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The 1313 phase of La3Ni2O7 is a degraded superconductor: pairing lives in its trilayer subsystems with s± symmetry, while a Mott-like single-layer spacer and hole doping suppress Tc to 3.6 K, so the genuine high-Tc phase is the 2222 phase.

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2026-08-02 15:39 UTC pith:7JULXV4W

load-bearing objection Solid DFT+DMFT/RPA study of 1313 La3Ni2O7 derailed by an internal inconsistency in the Josephson Tc-suppression formula. the 3 major comments →

arxiv 2604.21533 v2 pith:7JULXV4W submitted 2026-04-23 cond-mat.supr-con cond-mat.mtrl-scicond-mat.str-el

Pairing mechanism and superconductivity in 1313 phase La₃Ni₂O₇

Cui-Qun Chen , Ming Zhang , Fan Yang , Dao-Xin Yao This is my paper
classification cond-mat.supr-con cond-mat.mtrl-scicond-mat.str-el
keywords La3Ni2O7 1313 phasenickelate superconductivityDFT+DMFTrandom phase approximations±-wave pairinginterlayer Josephson couplingRuddlesden-Popper nickelateshole doping
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper argues that superconductivity in the 1313 phase of La3Ni2O7 lives almost entirely in its trilayer (TL) subsystems, which pair via spin fluctuations into an s±-wave state; the single-layer (SL) subsystems are nearly insulating bad metals and cannot host pairing. It claims that two things suppress the critical temperature to about 3.6 K compared with bulk La4Ni3O10: the TL subsystem is hole-doped, which weakens the pairing eigenvalue, and the SL subsystem acts as a normal-metal spacer that weakens interlayer phase coherence through a Josephson junction. From this, the authors conclude that the genuine high-Tc phase in the La3Ni2O7 family is the 2222 bilayer structure, not the 1313 phase, consistent with thin-film experiments. A careful reader would care because it assigns a concrete microscopic role to each layer in a hybrid Ruddlesden-Popper nickelate and gives a design rule: build superconductivity from strongly coupled like layers, not spacers.

Core claim

Using DFT+DMFT, the paper finds that the SL subsystem behaves as a nearly insulating bad metal with Mott physics in the dz2 orbital, while the TL subsystem is a correlated metal. From a DMFT-renormalized two-orbital model of the TL, RPA spin-fluctuation calculations yield an s±-wave pairing state whose leading nesting vector connects an electron pocket near Γ with a hole pocket near M. The TL's Ni-eg occupancy is reduced by about 0.17 electrons relative to bulk La4Ni3O10, and RPA shows this hole doping lowers the pairing eigenvalue. The paper further proposes that the SL subsystem forms an S-N-S Josephson junction between adjacent TL subsystems, and that the extremely small inter-trilayer tu

What carries the argument

Two computational frameworks: DFT+DMFT for correlated electronic structure, yielding a renormalized trilayer two-orbital tight-binding model with inter-trilayer hopping t_z^TL ≈ 10⁻⁴ eV, and multi-orbital RPA for pairing, which computes spin susceptibilities and pairing eigenvalues. The central identity is the s±-wave pairing mediated by spin fluctuations, with nesting between the ε and γ Fermi pockets, and the suppression mechanism is the Josephson-junction formula Tc ≈ (ρ0/π) ln(32/η), where η is the interlayer Josephson coupling strength proportional to t_z².

Load-bearing premise

The load-bearing premise is that the imported S-N-S Josephson-junction formula, Eq. (4), correctly describes how interlayer coupling controls the global Tc in this system; the paper uses it to conclude that weaker coupling (smaller η) suppresses Tc, even though the displayed formula increases as η decreases, so if the coupling-dependence runs the other way this suppression factor loses quantitative support.

What would settle it

An experiment that measures the c-axis Josephson critical current of 1313 La3Ni2O7 under pressure—or a calculation that derives Tc from the inter-trilayer tunneling without importing Eq. (4)—would settle whether the SL spacer really suppresses Tc; if weaker interlayer coupling yields higher Tc, the paper's second suppression factor is wrong.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • The SL subsystem is not a superconductor but a Mott-like bad metal; any superconductivity in 1313 La3Ni2O7 must be assigned to the TL subsystem.
  • The TL pairing symmetry is s±, with the strongest gap on the ε and γ pockets connected by the nesting vector Q; this mirrors bulk La4Ni3O10.
  • Hole doping the TL subsystem (relative to n=4) decreases the RPA pairing eigenvalue and therefore lowers Tc; restoring filling toward n=4 should strengthen pairing.
  • The interlayer Josephson coupling across the SL spacer governs global phase coherence, so the SL is detrimental in two independent ways—electronically and as a weak link.
  • The 2222 phase, with strong pairing and strong interlayer coherence, is the genuine high-Tc phase in the La3Ni2O7 family; 1313 films should not show intrinsic superconductivity.

