion Group Study for the High-T c Superconductivity in La3Ni2O7 under High Pressure, Chin. Phys. Lett.40, 127401 (2023)

    2023

  20. [20]

    Liu, J.-W

    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 La 3Ni2O7 under Pressure, Phys. Rev. Lett.131, 236002 (2023)

    2023

  21. [21]

    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)

    2024

  22. [22]

    Oh and Y.-H

    H. Oh and Y.-H. Zhang, Type-IIt−Jmodel and shared superexchange coupling from Hund’s rule in supercon- 9 ducting La3Ni2O7, Phys. Rev. B108, 174511 (2023)

    2023

  23. [23]

    Qu, D.-W

    X.-Z. Qu, D.-W. Qu, J. Chen, C. Wu, F. Yang, W. Li, and G. Su, Bilayert−J−J ⊥ Model and Magnetically Me- diated Pairing in the Pressurized Nickelate La 3Ni2O7, Phys. Rev. Lett.132, 036502 (2024)

    2024

  24. [24]

    Kaneko, H

    T. Kaneko, H. Sakakibara, M. Ochi, and K. Kuroki, Pair correlations in the two-orbital Hubbard ladder: Im- plications for superconductivity in the bilayer nickelate La3Ni2O7, Phys. Rev. B109, 045154 (2024)

    2024

  25. [25]

    Kakoi, T

    M. Kakoi, T. Kaneko, H. Sakakibara, M. Ochi, and K. Kuroki, Pair correlations of the hybridized orbitals in a ladder model for the bilayer nickelate La 3Ni2O7, Phys. Rev. B109, L201124 (2024)

    2024

  26. [26]

    Kaneko, M

    T. Kaneko, M. Kakoi, and K. Kuroki,t−Jmodel for strongly correlated two-orbital systems: Application to bilayer nickelate superconductors, Phys. Rev. B112, 075143 (2025)

    2025

  27. [27]

    Kamiyama, T

    S. Kamiyama, T. Kaneko, K. Kuroki, and M. Ochi, Opti- cal control of the crystal structure in the bilayer nickelate superconductor La3Ni2O7 via nonlinear phononics, Phys. Rev. B112, 094115 (2025)

    2025

  28. [28]

    Ushio, S

    K. Ushio, S. Kamiyama, Y. Hoshi, R. Mizuno, M. Ochi, K. Kuroki, and H. Sakakibara, Theoretical study on ambient-pressure superconductivity in La 3Ni2O7 thin films: Structural analysis, model construction, and ro- bustness ofs ±-wave pairing, Phys. Rev. B (2026)

    2026

  29. [29]

    R. Asai, R. Arita, T. Chida, R. Masuki, K. Kuroki, and T. Tadano, Finite-Temperatureab initioStructural Optimization of the Bilayer Nickelate Superconductor La3Ni2O7, arXiv:2512.08251

    arXiv

  30. [30]

    Watanabe, H

    H. Watanabe, H. Sakakibara, and K. Kuroki, Hi- erarchical structure of primary and hybridization- induced superconducting correlations in bilayer nicke- lates, arXiv:2603.13604

    arXiv

  31. [31]

    Sakakibara, M

    H. Sakakibara, M. Ochi, H. Nagata, Y. Ueki, H. Saku- rai, R. Matsumoto, K. Terashima, K. Hirose, H. Ohta, M. Kato, Y. Takano, and K. Kuroki, Theoretical analy- sis on the possibility of superconductivity in the trilayer Ruddlesden-Popper nickelate La 4Ni3O10 under pressure and its experimental examination: Comparison with La3Ni2O7, Phys. Rev. B109, 144511 (2024)

    2024

  32. [32]

    Li, Y.-J

    Q. Li, Y.-J. Zhang, Z.-N. Xiang, Y. Zhang, X. Zhu, and H.-H. Wen, Signature of Superconductivity in Pressur- ized La4Ni3O10, Chin. Phys. Lett.41(2024)

    2024

  33. [33]

    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, Superconduc- tivity in pressurized trilayer La4Ni3O10−δ single crystals, Nature (London)631, 531 (2024)

    2024

  34. [34]

