{"id":"7947b52d-0bb6-49b4-aca8-343cc9d716d0","arxiv_id":"1908.07167","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Nematic susceptibility in (Bi,Pb)2212 diverges near the endpoint of the pseudogap line, indicating a nematic quantum critical point tied to high-temperature superconductivity.","lead":"Elastoresistance measurements on the cuprate superconductor (Bi,Pb)2212 show that its electronic response to strain grows sharply near the doping where the pseudogap transition line ends. The authors interpret this as a quantum critical point for electronic nematic order, linking the pseudogap and strange-metal physics to high-temperature superconductivity.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"At p=0.20, the low-temperature downturn is exactly the signature of a finite-T nematic transition below Tc; without sub-Tc data, T0=0 cannot distinguish a QCP from hidden nematic order.","rationale":"The paper's finite-T anomaly at T* for underdoped and optimally doped samples is convincing evidence for a nematic transition at the pseudogap onset, and the use of Pb-substituted crystals to remove supermodulations is a good control. The central extension to a quantum critical point, however, rests on exactly one experimental fact: the sign change of the fitted Weiss temperature T0 near p approximately 0.2. That fact is degenerate with the alternative that the actual nematic transition Tnem stays finite below Tc for the overdoped samples, because the low-temperature 'downward deviation' at p=0.20 is the expected signature of a pole below the measured window, and the paper explicitly allows Tnem > T0 due to electron-lattice coupling. The reader's conditional verdict is therefore appropriate: the paper should not be read as establishing a nematic QCP until sub-Tc measurements or a quantitative model separates T0=0 from Tnem < Tc. I see no inconsistency or misconduct; the concern is about extrapolative inference, not the raw observations.","tokens_in":9383,"tokens_out":9053,"duration_ms":97502,"concrete_test":"Measure elastoresistance of the p=0.20 and p=0.22 crystals below zero-field Tc in a magnetic field large enough to suppress superconductivity (for example, pulsed fields above Hc2), and look for a kink or pole in -chi_nem(T) at finite T. Appearance of a finite-T anomaly would identify the p=0.20 downturn as a nematic transition rather than a QCP; continued 1/T growth to the lowest accessible temperature would support the QCP. As a zero-cost first step, refit the published p=0.20 data with chi_nem = chi0 + lambda/[a(T - Tnem)] allowing Tnem < 75 K and compare with the constrained T0=0 fit, checking whether the finite-Tnem model is preferred within the scatter.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The QCP conclusion turns on the p=0.20 and p=0.22 overdoped data, where no kink is observed and chi_nem grows monotonically down to Tc. The paper's text (Fig. 3d/i discussion) states that the p=0.20 sample shows a 'downward deviation from Curie-Weiss law' at low temperature and assigns this to quantum-critical effects by analogy with FeSe-based superconductors. But exactly this deviation is what a finite-T nematic transition just below Tc would produce: if the true response is chi proportional to 1/(T - Tnem) with 0 < Tnem < Tc, the low-temperature points lie below the high-T Curie-Weiss extrapolation that gives T0 approximately 0. Because the measurements stop at Tc approximately 75 K, a divergence at T=0 and a pole at finite Tnem below Tc are not distinguishable. The problem is compounded by the paper's own statement that electron-lattice coupling makes Tnem exceed T0 by a sizable amount; hence T0 crossing zero near p approximately 0.2 does not establish that the coupled nematic transition temperature vanishes at the pseudogap endpoint. The sign change of T0 is inferred from high-T fits with no reported error bars, so the data are consistent with Tnem remaining finite inside the superconducting dome.