{"id":"6c469a2e-526e-419d-9fef-6bbbf650e77d","arxiv_id":"2510.12786","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"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.","lead":"The paper reports a logarithmic divergence in the Seebeck coefficient divided by temperature at a specific strontium doping in an infinite-layer nickelate superconductor, which it interprets as evidence for a quantum critical point at the end of a pseudogap-like phase. If correct, this links nickelates to the cuprate pattern where strange-metal behavior grows out of quantum criticality.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The two-band Hall model as stated predicts R_H positive at high T and negative as T→0, the opposite of Fig. 3a, so the carrier-density collapse and pseudogap conclusion are unsupported.","rationale":"The reader's weakest assumption focused on the Seebeck-coefficient proxy for specific heat. That is a legitimate concern, but the more decisive problem is internal: the Hall two-band model, as written, cannot reproduce the sign of R_H(T) shown in Fig. 3a. With 1/τ_d ∝ T and 1/τ_s ∝ T^2, the electron pocket must dominate at low T and the hole pocket at high T — the reverse of the data. This is not a missing calibration or an unverified proxy; it is a logical inconsistency in a central piece of the argument. The paper's headline claim — that the nickelate underdoped phase is pseudogap-like, with nd falling from 1+p to p — rests on inverting R_H(T→0) using this model. If the model as stated cannot produce even the correct sign of the Hall crossover, the extracted carrier-density collapse is not credible. The S/T logarithmic divergence may still indicate quantum criticality, but the identification of the terminating phase as 'pseudogap-like' is unsupported. A corrected model (e.g., including residual scattering) might salvage the analysis, but the current manuscript presents the flawed version as quantitative agreement. Given that this affects the central claim and cannot be fixed by simply adding data, the verdict should move to REJECT.","tokens_in":9982,"tokens_out":13360,"duration_ms":118502,"concrete_test":"Recompute R_H(T) from the two-band formula using the stated model: n_d and n_s from the Sun et al. tight-binding parameters, 1/τ_d = k_B T/ℏ, 1/τ_s = B T^2, with no residual scattering. Plot R_H(T) over the measured range and overlay Fig. 3a. If the model yields R_H positive at high T and negative as T→0, the claimed fit is impossible and the nd(x) inversion is invalid. To test a possible repair, add a residual width Γ to 1/τ_s and check whether the 1+p→p collapse survives; if it requires fine-tuning or produces a different nd drop, the pseudogap claim fails.","verdict_should_be":"REJECT","load_bearing_attack":"In §II (Hall effect), the two-band model assumes 1/τ_d = k_B T/ℏ (Planckian) and 1/τ_s = B T^2 (Fermi liquid). Thus the d-hole mobility scales as 1/T and the s-electron mobility as 1/T^2. As T→0, the s-electron mobility diverges faster and must dominate the Hall response, giving R_H(T→0) < 0; at high T, the T^2 s-scattering suppresses the electron pocket, giving R_H > 0. This is exactly the opposite of the Lee et al. data in Fig. 3a, which is negative at high T and positive in the T→0 limit. The paper's explanation — that Planckian T-linear scattering suppresses the d-pocket relative to the T^2 s-scattering as T increases — reverses the temperature dependence: T^2 scattering grows faster with T, so it suppresses the s-pocket, not the d-pocket. Therefore the claimed 'quantitative agreement' cannot be obtained from the stated scattering rates unless an unstated residual (T-independent) scattering term is added to the s-pocket. Because the central 1+p→p collapse of nd is extracted by inverting R_H under exactly this model, the pseudogap-like phase conclusion is not supported by the current analysis. This is an internal inconsistency, not merely a parameter-uncertainty issue.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":10363,"tokens_out":6277,"duration_ms":56422,"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":[{"comment":"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","section":"§II Hall effect, Fig. 3a"},{"comment":"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.'","section":"§I Introduction; §II Seebeck effect"},{"comment":"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.","section":"Abstract vs. §II, Fig. 2c"},{"comment":"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.","section":"§II Hall effect, Fig. 3c"},{"comment":"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.","section":"Methods and extended data (referenced but not included)"}],"minor_comments":[{"comment":"The compound notation is inconsistent: both LNSO and LSNO are used for La1−xSrxNiO2. Please standardize.","section":"Throughout"},{"comment":"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.","section":"Fig. 2a"},{"comment":"The phrase 'mirroring the cuprate pseudogap transition in cuprates' is redundant; remove one occurrence.","section":"Introduction, last paragraph"},{"comment":"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.