    Nagata, H

    H. Nagata, H. Sakurai, Y. Ueki, K. Yamane, R. Mat- sumoto, K. Terashima, K. Hirose, H. Ohta, M. Kato, and Y. Takano, Pressure-Induced Superconductivity in La4Ni3O10+δ (δ= 0.04 and−0.01), J. Phys. Soc. Jpn. 93, 095003 (2024)

    2024

  35. [35]

    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)

    2025

  36. [36]

    Zhang, D

    E. Zhang, D. Peng, Y. Zhu, L. Chen, B. Cui, X. Wang, W. Wang, Q. Zeng, and J. Zhao, Bulk Superconductivity in Pressurized Trilayer Nickelate Pr4Ni3O10 Single Crys- tals, Phys. Rev. X15, 021008 (2025)

    2025

  37. [37]

    D. Peng, Y. Bian, Z. Xing, L. Chen, J. Cai, T. Luo, F. Lan, Y. Liu, Y. Zhu, E. Zhang, Z. Wang, Y. Sun, Y. Wang, X. Wang, C. Wang, Y. Yang, Y. Yang, H. Dong, H. Lou, Z. Zeng, Z. Zeng, M. Tian, J. Zhao, Q. Zeng, J. Zhang, and H.-k. Mao, Nearly Isotropic Upper Critical Field in Pressurized Trilayer Nickelate La4Ni3O10−δ, Phys. Rev. X16, 021008 (2026)

    2026

  38. [38]

    Tian, H.-T

    P.-F. Tian, H.-T. Ma, X. Ming, X.-J. Zheng, and H. Li, Effective model and electron correlations in trilayer nicke- late superconductor La4Ni3O10, J. Phys.: Condens. Mat- ter36, 355602 (2024)

    2024

  39. [39]

    Q. Qin, J. Wang, and Y. feng Yang, Frustrated supercon- ductivity and intrinsic reduction ofT c in trilayer nicke- late, Innov. Mater.2, 100102 (2024)

    2024

  40. [40]

    C.-Q. Chen, Z. Luo, M. Wang, W. W´ u, and D.-X. Yao, Trilayer multiorbital models of La4Ni3O10, Phys. Rev. B 110, 014503 (2024)

    2024

  41. [41]

    Huang and T

    J. Huang and T. Zhou, Interlayer pairing-induced par- tially gapped Fermi surface in trilayer La 4Ni3O10 super- conductors, Phys. Rev. B110, L060506 (2024)

    2024

  42. [42]

    Zhang, H

    M. Zhang, H. Sun, Y.-B. Liu, Q. Liu, W.-Q. Chen, and F. Yang,s ±-wave superconductivity in pressurized La4Ni3O10, Phys. Rev. B110, L180501 (2024)

    2024

  43. [43]

    LaBollita, J

    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. B109, 195151 (2024)

    2024

  44. [44]

    Zhang, H

    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. B111, 144502 (2025)

    2025

  45. [45]

    C. Lu, Z. Pan, F. Yang, and C. Wu, Superconductivity in La4Ni3O10 under pressure, Phys. Rev. B111, 134515 (2025)

    2025

  46. [46]

    Zheng and T

    S. Zheng and T. Zhou, Layer-resolved impurity states reveal competing pairing mechanisms in trilayer nickelate superconductor La 4Ni3O10, Phys. Rev. B113, 024504 (2026)

    2026

  47. [47]

    J. Chen, C. Xu, Q. Li, and W. Li, Magnetically medi- ated cross-layer pairing in pressurized trilayer nickelate La4Ni3O10, Sci. China Phys. Mech. Astron.69, 247413 (2026)

    2026

  48. [48]

    Arrigoni, Spin and charge excitations in a three-legs fermionic ladder: a renormalization-group study, Phys

    E. Arrigoni, Spin and charge excitations in a three-legs fermionic ladder: a renormalization-group study, Phys. Lett. A215, 91 (1996); Phase diagram of three fermionic chains: A renormalization-group study, Phys. Status So- lidi B195, 425 (1996)

    1996

  49. [49]

    M. Y. Kagan, S. Haas, and T. Rice, Phase diagram of three-leg ladders at strong coupling along the rungs, Physica C: Supercond.317-318, 185 (1999)

    1999

  50. [50]

