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REVIEW 4 major objections 4 minor 33 references

Divergent nematic susceptibility near the pseudogap critical point in a cuprate superconductor

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 1908.07167 v1 pith:3ESPBG3N submitted 2019-08-20 cond-mat.supr-con cond-mat.str-el

K. Ishida , S. Hosoi , Y. Teramoto , T. Usui , Y. Mizukami , K. Itaka , Y. Matsuda , T. Watanabe
show 1 more author
T. Shibauchi
This is my paper · ORCID
classification cond-mat.supr-concond-mat.str-el PACS 74.72.-h74.25.Dw71.27.+a
keywords nematicsusceptibilityelastoresistancepseudogapquantumcriticalpointcupratesuperconductorsBi2212electronicnematicityCurie-Weisslaw
topics High-Temperature Superconductivity
open problems High-Temperature Superconductivity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

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.

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 (4)
  1. [§3, Fig. 3f-j and Eq. (1)] 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.
  2. [Fig. 3d,i and the discussion following it] 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.
  3. [Fig. 4b and the discussion of electron-lattice coupling] 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.
  4. [Figs. 3 and 4] 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.
minor comments (4)
  1. [Main text, paragraph on the pseudogap phase] The word 'psuedo-gap' appears in the sentence 'or some secondary effect of the psuedo-gap' and should be corrected to 'pseudogap'.
  2. [Fig. 3 caption] 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.
  3. [Methods, elastoresistance section] 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.
  4. [Fig. 4b] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the nematic susceptibility is directly measured, and the QCP inference is an extrapolation from standard Curie-Weiss fits anchored to independent probes.

full rationale

The paper's derivation chain starts from a directly measured elastoresistance response (Fig. 1b,c; Methods), from which the nematic susceptibility is defined as dη/dε without assuming the pseudogap or the QCP. The Curie-Weiss form χnem = χ0 + λ/(a(T-T0)) (Eq. 1) is a standard fitting form; T0 and χ0 are parameters extracted from the high-temperature data, and the sign change of T0 near p≈0.2 is a fitted result, not a quantity that is then 'predicted' from itself. The identification of Tnem with T* is anchored to independent ARPES, SIS tunneling, STS, and Raman determinations (Fig. 4a), so the claim that the pseudogap onset is a nematic transition is an external comparison, not a self-referential definition. The one self-citation [15] (Hosoi et al., PNAS 2016) is used only as an empirical analogy from FeSe1-xSx data to interpret the low-temperature downturn at p=0.20; that prior data set is external to the present fitted values and is not being used as a uniqueness theorem. The ambiguity at p=0.20—whether the downturn signals a QCP or a finite-T transition below Tc—is a genuine extrapolation and underdetermination risk, but the paper does not assume its conclusion in constructing χnem or in defining T0. No derivation step reduces, by the paper's own equations or by a load-bearing self-citation, to its own inputs.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the domain interpretation of the elastoresistance signal as an electronic nematic susceptibility, the volume-preserving strain correction, and the use of Curie-Weiss fits with a free Weiss temperature. The QCP is inferred from the fitted T0 crossing zero, not from a direct observation of divergent susceptibility at T = 0.

free parameters (3)
  • A = λ/a, Curie-Weiss amplitude = not reported; doping dependent
    Each χ_nem(T) curve is fit to χ0 + A/(T - T0); amplitude is a free parameter per sample (Eq. 1).
  • T0, Weiss temperature = not reported numerically; changes sign near p = 0.2
    Extracted from linear extrapolation of 1/|χ_nem - χ0| to zero (Fig. 3f-j); the sign change is used to locate the QCP.
  • χ0, temperature-independent offset = not reported
    Free parameter in the Curie-Weiss fits; includes intrinsic piezoresistive background.
assumptions (5)
  • domain assumption The elastoresistance coefficient dη/dε directly measures the electronic nematic susceptibility.
    Definition used in iron-based superconductors (refs 9,10); requires that strain couples linearly to the nematic order parameter and that other resistivity contributions are negligible.
  • domain assumption The sample volume is preserved under strain, so η ≈ ΔR/R - 2ε.
    Stated in Methods; if the glued thin sample does not deform affinely or volume changes, the extracted χ_nem is biased.
  • domain assumption A kink in χ_nem(T) indicates a second-order nematic phase transition at T_nem.
    Inferred by analogy with the structural/nematic transition in Fe-based superconductors; no direct thermodynamic measurement is presented.
  • domain assumption The nematic transition temperature T_nem coincides with the pseudogap onset T* reported by other spectroscopies.
    The paper overlays its T_nem on literature T* points; this assumes the pseudogap transition is the same as the nematic transition.
  • domain assumption The linear extrapolation of T* to zero at p_c ~ 0.22 is valid.
    The T* line is only measured down to finite temperatures; the QCP claim depends on this extrapolation (Fig. 4a).

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Cite this review

Pith. "Pith review of Divergent nematic susceptibility near the pseudogap critical point in a cuprate superconductor." pith.science (2026). https://pith.science/paper/3ESPBG3N

@misc{pith2026190807167,
  author       = {Pith},
  title        = {Pith review of: Divergent nematic susceptibility near the pseudogap critical point in a cuprate superconductor},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3ESPBG3N}},
  note         = {Machine review of arXiv:1908.07167}
}
read the original abstract

Superconductivity is a quantum phenomenon caused by bound pairs of electrons. In diverse families of strongly correlated electron systems, the electron pairs are not bound together by phonon exchange but instead by some other kind of bosonic fluctuations. In these systems, superconductivity is often found near a magnetic quantum critical point (QCP) where a magnetic phase vanishes in the zero-temperature limit. Moreover, the maximum of superconducting transition temperature Tc frequently locates near the magnetic QCP, suggesting that the proliferation of critical spin fluctuations emanating from the QCP plays an important role in Cooper pairing. In cuprate superconductors, however, the superconducting dome is usually separated from the antiferromagnetic phase and Tc attains its maximum value near the verge of enigmatic pseudogap state that appears below doping-dependent temperature T*. Thus a clue to the pairing mechanism resides in the pseudogap and associated anomalous transport properties. Recent experiments suggested a phase transition at T*, yet, most importantly, relevant fluctuations associated with the pseudogap have not been identified. Here we report on direct observations of enhanced nematic fluctuations in (Bi,Pb)2Sr2CaCu2O8+d by elastoresistance measurements, which couple to twofold in-plane electronic anisotropy, i.e. electronic nematicity. The nematic susceptibility shows Curie-Weiss-like temperature dependence above T*, and an anomaly at T* evidences a second-order transition with broken rotational symmetry. Near the pseudogap end point, where Tc is not far from its peak in the superconducting dome, nematic susceptibility becomes singular and divergent, indicating the presence of a nematic QCP. This signifies quantum critical fluctuations of a nematic order, which has emerging links to the high-Tc superconductivity and strange metallic behaviours in cuprates.

Figures

Figures reproduced from arXiv: 1908.07167 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
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Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

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