Where Pith is reading between the lines

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

  • A direct doping experiment that fills the TL hole pocket toward n=4 in 1313 La3Ni2O7 would test the hole-doping suppressor: if Tc rises substantially, the pairing-strength argument is confirmed; if not, the Josephson suppression dominates.
  • If the Josephson-junction formula's η-dependence is read literally, weaker coupling (smaller η) would raise Tc, the opposite of the paper's claim; resolving this requires a microscopic derivation of Eq. (4) for this layered system or a measurement of the c-axis phase stiffness.
  • The same SL-spacer logic should apply to other hybrid RP nickelates such as 1212 La5Ni3O11; the paper's design rule implies that replacing the spacer by a metallic layer or reducing the number of spacer layers should enhance Tc.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The manuscript investigates the 1313 polymorph of La3Ni2O7 using DFT+DMFT and RPA. It reports that the single-layer (SL) subsystem is a nearly insulating bad metal with strong Mott-like correlations, while the trilayer (TL) subsystem is metallic. From a DMFT-renormalized TL two-orbital model, the RPA spin-fluctuation calculation yields an s±-wave pairing state. The paper attributes the low experimental Tc ≈ 3.6 K relative to bulk La4Ni3O10 to two factors: hole doping of the TL subsystem, which weakens the pairing eigenvalue, and weak interlayer Josephson coupling through the SL subsystem, which suppresses global phase coherence. It concludes that the genuine high-Tc phase in the La3Ni2O7 family is the 2222 phase rather than the 1313 phase.

Significance. If the central claims hold, the paper is a useful contribution to the ongoing debate on the superconducting mechanism in hybrid Ruddlesden-Popper nickelates. The DFT+DMFT layer-resolved electronic structure and the RPA pairing calculation are concrete, and the conclusion that SC resides in the TL subsystem with s± symmetry is consistent with a growing body of experimental work on thin films and the 1212/1313/2222 comparison. The paper also provides tabulated tight-binding parameters and an explicit doping trend, which are falsifiable. However, the quantitative Tc-suppression argument relies on Eq. (4), and that equation as written has an internal sign inconsistency with the text. This flaw affects one of the two key factors behind the paper's main conclusion and must be corrected before the manuscript can be accepted.

major comments (3)
  1. [§5, Eq. (4) and Fig. 5(d)] The displayed formula Tc ≈ (ρ0/π) ln(32/η) predicts a higher Tc for smaller η. For the authors' estimates, η ≈ 1e-8 (1313) gives ln(32e8) ≈ 21.9, while η ≈ 1e-4 (bulk La4Ni3O10) gives ln(32e4) ≈ 12.7. Thus Eq. (4) says the weaker-coupled 1313 system has the higher Tc, which is the opposite of the text's claim that 'the bulk Tc of 1313 is lower than that of bulk La4Ni3O10'. This is not a minor wording issue: the second suppression factor—weak interlayer Josephson coupling through the SL subsystem—is quantitatively unsupported as written. The authors should re-derive Eq. (4) from Ref. [54] and correct the formula, the sign, the figure, or the interpretation, whichever is appropriate.
  2. [§5, around Eq. (4)] The application of Eq. (4), which is taken from a study of quantum 3D Josephson junction arrays, to an S-N-S stack with a nearly Mott-insulating spacer is not justified without a microscopic derivation. The paper asserts η ∝ t_z^2 without derivation, and the SL subsystem is described as having a suppressed spectral function near the Fermi level and no well-defined quasiparticles. Treating such a layer as a normal-metal weak link requires a model of tunneling through a correlated insulator. The authors should provide a derivation of the Josephson coupling for this specific heterostructure or explicitly state the limits of the analogy. Without this, the second key factor remains a heuristic.
  3. [Conclusion section] The final claim that 'the genuine high-Tc phase in La3Ni2O7 family is the 2222 bilayer structure' goes beyond the calculations reported here. The paper does not compute the pairing strength or phase stiffness for 2222 La3Ni2O7; the evidence is indirect (comparative η estimates and citations to thin-film experiments). While this may be a plausible conclusion, it should be presented as an inference from the present study plus the cited experiments, not as a direct result of the RPA calculation. This is a matter of framing and does not require new calculations, but it should be adjusted.
minor comments (6)
  1. [Table II and text after Fig. 3] The mapping from the DMFT occupations in Table I to the TB-model filling n_TL = 3.9 is not immediately obvious. Table I reports per-Ni e_g occupations around 2.0, so the provenance of 3.9 should be stated explicitly to avoid confusion.
  2. [§2, Fig. 2 caption] The notation 'Im P(iωn)' is unusual; presumably this is the imaginary part of the self-energy Σ(iωn). Please use standard notation or define P.
  3. [Conclusion] Typo: 'recent experiments hves shown' should be 'have shown'.
  4. [Table II] The last row of Table II appears garbled in the manuscript (the '/s8722 /s48/...' characters). Please ensure the table is typeset correctly.
  5. [§4, Eq. (2)] The convention for the Hund's coupling and pair-hopping terms in Eq. (2) should be checked; the notation with σ, σ′ is not fully specified. In particular, the pair-hopping term appears only for spin species, and the relation U_eff = V_eff + 2J_eff^H should be stated with the standard Kanamori conventions.
  6. [§1, Introduction] The body text switches between Tc and T_c and between '1313 La3Ni2O7' and '1313 La3Ni2O7'; please standardize.

