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Superconductivity in bilayer La3Ni2O7 emerges with zero resistance only after two density-wave orders are fully suppressed, from a T-linear strange-metal state at the Planckian limit.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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In clean La3Ni2O7 single crystals, pressure suppresses two density-wave orders and yields zero-resistance superconductivity from a Planckian T-linear strange metal.

T0 review reviewed 2026-07-30 challenge →

load-bearing objection Clean single-crystal anisotropic transport and a reproducible DW/SC phase diagram are the real advance; the Planckian α is a secondary, model-dependent add-on. the 4 major comments →

arxiv 2607.26990 v1 pith:XY6AXPRL submitted 2026-07-29 cond-mat.supr-con

Density-wave phases, anisotropic transport, and Planckian dissipation in single crystals of the superconductor La3Ni2O7

Zhehong Liu , Masamichi Nakajima , Markus Kriener , Shunsuke Kitou , Xiaowei Lyu , Chieko Terakura , Kosuke Karube , Ka Man Yip
show 9 more authors
Sorin Lazar Nobuto Nakanishi Keiko Shimada Akiko Kikkawa Yukako Fujishiro Xiuzhen Yu Taka-hisa Arima Yoshinori Tokura Yasujiro Taguchi
This is my paper
classification cond-mat.supr-con PACS 74.70.-b74.62.Fj74.25.F-71.45.Lr
keywords La3Ni2O7bilayer nickelatedensity-wave orderPlanckian dissipationstrange metalanisotropic transporthigh-pressure superconductivityRuddlesden-Popper
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 reading

This paper maps how charge and spin density-wave orders, anisotropic resistivity, and superconductivity evolve together under pressure in high-quality La3Ni2O7 single crystals. Using absolute in-plane and out-of-plane transport, it shows two distinct density-wave anomalies with opposite pressure trends, a sharp rise in low-temperature resistivity anisotropy across the orthorhombic-to-tetragonal transition, and superconductivity that appears only once those density-wave signatures are gone. Above Tc the normal-state resistivity is linear in temperature over a wide range, and the inferred scattering rate sits near the Planckian bound. The work supplies the missing quantitative transport backbone—absolute resistivities, anisotropy, and scattering rate—for a material whose superconductivity had been hard to pin down because of crystal quality and sample-to-sample scatter. A sympathetic reader cares because it places this nickelate in the same strange-metal family as other unconventional superconductors and ties the superconducting dome to the collapse of robust density-wave order.

Core claim

On oxygen-stoichiometric, stacking-fault-free La3Ni2O7 single crystals, high-pressure transport establishes a precise pressure–temperature phase diagram in which two density-wave anomalies (T1 and T2) have contrasting pressure dependences, the structural transition strongly enhances low-T resistivity and its anisotropy via modified density-wave order, and zero-resistance superconductivity emerges only near the boundary where both density-wave phases are fully suppressed. Above Tc the resistivity is T-linear over a wide range and the scattering rate falls in the Planckian regime, so robust density-wave correlations and Planckian dissipation are defining features of the material.

What carries the argument

The high-precision pressure–temperature transport phase diagram built from absolute in-plane (ρ_ab) and out-of-plane (ρ_c) resistivities—including Montgomery-method anisotropy—on large, homogeneous bilayer crystals free of oxygen vacancies and Ruddlesden–Popper intergrowths. That map resolves T1 and T2, tracks their suppression, and supplies the resistivity slope used to extract the Planckian coefficient α.

Load-bearing premise

The claim that scattering sits at the Planckian limit depends on converting the measured resistivity slope into a scattering rate with ambient-pressure Fermi-surface parameters scaled by a theoretical high-pressure bandwidth increase.

What would settle it

A high-pressure measurement of the Fermi surface and velocities (for example ARPES or quantum oscillations near 20 GPa) that, when inserted into the same multi-band Drude formula, yields a Planckian coefficient α far from order one, or cleaner crystals in which clear density-wave anomalies persist through a true zero-resistance superconducting state.

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

If this is right

  • Zero-resistance superconductivity in La3Ni2O7 is confined to the tetragonal side of the phase diagram after both density-wave anomalies disappear.
  • The normal state above Tc is a wide-range T-linear strange metal whose scattering rate is of order k_B T/ℏ.
  • The orthorhombic-to-tetragonal transition mainly boosts low-temperature transport anisotropy by changing density-wave order (possibly c-axis stacking), not by simple band hybridization alone.
  • Absolute resistivities and anisotropy values become reliable benchmarks for theory of bilayer nickelates under pressure.
  • Sample-to-sample pressure offsets can shift onsets, but the overall hierarchy—density waves first, then strange metal and superconductivity—is intrinsic.

