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REVIEW 5 major objections 4 minor 37 references

The paper reports that in La1−xSrxNiO2 at x=0.20, S/T diverges logarithmically as T→0 and the Ni-dx2−y2 carrier density drops from 1+x to x holes, identifying a quantum critical point at the end of a pseudogap-like phase.

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 superconducting infinite-layer nickelates, S/T diverges logarithmically at the strange-metal onset doping, identifying a quantum critical point and a cuprate-like collapse of the Ni-d band carrier density.

T0 review reviewed 2026-08-04 challenge →

load-bearing objection The raw S/T log divergence is a real new data point, but the Hall-carrier-collapse claim rests on a two-band model that, as stated, predicts the opposite sign of R_H(T) from the data. the 5 major comments →

arxiv 2510.12786 v2 pith:665K3XYJ submitted 2025-10-14 cond-mat.str-el cond-mat.supr-con

Quantum critical origin of strange-metals at the end of a pseudogap phase in infinite-layer nickelates

C. Iorio-Duval , E. Beauchesne-Blanchet , F. Perreault , J. L. Santana Gonz\'alez , S. \"Ust\"un Kaykusuz , W. Sun , D. Graf , Y. F. Nie
show 2 more authors
A. Gourgout G. Grissonnanche
This is my paper
classification cond-mat.str-el cond-mat.supr-con
keywords infinite-layer nickelatesstrange metalquantum critical pointSeebeck coefficientpseudogapHall effectcarrier density collapseT-linear resistivity
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 sets out to show that strange-metal behavior in superconducting infinite-layer nickelates has a quantum-critical origin. It reports that in La1−xSrxNiO2 at x=0.20 — the doping where T-linear resistivity begins — the Seebeck coefficient divided by temperature, S/T, diverges logarithmically as T→0, the same signature that in other materials identifies a zero-temperature quantum critical point (QCP) via the electronic specific heat. Since thin-film nickelates cannot be measured by calorimetry, the Seebeck coefficient is used as a proxy for entropy per carrier. The paper then shows that Hall-effect data across Nd1−xSrxNiO2, analyzed with a two-band model, reveal a collapse of the Ni-dx2−y2 carrier density from 1+x to x holes near the same critical doping, mirroring the cuprate pseudogap transition. The conclusion is that the strange metal emerges from a QCP terminating a pseudogap-like phase, extending a pattern seen across several families of unconventional superconductors.

Core claim

The central claim is that the onset of T-linear resistivity in superconducting infinite-layer nickelates marks a genuine zero-temperature quantum critical point, not merely a crossover. The evidence is thermodynamic in character: in La1−xSrxNiO2 at x=0.20, the Seebeck coefficient divided by temperature is constant at high temperature and then diverges as log T below about 60 K, persisting down to the lowest temperatures when superconductivity is suppressed by a 41.5 T magnetic field. Because the Seebeck coefficient at low temperature can be treated as the specific heat per carrier, this log divergence is the same signature as C/T ∝ log T observed at QCPs in other materials. In a second step,

What carries the argument

The load-bearing object is the Seebeck coefficient used as a low-temperature proxy for entropy per carrier: the paper takes S/T ∝ log T to be the transport equivalent of the thermodynamic C/T ∝ log T that defines a QCP. To support this, it uses Boltzmann transport calculations on the ARPES-derived tight-binding band structure, which reproduce the high-temperature S/T and indicate a threefold mass renormalization. For the carrier-density collapse, the central mechanism is a two-band Hall model: the Ni-dx2−y2 pocket is assigned a Planckian T-linear scattering rate (1/τ_d = k_B T/ℏ) and the rare-earth s pocket a Fermi-liquid T^2 rate, and the zero-temperature Hall coefficient is inverted under

Load-bearing premise

The whole quantum-critical identification rests on the premise that at low temperatures the Seebeck coefficient measures the entropy per carrier, so that S/T ∝ log T is the same thermodynamic signature as C/T ∝ log T; if the log divergence instead comes from energy-dependent scattering, phonon drag, or multi-band transport weights, the thermodynamic QCP conclusion does not follow.