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The Hall sign contradiction is the most serious issue: as written, the model cannot reproduce the data it claims to fit, and the carrier-density collapse rests on that model. The 41.5 T discrepancy between the abstract and the main text also needs to be resolved. If the authors can correct the Hall analysis or provide the missing data and a robust sensitivity analysis, the paper could become a valuable contribution; in its current form, the central pseudogap-like conclusion is not supported."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe one thing you need to know: the raw Seebeck result is real and new, but the Hall-based carrier collapse—the paper's main claim of a 1+p→p pseudogap-like transition—is not supported by the model as written. The two-band model with Planckian d scattering and T^2 s scattering predicts R_H negative at low T and positive at high T, because the s mobility diverges faster. That is the opposite of the Lee et al. data and the paper's own description. So the inversion that produces the carrier collapse is suspect.\n\nWhat is genuinely good: the S/T logarithm at x=0.20 in LSNO is an independent measurement, and it is a meaningful addition to the nickelate picture. The high-temperature Boltzmann match using the ARPES band structure is a solid sanity check, even if the threefold mass renormalization is a fit parameter. The paper is honest about the inability to do calorimetry on thin films and about the assumption of constant n_s.\n\nThe soft spots: the Seebeck-as-specific-heat proxy is reasonable but unverified; there is only one doping, no error bars, and no C/T check possible in films. That was the reader's main concern, and it stands. But the Hall model problem is more serious than the reader's report suggests. The temperature dependence of the scattering rates is backwards. T^2 scattering suppresses the s pocket at high T, not the d pocket, so the stated model cannot reproduce the observed sign change. The only way out would be an unstated T-independent residual scattering on the s pocket, which would make the model less clean. Either way, the extraction of n_d from R_H is not reliable, and with it the pseudogap conclusion.\n\nThis is a paper worth a serious referee, not a desk reject, because the S/T data are new and the methodological error is diagnosable and fixable. But I would not cite the carrier collapse until the model is corrected and the predicted R_H(T) is actually checked against the data. For a reading group, it's a good case study in checking whether a model's temperature dependence goes in the right direction.","headline":"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.","tokens_in":10922,"tokens_out":3342,"would_cite":false,"duration_ms":26935,"reading_group":"yes","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["infinite-layer nickelates","strange metal","quantum critical point","Seebeck coefficient","pseudogap","Hall effect","carrier density collapse","T-linear resistivity"],"falsifier":"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.","tokens_in":9915,"feed_emoji":"","tokens_out":7570,"duration_ms":59297,"temperature":0.7,"pith_summary":"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.","feed_headline":"Seebeck log-divergence reveals nickelate quantum critical point","feed_subtitle":"S/T log-divergence at x=0.20 plus carrier collapse places a QCP under the superconducting dome.","key_machinery":"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","core_discovery":"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,","pith_inferences":["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."],"forward_implications":["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."],"fun_headline_variants":["Seebeck log-divergence identifies true quantum critical point in nickelates","Nickelate pseudogap ends at a quantum critical point","Carrier collapse and log-T Seebeck expose nickelate QCP","Log-T divergence in Seebeck points to nickelate criticality","Quantum critical point underlies strange metal in nickelates"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Seebeck log-divergence identifies true quantum critical point in nickelates","Nickelate pseudogap ends at a quantum critical point","Carrier collapse and log-T Seebeck expose nickelate QCP","Log-T divergence in Seebeck points to nickelate criticality","Quantum critical point underlies strange metal in nickelates"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000747,"raw_usage":{"total_tokens":3270,"prompt_tokens":952,"completion_tokens":2318,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":696,"completion_tokens_details":{"reasoning_tokens":2228}},"tokens_in":696,"tokens_out":2318,"duration_ms":14487,"temperature":1.0,"reasoning_tokens":2228,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T09:50:37.790193+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}