Where Pith is reading between the lines

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

  • If density-wave fluctuations survive as the pairing glue after long-range order is gone, high-pressure inelastic probes should still see soft charge or spin modes inside the superconducting dome.
  • The large low-T anisotropy jump suggests interlayer decoupling analogous to stripe cuprates; c-axis coherence length or Josephson plasma data under pressure would test that analogy directly.
  • Reproducing α with pressure-tuned carrier density (rather than only bandwidth rescaling) would tighten or refute the Planckian assignment without new spectroscopies.
  • The same single-crystal protocol applied to related bilayer or trilayer nickelates should reveal whether Planckian strange metallicity is universal once density waves are suppressed.
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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

4 major / 6 minor

Summary. The manuscript reports high-pressure in-plane and out-of-plane resistivity on multiple high-quality La3Ni2O7 single crystals, establishing a P–T phase diagram that resolves two density-wave anomalies (T1, T2) with contrasting pressure dependences, a strong enhancement of low-T resistivity and anisotropy across the orthorhombic–tetragonal boundary near 8–10 GPa, and zero-resistance superconductivity that appears only after both DW features are suppressed. Above Tc at 18–20 GPa the ab-plane resistivity is T-linear from ~80–300 K with near-zero residual resistivity; using ambient-pressure ARPES Fermi-surface parameters (rescaled by a DFT-motivated ~20% bandwidth enhancement) the authors extract a Planckian coefficient α = 1.6 ± 0.4. Crystal quality is supported by synchrotron XRD (Am2m, no detectable O vacancies), STEM/EDS (no RP intergrowths), and multi-crystal reproducibility of the overall phase diagram.

Significance. Absolute resistivities, ρc/ρab anisotropy via the Montgomery method, and a multi-crystal transport phase diagram fill a genuine gap left by prior polycrystalline and small-crystal work on bilayer nickelates. The demonstration that zero-resistance SC onsets at the full suppression of both DW anomalies, together with a clean T-linear normal state, is a substantial and falsifiable experimental contribution. The crystal-quality documentation (Am2m charge order, stoichiometry, stacking-fault-free bilayers) and cross-sample comparison (including polycrystalline data) are particular strengths. If the phase-diagram and anisotropy results hold, they become reference data for theories of intertwined DW order and pairing in La3Ni2O7; the Planckian placement is secondary and more assumption-dependent.

major comments (4)
  1. [Supplementary: Estimation of the scattering rate; Fig. 4c,f; Abstract; Conclusion] Supplementary estimation of α (and Fig. 4c): α = 1.6 ± 0.4 is obtained from the measured dρab/dT by inserting ambient-pressure ARPES kF and vF for the α/β sheets (Yang et al.), multiplying vF by a ~20% enhancement taken from ambient-to-20 GPa DFT, and using bilayer spacing d = 10.26 Å in the multi-band Drude form of Bruin et al. No high-P Fermi-surface or mass data are provided. Because α ∝ Σi kFi vFi, a factor-of-two change in high-P sheet parameters (plausible across the ortho–tetra reconstruction) moves α well outside the order-1 window even though T-linear ρ is measured cleanly. The abstract and conclusion state that the scattering rate “falls within a regime of the Planckian limit” as a defining feature. Please (i) report a sensitivity band on α under reasonable variations of kF, vF, and n; (ii) separate the model-independent observation (T-linear ρ, small residual) from the model-d
  2. [Reproducibility and sample-dependent pressure response; Fig. 4b,d,e] Figs. 4b,d,e and main text (“slight sample-dependent response”): crystal 2#-e at 18–20 GPa closely matches crystal 2#-a at 12–14 GPa in magnitude, T-dependence, and SC onset—an offset of several GPa. The paper still advertises a “high-precision” P–T diagram. The overall topology is reproducible, but the absolute pressure scale for DW suppression and SC onset is sample-dependent at a level comparable to the claimed precision. Quantify the pressure uncertainty (calibration, medium, local strain) and state explicitly which features are robust in absolute P and which only in relative ordering (T1 vs T2 vs Tc).
  3. [Introduction; Fig. 2e; Fig. 3; Ref. [34]] The orthorhombic–tetragonal boundary near 8–10 GPa is central to the interpretation of the jump in T1, the rise in low-T ρ and ρc/ρab, and the exclusive appearance of SC in the tetragonal phase, yet it is cited only as unpublished Sasaki et al. [34]. For a load-bearing structural assignment, either include the essential diffraction evidence (even as a brief Extended Data panel) or clearly mark the boundary as adopted from external work and discuss how much of the transport interpretation survives if the structural line shifts by a few GPa.
  4. [Transport signature of density-wave phases; Extended Data Fig. 1; Fig. 2e] Assignment of T1 and T2 (Extended Data Figs. 1, 3, 7): T2 is identified with SDW following prior work; T1 is a “DW-like” anomaly whose microscopic character is left open, yet both are treated symmetrically as “density-wave phases” whose full suppression coincides with zero-resistance SC. Several additional features (resistivity max/min, high-T upturn, “tiny anomalies” below T1) are plotted on the phase diagram without a clear hierarchy. Tighten the operational definitions (derivative criteria, reproducibility across ρab vs ρc) and avoid over-interpreting T1 as a long-range DW order parameter until microscopic probes under pressure are available.
minor comments (6)
  1. [Fig. 1 caption] Fig. 1 panel labels in the caption (b,c,e,d,f,g) do not match the order described in the text; renumber for consistency.
  2. [Planckian dissipation; Fig. 4f] In the Planckian paragraph, “0.28 μΩ cm/K” is quoted in the text while Fig. 4f reports 0.264 and 0.287 μΩ cm K−1 at 18 and 20 GPa; state which slope enters α.
  3. [Methods; Fig. 3 inset] Montgomery geometry and the correction for pressure-induced lattice contraction are mentioned only briefly; a short Extended Data note on contact placement, aspect-ratio uncertainty, and the size of the contraction correction would help others reproduce ρc/ρab.
  4. [References] Several references are preprints or “unpublished” (e.g. [27], [34], [37]); update status where possible and ensure that claims resting on them are flagged as such in the main text.
  5. [Main text; figure labels] Typographical inconsistencies: “deceases” → “decreases” (p. 5); mixed “behavio(u)r”; “Orth o” spacing in figure labels; “T S” → “Ts”.
  6. [Abstract; Oxygen-stoichiometric… section] Abstract claims “large single crystals” enabling absolute resistivity; give typical lateral dimensions in the abstract or opening results paragraph so the advance over prior work is quantitative.