What would settle it

Perform a Boltzmann transport calculation of S/T using the ARPES-measured band structure with a realistic energy-dependent scattering rate but no critical contribution: if it reproduces the observed S/T ∝ log T at x=0.20, the divergence is a transport artefact and the QCP identification fails. Alternatively, measure C/T on the same material through an independent thermodynamic probe such as magnetic torque or thermal expansion and show it stays constant while S/T diverges.

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

If this is right

  • If x≈0.20 in LSNO and x≈0.15 in NSNO are true QCPs, the T-linear resistivity of nickelate strange metals is a quantum-critical property rather than an incidental scattering law.
  • The carrier-density collapse from 1+x to x in the Ni-dx2−y2 band establishes a Fermi-surface reconstruction across the critical doping, analogous to the cuprate pseudogap.
  • Infinite-layer nickelates then join heavy-fermion, iron-based, ruthenate, and twisted-bilayer systems in which strange-metal behavior coexists with a terminating zero-temperature phase transition.
  • The two-band Hall model with one Planckian and one Fermi-liquid pocket provides a quantitative framework for extracting band-resolved carrier densities in multiband correlated metals.
  • Because the pseudogap-like underdoped phase is metallic and lacks long-range order, the QCP must be driven by a hidden order or a Fermi-volume-changing transition rather than conventional magnetism.

Where Pith is reading between the lines

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

  • A testable extension: the same Seebeck protocol could be applied to other multiband thin-film superconductors where calorimetry is unavailable, turning S/T into a standard quantum-criticality screen.
  • If the carrier collapse is real, underdoped nickelates should show growing pseudogap-like spectroscopic signatures such as suppressed spectral weight or Fermi arcs; the paper does not report such data.
  • The conclusion depends on the Nd-s pocket being a doping-independent spectator; quantum oscillations or a doping-dependent measurement of the s-pocket volume could check this, and a change in ns would soften the reported nd collapse.
  • One might look for a specific-heat analogue in nickelate superlattices or bulk 5-layer nickelates, where calorimetry may become feasible, to confirm that the S/T log divergence is a true entropy signature rather than a transport artifact.
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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

5 major / 4 minor

Summary. The paper reports Seebeck measurements on La1−xSrxNiO2 (LSNO) at x = 0.20 and finds that S/T is roughly constant above 60 K, changes sign near 60 K, and appears to diverge logarithmically below about 35 K down to the superconducting transition at fields up to 14 T. A Boltzmann calculation using an ARPES-derived tight-binding band structure with a three-fold mass renormalization is claimed to quantitatively capture the high-temperature S/T. The authors then analyze published Hall data on Nd1−xSrxNiO2 (NSNO) using a two-band model in which the Ni-d band has Planckian T-linear scattering and the Nd-s band has Fermi-liquid T^2 scattering. Inverting the zero-temperature Hall coefficient under the assumption of a constant Nd-s pocket carrier density, they extract a Ni-d band carrier density nd that drops from 1+x to x across the critical doping, which they interpret as a pseudogap-like transition. The central claim is that x* is a quantum critical point terminating a pseudogap-like phase in infinite-layer nickelates, with the strange-metal behavior emerging from this QCP.

Significance. If established, this result would extend the quantum-critical strange-metal paradigm to infinite-layer nickelates and strengthen the analogy with cuprates. The raw observation of a log-like upturn in S/T at the doping where T-linear resistivity onsets is an original and potentially important experimental clue, especially because calorimetry is inaccessible in these thin films. The high-temperature comparison with ARPES-derived Boltzmann transport is also a strong feature. However, the significance is conditional: the thermodynamic interpretation of S/T rests on an unproven proxy assumption, and the Hall-derived carrier-density collapse is supported by a two-band model that, as written, appears internally inconsistent with the data it is supposed to fit. These issues must be resolved before the central conclusions can be accepted.