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript reports elastoresistance measurements on (Bi,Pb)2Sr2CaCu2O8+δ and Bi2212 at six hole concentrations between p = 0.13 and p = 0.22. The authors extract the nematic susceptibility χ_nem = dη/dε and observe Curie-Weiss-like behavior at high temperature, described by Eq. (1), with a kink at a temperature T_nem that tracks the pseudogap temperature T* determined by independent ARPES, tunneling, and Raman experiments. For the overdoped samples, the inverse susceptibility extrapolates to a Weiss temperature T0 that changes sign near p ≈ 0.2, and the authors interpret this as evidence for a nematic quantum critical point (QCP) at the pseudogap endpoint, with nematic fluctuations that diverge toward zero temperature and remain strong down to Tc.","tokens_in":9650,"tokens_out":4803,"duration_ms":51721,"significance":"If the central claim holds, the manuscript would identify the fluctuating order associated with the pseudogap critical point as electronic nematicity and would connect this nematic QCP to superconductivity and strange-metal behavior in cuprates. The paper has several concrete strengths: the nematic susceptibility is a directly measured quantity; the comparison of T_nem with independent T* determinations provides an external anchor; the use of Pb-substituted Bi2212 suppresses superstructure modulations; and the Methods include a first-order geometric correction for extracting resistivity anisotropy from resistance changes. The paper also makes a falsifiable prediction—divergent nematic susceptibility at a doping around p ≈ 0.2—that can be tested by measurements below Tc. The main weakness, detailed below, is that the key extrapolation from high-temperature data to a zero-temperature divergence is not yet supported by error analysis or by data that distinguish a T = 0 QCP from a finite-T transition hidden below Tc.","major_comments":[{"comment":"The Weiss temperatures T0 are the load-bearing quantities for the quantum-critical claim, but the manuscript reports no uncertainties for the Curie-Weiss fits and no sensitivity analysis with respect to the fitted temperature window. Because T0 for p = 0.20 and p = 0.22 is obtained by extrapolating from data that end at Tc ≈ 70–75 K, the statement that T0 crosses zero near p ≈ 0.2 requires error bars and a demonstration that the sign change is not an artifact of the choice of fit range or of the temperature-independent offset χ0.","section":"§3, Fig. 3f-j and Eq. (1)"},{"comment":"The downward deviation from Curie-Weiss behavior at p = 0.20 is assigned to quantum-critical effects by analogy with FeSe-based superconductors, but this assignment is not unique. For a finite-temperature nematic transition at T_nem below Tc, the same downward curvature relative to the high-temperature Curie-Weiss line occurs because χ ∝ 1/(T − T_nem) lies below the extrapolation 1/(T − T0) when 0 < T_nem < Tc. Since the measurements stop at Tc, the data cannot distinguish a divergence at T = 0 from a pole at finite T_nem below Tc. The authors should provide sub-Tc data, for example in high magnetic fields, or an independent criterion to break this degeneracy.","section":"Fig. 3d,i and the discussion following it"},{"comment":"The manuscript states that electron-lattice coupling makes the actual nematic transition temperature T_nem exceed the Weiss temperature T0 by a sizable amount, citing Ref. [16]. It follows that T0 ≈ 0 does not, by itself, imply that the coupled nematic transition temperature vanishes at the pseudogap endpoint. The quantum-critical interpretation requires a quantitative estimate of the electron-lattice correction at each doping, or a specific argument that this correction vanishes at the endpoint, rather than only a comparison of T0 with the extrapolated T* line.","section":"Fig. 4b and the discussion of electron-lattice coupling"},{"comment":"The kink that defines T_nem and the values plotted in the phase diagram are presented without statistical or systematic uncertainties, and the identification of the kink appears to be made by visual inspection. Given that the central claims are the coincidence of T_nem with T* and the sign change of T0, the authors should provide representative error bars and a reproducible criterion for defining T_nem from the elastoresistance data.","section":"Figs. 3 and 4"}],"minor_comments":[{"comment":"The word 'psuedo-gap' appears in the sentence 'or some secondary effect of the psuedo-gap' and should be corrected to 'pseudogap'.","section":"Main text, paragraph on the pseudogap phase"},{"comment":"The panel order in the caption lists p = 0.13 (a), p = 0.14 (b), p = 0.16 (c), p = 0.20 (d), and p = 0.22 (e), but the text refers to 'Fig. 3d,e' for the overdoped samples before mentioning the intermediate panel; please standardize the order and the cross-references.","section":"Fig. 3 caption"},{"comment":"The relation Δρ/ρ ≈ ΔR/R − 2ε is derived under the assumption of constant sample volume; since this correction directly enters the magnitude and temperature dependence of χ_nem, an estimate of the systematic error from