Circularity Check

0 steps flagged

No circularity found: central pairing and suppression claims are computed outputs of DFT+DMFT and RPA, not imposed inputs.

full rationale

The paper's central derivation chain is self-contained at the level tested here. The DFT+DMFT calculation outputs the layer-resolved electronic structure (SL nearly insulating, TL metallic), from which the paper constructs a renormalized TL two-orbital TB model; no superconducting Tc is used as input. The RPA calculation then produces the spin susceptibility, leading pairing eigenvalue, and s± gap structure without imposing the final symmetry. The comparison of pairing strength between the 1313 TL subsystem and bulk La4Ni3O10 is made by varying the TL filling, and the lower λ for the hole-doped case is an output of the same RPA machinery, not a fitted parameter. There are self-citations to prior same-group work (e.g., [38], [49]), but the load-bearing statements are independently supported by calculations in this paper: the doping trend appears in Fig. 5(b) of this paper, and the 1212 IJC analogy is explicitly a parallel mechanism, not the basis of the 1313 conclusion. The Josephson suppression estimate relies on Eq. (4) imported from ref. [54]; its quantitative sign appears questionable as displayed (smaller η gives larger ln(32/η), opposite to the text's argument), and the mapping η ∝ t_z^2 is asserted rather than derived. However, these are correctness concerns about an imported approximation, not a circular reduction: Eq. (4) is not the output being predicted, and no fitted Tc is renamed as a prediction. Under the rule that circularity requires a specific reduction, no step qualifies.

Axiom & Free-Parameter Ledger

6 free parameters · 5 axioms · 0 invented entities

The central prediction rests on the DFT+DMFT-derived TL two-orbital model plus RPA. Free choices include U_eff and J_H/U_eff, the TL filling, and the Josephson estimates η and ρ0 used in Eq. (4). No new physical entities are introduced. The SL-Mott behavior and TL doping are results of DMFT, not fitted parameters.

free parameters (6)
  • U_eff = 0.23 eV (varied up to U_c≈0.288 eV)
    Residual Hubbard interaction in the RPA calculation, renormalized by quasiparticle weight Z^2; pairing eigenvalues and critical U_c depend on it.
  • J_H/U_eff ratio = 1/4
    Hund's coupling set to U_eff/4; affects the spin susceptibility and pairing channel competition.
  • TL electron filling n_TL = 3.9
    Hole doping level relative to La4Ni3O10 (n=4); drives the claim that doping suppresses λ.
  • Inter-trilayer hopping t_z^TL = 1.12×10^-4 eV
    From the renormalized TB model; used to estimate η∝t_z^2≈10^-8 and hence the Josephson suppression.
  • Josephson estimate η = ~10^-8 (1313) and ~10^-4 (bulk)
    Chosen as proportional to t_z^2; enters Eq. (4) for global Tc. Not computed microscopically.
  • ρ0 = RPA ω_D e^{-1/λ}
    Approximated as the pairing temperature from RPA; not independently determined, used as the prefactor in Eq. (4).
axioms (5)
  • standard math RPA susceptibility formula χ=[I−χ0U]^{-1}χ0 and the BCS-like relation Tc ∝ ω_D e^{-1/λ} correctly describe the pairing instability.
    Used in Eq. (3) and the 'RPA study of the SC' section; these are standard many-body approximations.
  • domain assumption DFT+DMFT with the chosen impurity solver/double-counting gives quantitatively reliable layer-resolved spectral functions and occupations.
    The SL-Mott/TL-metal conclusion and Table I occupations depend on this; no cross-benchmark is given in the text.
  • domain assumption Spin fluctuations mediate pairing, and the leading RPA eigenvalue identifies the pairing symmetry.
    The s±-wave claim in Fig. 4(d) relies on this assumption; no other pairing mechanisms are compared.
  • ad hoc to paper The SL subsystem can be treated as a normal-metal weak link, and the global Tc is set by the Josephson-array formula Eq. (4).
    This is the second suppression factor; Eq. (4) is imported from [54] with ρ0 approximated by the RPA pairing temperature, and the SL weak-link picture is asserted.
  • ad hoc to paper Interlayer Josephson coupling strength η is proportional to t_z^2.
    Used to set η~10^-8 for 1313 and η~10^-4 for bulk; the scaling is stated, not derived.