major comments (5)
  1. [§II Hall effect, Fig. 3a] The two-band Hall model as stated predicts the opposite sign of the data it claims to fit. With 1/τ_d = k_B T/ℏ and 1/τ_s = B T^2, the mobility ratio is μ_s/μ_d = τ_s/τ_d = k_B/(B ℏ T), which diverges as T→0. The electron-like Nd-s pocket therefore dominates the zero-temperature Hall response, giving R_H < 0, while at high temperature the T^2 scattering of the s pocket grows faster than the Planckian rate, so the hole-like d pocket dominates, giving R_H > 0. This is exactly the opposite of the stated Lee et al. data in Fig. 3a, which are described as negative at high T and positive in the T→0 limit. The claimed 'quantitative agreement' cannot be obtained from the stated scattering rates unless an unstated residual scattering term or a reversed assignment is introduced. Because the central 1+p→p collapse of nd in Fig. 3c is extracted by inverting precisely this model, this internal incons
  2. [§I Introduction; §II Seebeck effect] The inference S/T ∝ log T ⇒ C/T ∝ log T is load-bearing for the QCP claim. The premise that at low temperature S can be regarded as the specific heat per carrier is asserted, not derived. In a multiband system with strongly different mobilities, S/T carries transport weighting and can exhibit a logarithmic divergence from energy-dependent scattering, phonon drag, or multiband transport even without a thermodynamic QCP. Because calorimetry is impossible in these thin films, the thermodynamic nature of the observed S/T divergence is not directly confirmed. The authors should either provide a quantitative transport-based argument ruling out these alternatives or temper the claim that this 'identifies x* as a QCP.'
  3. [Abstract vs. §II, Fig. 2c] The abstract states that the logarithmic divergence 'persists to the lowest temperature once superconductivity is suppressed by B = 41.5 T,' but the main text and Fig. 2c show only B = 0, 7, and 14 T, with no 41.5 T data described anywhere. Either the high-field data must be presented, or the abstract must be corrected. In addition, Fig. 2 reports no error bars or measurement uncertainty, and the log window below 35 K rests on a single sample, making the robustness of the central Seebeck observation difficult to assess.
  4. [§II Hall effect, Fig. 3c] The extraction of nd across the phase diagram assumes that the Nd-s pocket carrier concentration ns remains constant as a function of doping. This is an assumption, not an experimental constraint. If ns varies with x, the apparent collapse of nd from 1+x to x could be an artifact of the inversion. The paper should report how sensitive the extracted nd values are to plausible variations in ns and provide independent evidence for a constant ns across the critical doping.
  5. [Methods and extended data (referenced but not included)] The two-band Hall model, the Fermi-liquid coefficient B, and the Boltzmann transport calculation are described only qualitatively in prose. The referenced 'Methods' section, extended data, and supplementary figures are not present in the submitted manuscript, so the 'quantitative agreement' in Fig. 3a cannot be evaluated. Please provide the full model equations, parameter values, and error propagation for the inversion of R_H.
minor comments (4)
  1. [Throughout] The compound notation is inconsistent: both LNSO and LSNO are used for La1−xSrxNiO2. Please standardize.
  2. [Fig. 2a] The Boltzmann calculation uses m* = 3× the ARPES mass; this is an adjustable parameter chosen to match the data. The text should state explicitly that this is a fit parameter and discuss its uncertainty rather than presenting the match as fully parameter-free.
  3. [Introduction, last paragraph] The phrase 'mirroring the cuprate pseudogap transition in cuprates' is redundant; remove one occurrence.
  4. [Throughout] There are several typographical errors, e.g., 'familiy', 'developped', 'onset of T-linear resistivity (x = 0.20)' with inconsistent punctuation. A careful proofread is needed.

Circularity Check

2 steps flagged

Core S/T log-divergence is an independent raw measurement, but the 'quantitative' S/T band-structure match uses a mass factor fitted to the same data, and the Hall-derived n_d collapse is a model-inverted restatement of the R_H drop.

specific steps
  1. fitted input called prediction [§II Seebeck effect, Fig. 2a; abstract]
    "The Boltzmann calculation was performed using Sun et al.'s tightbinding model [12] and by considering the effective mass three times larger than what was reported by ARPES; ... Our calculations reproduce the same temperature dependence and sign as the data (Fig. 2a). We find that the effective mass m⋆ is three times higher at the Fermi level compared to what is determined from the bandwidth measured by ARPES and calculated from DFT."