deviations from constant volume would help the reader assess the absolute scale of the reported susceptibility.","section":"Methods, elastoresistance section"},{"comment":"The color scale for the magnitude of χ_nem is not defined in the caption; please specify whether it is the raw elastoresistance coefficient or a normalized quantity, and state how the color contours are interpolated between the measured doping points.","section":"Fig. 4b"}],"recommendation":"major_revision","confidential_remarks":"The paper is potentially important for the cuprate community, and the central concern is not circularity: the T_nem–T* comparison uses independent external data. The main risk is the extrapolation from high-temperature Curie-Weiss fits to a zero-temperature divergence when data stop at Tc. I would ask the authors to provide error bars, fit-range robustness tests, and, if at all possible, sub-Tc measurements or a quantitative treatment of the finite-T alternative before publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is the first elastoresistance study of nematic susceptibility across a wide doping range in a cuprate, and the kink at T* in the underdoped and optimally doped samples is a genuinely new, clean observation. The comparison of Tnem with T* from ARPES, tunneling, and Raman is a nice external anchor, and the choice of (Bi,Pb)2212 to avoid the Cu-O chain complications of YBCO is well reasoned. Credit where due: the high-temperature Curie-Weiss form, the doping-dependent Weiss temperature, and the disappearance of the kink in the overdoped samples are all interesting and internally consistent.\n\nThe soft spot is the central claim. The paper takes the p = 0.20 and 0.22 data, where no kink is observed and -chi_nem grows monotonically down to Tc, and infers a divergent nematic susceptibility at a QCP. But the data stop at Tc ~ 70-75 K. The downward deviation from the Curie-Weiss fit at p = 0.20 is exactly what a finite-T nematic transition just below Tc would produce, and the paper's own text says electron-lattice coupling makes Tnem exceed T0 by a sizable amount. So a T0 crossing zero does not establish that the actual nematic transition temperature vanishes. The claim that the low-temperature deviation is 'likely related to the effect of QCP' is asserted by analogy with FeSe1-xSx, not demonstrated. No error bars are shown on the Curie-Weiss fits, so the sign change of T0 is not quantitatively secured. I don't think this kills the paper, but the headline 'divergent' is not supported by direct observation; it is a model-dependent extrapolation.\n\nThat said, the stress-test concern is fair but not fatal. The paper is careful in its methods, the resistance-to-resistivity correction is addressed, and the Tnem/T* coincidence is a solid result independent of the QCP interpretation. The authors are not sloppy; they are pushing an interpretation beyond what the data can strictly distinguish.\n\nWho is this for? Anyone working on cuprate phase diagrams, nematicity, or quantum criticality in strongly correlated electron systems. It deserves a serious referee, but the referee should push for error bars, lower-temperature data (or high-field data to suppress superconductivity), and a more even-handed discussion of the finite-T nematic alternative. In its current form I would not accept the QCP claim at face value, but the experimental core is worth publishing after revision.","headline":"First elastoresistance mapping of nematic susceptibility across the cuprate phase diagram, but the divergent-QCP claim is an extrapolation that cannot rule out a finite-T nematic transition just below Tc.","tokens_in":10241,"tokens_out":1633,"would_cite":true,"duration_ms":18581,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["74.72.-h","74.25.Dw","71.27.+a"],"model":"deepseek-v4-flash","headline":"Using elastoresistance measurements in (Bi,Pb)₂Sr₂CaCu₂O₈₊δ, this paper shows that the nematic susceptibility diverges near the doping where the pseudogap line ends, indicating a nematic quantum critical point.","keywords":["nematic susceptibility","elastoresistance","pseudogap","quantum critical point","cuprate superconductors","Bi2212","electronic nematicity","Curie-Weiss law"],"falsifier":"Measure the nematic susceptibility of (Bi,Pb)2212 at $p = 0.2$ down to millikelvin temperatures while suppressing superconductivity with a high magnetic field: if $|\\chi_{\\rm nem} - \\chi_0|^{-1}$ fails to extrapolate to zero or develops a kink at a finite temperature, the claimed nematic quantum critical point