    Yamada, T

    Y. Yamada, T. Kaneko, M. Kakoi, R. Ueda, and K. Kuroki, Pairing properties of correlated three-leg lad- ders with strong interchain couplings near 1/3 filling, arXiv:2604.17812

    Pith/arXiv arXiv

  51. [51]

    N. E. Bickers, D. J. Scalapino, and S. R. White, Con- serving Approximations for Strongly Correlated Electron Systems: Bethe-Salpeter Equation and Dynamics for the Two-Dimensional Hubbard Model, Phys. Rev. Lett.62, 961 (1989)

    1989

  52. [52]

    Dahm and L

    T. Dahm and L. Tewordt, Quasiparticle and Spin Exci- 10 tation Spectra in the Normal andd-Wave Superconduct- ing State of the Two-Dimensional Hubbard Model, Phys. Rev. Lett.74, 793 (1995)

    1995

  53. [53]

    Kimura, K

    T. Kimura, K. Kuroki, and H. Aoki, Correlation func- tions in the three-chain Hubbard ladder, Phys. Rev. B 54, R9608 (1996); Pairing Correlation in the Three-Leg Hubbard Ladder – Renormalization Group and Quantum Monte Carlo Studies, J. Phys. Soc. Jpn.67, 1377 (1998)

    1996

  54. [54]

    H.-H. Lin, L. Balents, and M. P. A. Fisher,N-chain Hub- bard model in weak coupling, Phys. Rev. B56, 6569 (1997)

    1997

  55. [55]

    Kuroki, T

    K. Kuroki, T. Higashida, and R. Arita, High-T c super- conductivity due to coexisting wide and narrow bands: A fluctuation exchange study of the Hubbard ladder as a test case, Phys. Rev. B72, 212509 (2005)

    2005

  56. [56]

    Mishra, D

    V. Mishra, D. J. Scalapino, and T. A. Maier, s±pairing near a Lifshitz transition, Sci. Rep.6, 32078 (2016)

    2016

  57. [57]

    T. A. Maier, V. Mishra, G. Balduzzi, and D. J. Scalapino, Effective pairing interaction in a system with an incipient band, Phys. Rev. B99, 140504 (2019)

    2019

  58. [58]

    Matsumoto, D

    K. Matsumoto, D. Ogura, and K. Kuroki, Strongly En- hanced Superconductivity Due to Finite Energy Spin Fluctuations Induced by an Incipient Band: A FLEX Study on the Bilayer Hubbard Model with Vertical and Diagonal Interlayer Hoppings, J. Phys. Soc. Jpn.89, 044709 (2020)

    2020

  59. [59]

    Kato and K

    D. Kato and K. Kuroki, Many-variable variational Monte Carlo study of superconductivity in two-band Hubbard models with an incipient band, Phys. Rev. Res.2, 023156 (2020)

    2020

  60. [60]

    Kobayashi, M

    K. Kobayashi, M. Okumura, S. Yamada, M. Machida, and H. Aoki, Superconductivity in repulsively interacting fermions on a diamond chain: Flat-band-induced pairing, Phys. Rev. B94, 214501 (2016)

    2016

  61. [61]

    T. Aida, K. Matsumoto, D. Ogura, M. Ochi, and K. Kuroki, Theoretical study of spin-fluctuation- mediated superconductivity in two-dimensional Hubbard models with an incipient flat band, Phys. Rev. B110, 054516 (2024)

    2024

  62. [62]

    Kakoi and K

    M. Kakoi and K. Kuroki, Spin-fluctuation-mediated chi- rald+id ′-wave superconductivity in theα–T3 lattice with an incipient flat band, Phys. Rev. B113, 165104 (2026)

    2026

  63. [63]

    A. J. Millis, S. Sachdev, and C. M. Varma, Inelastic scat- tering and pair breaking in anisotropic and isotropic su- perconductors, Phys. Rev. B37, 4975 (1988)

    1988

  64. [64]

    Kouchi, S

    T. Kouchi, S. Nishioka, K. Suzuki, M. Yashima, H. Mukuda, T. Kawashima, H. Tsuji, K. Kuroki, S. Miyasaka, and S. Tajima, Enhanced superconductiv- ity and moderate spin fluctuations suppressed at low en- ergies in heavily electron-doped La1111-based supercon- ductor, Phys. Rev. B105, 144510 (2022)

    2022