    The magnitude of the high-T S/T agreement is set by the fitted factor 3 in m⋆. In the free-electron expression S ≈ −(π²/3)(kB/e)(T/TF), TF and hence m⋆ are fixed by the measured S/T, so the 'quantitative capture' of the amplitude is by construction. The remaining content—sign and temperature dependence—is independent, so this is partial rather than total circularity.

  2. renaming known result [§II Hall effect / Fig. 3c]
    "To quantify the carrier concentration nd of the correlated Ni-d pocket with doping, we used the extrapolated RH(T→0) from the measured data [13] (Fig. S2) and inverted the two-band expression for the Hall coefficient. In doing so, we assumed that the uncorrelated Nd-s pocket remains unaffected across the quantum critical point, i.e. its carrier concentration ns is constant throughout the phase diagram. Under this assumption, we find that nd collapses from 1+p carriers above the quantum critical point to p carriers just below it."

    With ns fixed constant and the T→0 Hall response assigned to the d-pocket, the two-band inversion is effectively nd ≈ 1/(e RH(0)). The 'collapse from 1+p to p' is therefore a one-to-one mapping of Lee et al.'s RH(0)(x) drop, not an independent probe of the Ni-d band. The conclusion is contained in the chosen inversion and the constancy assumption; no additional data are used.

full rationale

The central QCP claim rests on a raw, independently measured S/T ∝ log T divergence, so it is not circular in origin; the analogy to cuprate C/T and S/T log divergences uses external data (Michon et al., Gourgout et al.). The high-T S/T 'quantitative capture' is weakened because a 3× effective-mass enhancement is selected to match the measured amplitude, though the sign and T-dependence remain nontrivial. The Hall-based n_d collapse is a model-inverted restatement of the published R_H drop under an assumed constant n_s and assumed scattering hierarchy, so it supports the pseudogap-like interpretation only insofar as those assumptions hold; the stated 1/τ_d = kBT/ℏ and 1/τ_s = BT² rates, if evaluated with the standard two-band formula, imply a sign-change direction opposite to the one claimed for Fig. 3a, an internal-consistency/correctness concern rather than circularity. Self-citations (Refs. 12, 16, 19) are to externally published ARPES/Seebeck data and methodology, and are not themselves the forcing mechanism for the QCP conclusion. Overall, partial circularity in the supporting transport analyses, but the principal measurement is independent.

Axiom & Free-Parameter Ledger

4 free parameters · 6 axioms · 0 invented entities

The central QCP claim rests on the S/T-as-entropy proxy and the absence of alternative explanations; the Hall-derived carrier collapse rests on the two-band model with assumed scattering laws and a constant ns. No new entities are introduced.