is falsified.","tokens_in":9183,"feed_emoji":"🔬","tokens_out":6457,"duration_ms":51139,"temperature":0.7,"pith_summary":"By measuring how the resistivity of (Bi,Pb)₂Sr₂CaCu₂O₈₊δ responds to a controlled uniaxial strain, the authors track the electronic nematic susceptibility across the cuprate phase diagram. They find that above the pseudogap temperature $T^*$, the susceptibility follows a Curie-Weiss law, and that at $T^*$ it shows a kink where a second-order transition with broken rotational symmetry appears to set in. Near the doping $p_c \\sim 0.22$ where $T^*$ extrapolates to zero, the Weiss temperature changes sign and the susceptibility becomes divergent, which the authors take as evidence for a nematic quantum critical point inside the superconducting dome. The result identifies, for the first time in a cuprate, the fluctuating order associated with the pseudogap critical point.","feed_headline":"Nematic fluctuations diverge at cuprate pseudogap critical point","feed_subtitle":"Elastoresistance links the pseudogap onset to a nematic quantum critical point near optimal doping.","key_machinery":"The central object is the nematic susceptibility $\\chi_{\\rm nem} = d\\eta/d\\epsilon$, measured by elastoresistance: a piezoelectric stack strains the crystal along the Cu-O-Cu direction while four-probe resistance records the induced resistivity anisotropy $\\eta = \\Delta\\rho/\\rho$. The Curie-Weiss form $\\chi_{\\rm nem} = \\chi_0 + \\lambda/[a(T-T_0)]$ provides the working machinery, because its Weiss temperature $T_0$ estimates where the nematic instability would occur in the absence of electron-lattice coupling; the lattice coupling shifts the actual transition to $T_{\\rm nem}$, observed as a kink in $-\\chi_{\\rm nem}$. Tracking $T_0$ and $T_{\\rm nem}$ across doping lets the authors locate the vanishing of the nematic instability and its divergence at the pseudogap end point.","core_discovery":"The paper's central claim is that the pseudogap critical point in a cuprate superconductor has a nematic character: as the hole doping approaches $p_c \\approx 0.22$, the electronic nematic susceptibility $\\chi_{\\rm nem}$ diverges toward zero temperature, signalling a quantum critical point of an order that breaks the fourfold rotational symmetry of the CuO$_2$ plane. This is established by elastoresistance measurements, in which the strain-induced change of resistivity defines $\\chi_{\\rm nem} = d\\eta/d\\epsilon$ with the nematic order parameter $\\eta = \\Delta\\rho/\\rho$. Above $T^*$, $-\\chi_{\\rm nem}$ follows $\\chi_{\\rm nem} = \\chi_0 + \\lambda/[a(T-T_0)]$; the fitted Weiss temperature $T_0$ changes sign at $p \\sim 0.2$ and, combined with a kink in $-\\chi_{\\rm nem}(T)$ at $T_{\\rm nem} \\approx T^*$ in underdoped and optimally doped samples, this locates the nematic instability at the pseudogap onset. The divergence of the susceptibility just below optimal doping, with $T_c$ still as high as about 70 K, implies that quantum critical nematic fluctuations coexist with high-temperature superconductivity and may contribute to pairing and to strange-metal transport.","pith_inferences":["If the nematic QCP survives closer scrutiny, theories of the pseudogap must explain why rotational symmetry breaking is the primary instability at $T^*$ (or why it is a slave to another intra-unit-cell order such as loop currents).","Because the data stop at $T_c \\approx 70$ K, the zero-temperature divergence is an extrapolation; high-field elastoresistance below $T_c$ could test whether the growth continues or saturates.","A similar elastoresistance study in a cuprate without Bi-O super-modulations, such as La- or Hg-based cuprates, would show whether the nematic signal is generic to the pseudogap or specific to Bi2212."],"forward_implications":["The pseudogap onset $T^*$ is a genuine second-order transition that breaks rotational symmetry, not a smooth crossover.","A nematic quantum critical point sits near $p_c \\approx 0.22$, inside the superconducting dome, where $T_c$ is still about 70 K.","Quantum critical nematic fluctuations are a candidate source of the pairing interaction for high-$T_c$ superconductivity near optimal doping.","The strange-metal $T$-linear resistivity and the carrier-density change observed near the pseudogap critical point may have a common origin in nematic quantum criticality.","The charge-density-wave order observed inside the pseudogap phase may be stabilised by the enhanced nematic fluctuations reported here."],"supporting_citations":[{"why":"Established