Circularity Check

1 steps flagged

No circular derivation: phase diagram, DW tracks, SC boundary, and T-linear ρ are direct measurements; only a minor non-load-bearing self-citation annotates the ortho–tetra line.

specific steps
  1. self citation load bearing [Results (Figs. 2d,e; 3; 4a,b); Methods/Refs. [34]]
    "Th is qualitative change occurs near 8-10 GPa, coincident with the structural transition [34]. ... The purple dashed line in (d,e) indicates the approximate boundary between the orthorhombic (Ortho) and tetragonal (Tetra) structural phases."

    The ortho–tetra boundary drawn on the phase diagrams is taken from an unpublished manuscript with overlapping authors (Sasaki, Liu, … Taguchi, Arima, Fujishiro). That citation is not machine-checked or externally published here. It is not load-bearing for the central claims: the transport anomalies, anisotropy jump, and SC onset are measured directly on the present crystals and remain well-defined without the structural label. Mild annotation-level self-citation only.

full rationale

This is an experimental transport paper. The load-bearing chain is measurement → anomaly identification → P–T diagram → observation that zero-resistance SC appears where T1/T2 and the low-T upturn vanish, plus a measured T-linear ρ_ab above Tc. None of these steps defines the output in terms of the input. T1/T2 labels follow an external assignment (Khasanov et al.), and the pressure tracks are read from dρ/dT on the present crystals. The Planckian coefficient α = 1.6 ± 0.4 is an estimate assembled from the measured slope dρ/dT together with external ARPES Fermi-surface parameters, a literature multi-band Drude/Planckian formula (Bruin et al.), and a ~20% vF rescaling taken from external DFT; that is standard parameter import with stated uncertainty, not a fit-then-predict loop or a self-sealing definition. The only mild self-reference is the unpublished overlapping-author structural study used to draw the ortho–tetra boundary near 8–10 GPa; the resistivity jumps and anisotropy changes at that pressure are independently measured and would stand without that label. No uniqueness theorem, ansatz smuggling, or renaming of a known result carries the central claim. Score 1 reflects that single non-load-bearing self-citation; the derivation is otherwise self-contained.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 0 invented entities

Experimental transport paper. Load-bearing external inputs are: prior DW/SDW temperature assignments, ambient ARPES Fermi-surface parameters rescaled by theory under pressure, the Drude/Planckian conversion formula from Bruin et al., Montgomery geometry factors including lattice contraction from unpublished [34], and the identification of the structural boundary itself from that same unpublished source. No new particles or forces are postulated.