free parameters (4)
  • Effective mass renormalization factor m*/m_ARPES = ≈3
    Introduced in Boltzmann transport calculation to reproduce high-temperature S/T magnitude (Fig. 2a caption and §II).
  • Nd-s pocket carrier concentration ns (held constant) = constant (value from tight-binding at overdoped doping)
    Assumed unchanged across QCP; the extracted nd collapse depends on this choice.
  • Fermi-liquid coefficient B in 1/τ_s = B T^2 = determined from band parameters
    Scattering rate for the Nd-s pocket in the two-band Hall model; no value or uncertainty given.
  • Planckian scattering rate 1/τ_d = k_B T/ℏ = k_B/ℏ
    Assumed for the Ni-d pocket; not fitted but is a modeling choice that drives the T dependence of RH.
axioms (6)
  • domain assumption The low-temperature Seebeck coefficient is a proxy for entropy per carrier (S/T ≈ C/T per carrier).
    Invoked in Introduction and Results to convert S/T log divergence into a thermodynamic QCP signature; cannot be verified by calorimetry in thin films.
  • domain assumption ARPES-derived tight-binding band structure for LSNO x=0.20 faithfully represents the Fermi surface and band parameters.
    Used in Boltzmann calculation and Hall inversion; systematic ARPES uncertainties are not propagated.
  • domain assumption No van Hove singularity/Lifshitz transition occurs at this doping in nickelates.
    Used in Discussion to rule out an alternative origin of log divergence; relies on ARPES band structure of one doping.
  • domain assumption A two-band model with only Ni-d and Nd-s pockets captures the Hall coefficient of NSNO across T and doping.
    Used in Section II to reproduce RH(T) and invert for nd; other bands/impurity channels are ignored.
  • domain assumption The d pocket has Planckian T-linear scattering and the s pocket T^2 Fermi-liquid scattering.
    The core assumption of the Hall model; motivated by ARPES/many-body studies but not measured directly.
  • domain assumption Superconductivity is fully suppressed by B=41.5 T so S/T at lowest T reflects the normal state.
    Abstract states this; main-text figures show only B=0-14 T, so the zero-field log divergence is cut off by Tc.

reviewed 2026-08-04 · how reviews work

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Cite this review

Pith. "Pith review of Quantum critical origin of strange-metals at the end of a pseudogap phase in infinite-layer nickelates." pith.science (2026). https://pith.science/paper/665K3XYJ

@misc{pith2026251012786,
  author       = {Pith},
  title        = {Pith review of: Quantum critical origin of strange-metals at the end of a pseudogap phase in infinite-layer nickelates},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/665K3XYJ}},
  note         = {Machine review of arXiv:2510.12786}
}
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read the original abstract

The quantum-critical origin of strange metals remains debated, particularly in cuprates where $T$-linear resistivity emerges at the end of the pseudogap phase, a regime without long-range order whose nature remains one of the largest mysteries of quantum materials~\cite{Michon2019Thermodynamic, zhong_2022}. Superconducting infinite-layer nickelates provide a new platform to revisit this issue, given their close similarities to cuprates. Here too, $T$-linear resistivity onsets at a critical doping $x^\star$ near the middle of the superconducting dome. Establishing whether $x^\star$ is a quantum critical point (QCP) -- a zero-temperature phase transition -- typically relies on the electronic specific heat $C_{\rm el}$, which follows $C_{\rm el}/T \propto \log(T)$ at a QCP, rather than the constant behaviour of a conventional metal. However, the thin-film form of infinite-layer nickelates precludes calorimetry. We therefore use the Seebeck coefficient as a low-temperature proxy for specific heat per carrier. In La$_{\rm 1-x}$Sr$_{\rm x}$NiO$_2$ at $x^\star$, the high-temperature Seebeck response is quantitatively captured by the ARPES-measured band structure, indicating well-defined quasiparticles. Below 60 kelvin, however, $S/T$ develops a logarithmic divergence, $S/T \propto \log(T)$, persisting to the lowest temperature once superconductivity is suppressed by $B=41.5$~T. This identifies $x^\star$ as a QCP terminating the underdoped phase. Finally, we find that the carrier density $n_{\rm d}$ of the Ni-$d_{\rm x^2-y^2}$ pocket drops from $1+x$ above $x^\star$ to $x$ below, mirroring the hallmark of the pseudogap phase in cuprates and iridates. These results point to a pseudogap-like underdoped regime ending at $x^\star$, from which strange-metal behaviour emerges.

Figures

Figures reproduced from arXiv: 2510.12786 by A. Gourgout, C. Iorio-Duval, D. Graf, E. Beauchesne-Blanchet, F. Perreault, G. Grissonnanche, J. L. Santana Gonz\'alez, S. \"Ust\"un Kaykusuz, W. Sun, Y. F. Nie.

Figure 1
Figure 1. Figure 1: FIG. 1. ( [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. ( [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. ( [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

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This paper was first reviewed by deepseek-v4-flash on August 4, 2026.