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Cite this review

Pith. "Pith review of Pairing mechanism and superconductivity in 1313 phase La$_3$Ni$_2$O$_7$." pith.science (2026). https://pith.science/paper/7JULXV4W

@misc{pith2026260421533,
  author       = {Pith},
  title        = {Pith review of: Pairing mechanism and superconductivity in 1313 phase La$_3$Ni$_2$O$_7$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7JULXV4W}},
  note         = {Machine review of arXiv:2604.21533}
}
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read the original abstract

Recently, the observation of superconductivity (SC) with $T_c$ $\approx$ 3.6 K in the pressurized 1313 La$_3$Ni$_2$O$_7$ has attracted considerable interest. Here, we systematically investigate the electronic properties and superconducting mechanism of 1313 La$_3$Ni$_2$O$_7$ using density functional theory plus dynamical mean-field theory (DFT+DMFT) and random phase approximation (RPA). Our DFT+DMFT calculations reveal that the single-layer (SL) subsystem exhibits nearly insulating behavior, with the $d_{z^2}$ orbital showing Mott physics, while the trilayer (TL) subsystem remains metallic. This indicates that SC primarily resides in the TL subsystem, whose Ni-$e_g$ orbitals are found to be hole-doped relative to bulk La$_4$Ni$_3$O$_{10}$. Based on DFT+DMFT-derived low-energy Hamiltonian, RPA-based analysis yields an $s^{\pm}$-wave pairing symmetry within the TL subsystem. Importantly, we identify two key factors that contribute to the significant suppression of $T_c$ in 1313 La$_3$Ni$_2$O$_7$ compared to bulk La$_4$Ni$_3$O$_{10}$. First, the hole doping in the TL subsystem, as established by DMFT, leads to a decreased pairing strength, as confirmed by RPA calculations -- a trend resembling that in bulk La$_4$Ni$_3$O$_{10}$. Second, the SL subsystem acts as a bridge connecting adjacent superconducting TL subsystems, thereby forming an S-N-S Josephson junction. The resulting interlayer Josephson coupling governs the phase coherence between TL subsystems and further suppresses the global $T_c$. Combinedly, our findings suggest that the high-$T_c$ phase in the RP La$_3$Ni$_2$O$_7$ family should be attributed to the 2222 La$_3$Ni$_2$O$_7$ rather than the 1313 La$_3$Ni$_2$O$_7$.

Figures

Figures reproduced from arXiv: 2604.21533 by Cui-Qun Chen, Dao-Xin Yao, Fan Yang, Ming Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1. Crystal structures of high-pressure view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. DFT+DMFT calculated momentum-resolved spectral functions view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Distribution of the largest eigenvalue of the spin view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Band structures at different filling level view at source ↗

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Symmetry-Based Microscopic Theory of the Unconventional Pairing Mechanism in La$_5$Ni$_3$O$_{11}$

    cond-mat.supr-con 2026-07 conditional novelty 5.0

    La5Ni3O11 superconductivity is predicted to be a two-gap s± state in the bilayer subsystem, with the T_c reduction tied to a reduced interlayer-to-intralayer hopping ratio.

  2. Tunable Superconductivity in 1313-La$_3$Ni$_2$O$_7$: Suppressed under Compression and Possible $s^{\pm}$ Pairing under Tension

    cond-mat.supr-con 2026-06 unverdicted novelty 5.0

    RPA calculations predict strain-tunable superconductivity in 1313-La3Ni2O7 films, with s± pairing emerging under tensile strain when the γ pocket is optimally sized.

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