free parameters (3)
  • 20% enhancement of v_F under 20 GPa = 1.2 × ambient v_F
    Ambient ARPES velocities are multiplied by 1.2 following DFT estimates before inserting into the α formula; the factor is not measured at high pressure in this work.
  • Multi-band averaged n, k_F, v_F for Fig. 4c normalization = n=(1.1±0.1)×10^28 m^-3, k_F=0.82±0.03 Å^-1, v_F=(2.5±0.7)×10^5 m/s
    Composite n = n_α+n_β, k_F^2 = Σ k_Fi^2, v_F = (Σ k_Fi v_Fi)/k_F constructed from ARPES sheet parameters to place one point on the Bruin plot.
  • dρ_ab/dT slope used for α = ≈0.28 μΩ cm/K (20 GPa)
    Linear fit to normal-state ρ_ab at 18–20 GPa (≈0.26–0.29 μΩ cm/K) is the sole experimental input to α; residual intercept forced near zero.
axioms (5)
  • domain assumption Resistivity anomalies at T1 and T2 correspond to a lower-T density-wave-like order and an SDW order, respectively, as assigned in prior work.
    Stated explicitly when constructing the phase diagram; microscopic character of T1 is acknowledged as unclear.
  • domain assumption Transport scattering rate follows the multi-band Drude form and the Planckian ansatz 1/τ = α k_B T / ℏ with α of order 1 indicating strange-metal physics.
    Used in the Supplementary α estimation and Fig. 4c comparison to Bruin et al.
  • domain assumption Montgomery method with pressure-corrected dimensions yields reliable ρ_ab and ρ_c on the measured platelets.
    Methods section; lattice contraction taken from unpublished ref. 34.
  • domain assumption Ortho–tetragonal structural boundary lies near 8–10 GPa and is the cause of the sharp low-T anisotropy jump.
    Invoked throughout phase diagrams and anisotropy discussion via unpublished Sasaki et al. [34].
  • domain assumption Crystals are representative bilayer La3Ni2O7 without oxygen vacancies or RP intergrowths that would dominate transport.
    Supported by synchrotron refinement (Am2m, O occupancies≈1), STEM/iDPC, and EDS; underpins claim of intrinsic behavior.

reviewed 2026-07-30 · how reviews work

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Cite this review

Pith. "Pith review of Density-wave phases, anisotropic transport, and Planckian dissipation in single crystals of the superconductor La3Ni2O7." pith.science (2026). https://pith.science/paper/XY6AXPRL

@misc{pith2026260726990,
  author       = {Pith},
  title        = {Pith review of: Density-wave phases, anisotropic transport, and Planckian dissipation in single crystals of the superconductor La3Ni2O7},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XY6AXPRL}},
  note         = {Machine review of arXiv:2607.26990}
}
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read the original abstract

Pressure-induced superconductivity in bilayer nickelates provides a platform for investigating intertwined roles of charge/spin orders and electric transport in unconventional superconductivity. However, important quantitative information on the transport, such as the absolute value of the resistivity, the anisotropy, and the scattering rate of carriers, remains insufficient due to the lack of accurate measurements using large single crystals. Here we establish a high-precision pressure-temperature phase diagram of high-quality La3Ni2O7 single crystals, by measuring the in-plane and out-of-plane resistivities. We resolve two distinct anomalies associated with density-wave formation with contrasting pressure dependences. The pressure-induced structural transition enhances not only the resistivity values for both directions, but also its anisotropy at low temperatures, demonstrating a pronounced effect of density-wave order on the charge dynamics. Superconductivity with zero-resistance emerges near the boundary where the density-wave phases are fully suppressed, and above Tc, the resistivity exhibits a temperature-linear dependence over a wide temperature range while the scattering rate falls within a regime of the Planckian limit. Our results show that pressure dramatically changes the anisotropic charge transport via modifying density-wave orders, and eventually produces a pronounced strange-metal state with strong scatterings, from which superconductivity develops. This establishes robust density-wave correlations and Planckian dissipation as remarkable features of La3Ni2O7.

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  1. Single-crystal structural phase diagram of stoichiometric bilayer nickelate La3Ni2O7 under hydrostatic pressure

    cond-mat.supr-con 2026-07 conditional novelty 6.0

    Single-crystal X-ray diffraction under hydrostatic helium pressure shows La3Ni2O7 transforms directly from the polar, charge-ordered Am2m phase to tetragonal I4/mmm near 10 GPa, at the onset of bulk superconductivity.

Reference graph

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This paper was first reviewed by grok-4.5 on July 30, 2026.