elastoresistance as the probe of nematic susceptibility and demonstrated its divergence in an iron-based superconductor.","marker":"[9]"},{"why":"Showed Curie-Weiss nematic susceptibility and its interpretation as nematic quantum critical signatures in Fe-based superconductors.","marker":"[10]"},{"why":"Provided the comparison case of a nonmagnetic nematic QCP in FeSe₁₋ₓSₓ, including the low-temperature deviation from Curie-Weiss near the QCP.","marker":"[15]"},{"why":"Gave thermodynamic evidence for a nematic transition at the pseudogap onset in YBa₂Cu₃O_y, the precedent this paper extends.","marker":"[4]"},{"why":"Theory of lattice effects on nematic quantum criticality used to explain the gap between T_nem and T_0.","marker":"[16]"},{"why":"Theory that nematic quantum critical fluctuations can drive superconductivity, connecting the observation to pairing.","marker":"[24]"},{"why":"Reported the change of carrier density at the pseudogap critical point, locating p_c independently.","marker":"[5]"},{"why":"Found quasiparticle mass enhancement near optimal doping, supporting a quantum critical point at p_c.","marker":"[6]"}],"fun_headline_variants":["Nematic QCP at pseudogap end links to high-Tc","Pseudogap critical point reveals nematic quantum criticality","Divergent nematic susceptibility signals pseudogap QCP","Cuprate pseudogap instability is a nematic critical point","Nematic order diverges near cuprate pseudogap end"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument assumes that the Weiss temperature $T_0$ extracted from high-temperature Curie-Weiss fits continues to mark the zero-temperature nematic instability at every doping, and that the low-temperature deviation from Curie-Weiss at $p = 0.2$ is a quantum-critical effect rather than a real finite-temperature nematic transition; the measurements only reach down to $T_c \\sim 70$ K, so the divergence to $T = 0$ is inferred by extrapolation.","fun_headline_variants_meta":{"raw":{"variants":["Nematic QCP at pseudogap end links to high-Tc","Pseudogap critical point reveals nematic quantum criticality","Divergent nematic susceptibility signals pseudogap QCP","Cuprate pseudogap instability is a nematic critical point","Nematic order diverges near cuprate pseudogap end"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000412,"raw_usage":{"total_tokens":2239,"prompt_tokens":1159,"completion_tokens":1080,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":775,"completion_tokens_details":{"reasoning_tokens":992}},"tokens_in":775,"tokens_out":1080,"duration_ms":10418,"temperature":1.0,"reasoning_tokens":992,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T12:23:51.410067+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the nematic susceptibility of (Bi,Pb)2212 at $p = 0.2$ down to millikelvin temperatures while suppressing superconductivity with a high magnetic field: if $|\\chi_{\\rm nem} - \\chi_0|^{-1}$ fails to extrapolate to zero or develops a kink at a finite temperature, the claimed nematic quantum critical point is falsified.","supporting_citations":[{"cited_title":"-H., Kuo, H","cited_arxiv_id":null,"evidence_quote":"Established elastoresistance as the probe of nematic susceptibility and demonstrated its divergence in an iron-based superconductor."},{"cited_title":"-H., Chu, J","cited_arxiv_id":null,"evidence_quote":"Showed Curie-Weiss nematic susceptibility and its interpretation as nematic quantum critical signatures in Fe-based superconductors."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provided the comparison case of a nonmagnetic nematic QCP in FeSe₁₋ₓSₓ, including the low-temperature deviation from Curie-Weiss near the QCP."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gave thermodynamic evidence for a nematic transition at the pseudogap onset in YBa₂Cu₃O_y, the precedent this paper extends."},{"cited_title":"& Garst, M","cited_arxiv_id":null,"evidence_quote":"Theory of lattice effects on nematic quantum criticality used to explain the gap between T_nem and T_0."},{"cited_title":"& Kivelson, S","cited_arxiv_id":null,"evidence_quote":"Theory that nematic quantum critical fluctuations can drive superconductivity, connecting the observation to pairing."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reported the change of carrier density at the pseudogap critical point, locating p_c independently."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Found quasiparticle mass enhancement near optimal doping, supporting a quantum critical point at p_c."}],"review_version":1}