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Magnetic field reveals vanishing Hall response in the normal state of stripe-ordered cuprates

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read In the field-revealed normal state of stripe-ordered La-214 cuprates, the Hall coefficient is zero for all T below T0(H) ≈ (2–6) Tc0, and the paper argues this zero implies a dynamically generated particle–hole symmetry.

desk verdict Robust zero Hall effect in the stripe-ordered normal state is a real experimental advance, but the particle-hole symmetry conclusion is overreach. read the letter →

arxiv 1909.02491 v2 pith:7QK5VIOC submitted 2019-09-05 cond-mat.supr-con cond-mat.str-el

Zhenzhong Shi , P. G. Baity , J. Terzic , Bal K. Pokharel , T. Sasagawa , Dragana Popović This is my paper · ORCID
classification cond-mat.supr-concond-mat.str-el
keywords cupratesuperconductorsHallcoefficientparticle-holesymmetrystripeorderchargespinstripespair-densitywavehighmagneticfields
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

High magnetic fields can suppress superconductivity and expose the underlying normal state of copper-oxide superconductors, but what that state is has remained unresolved. This paper reports that in two stripe-ordered cuprates, La1.7Eu0.2Sr0.1CuO4 and La1.48Nd0.4Sr0.12CuO4, the Hall coefficient $R_H$ becomes zero as the temperature is lowered below $T_0(H) \sim (2$–$6)T_c^0$ and stays zero down to 0.019 K, throughout the field-revealed normal state above $H_{\rm peak}$. Because an accidental zero of the Hall coefficient over such a wide range of temperature and field is implausible in standard transport models, the authors conclude that this normal state has a dynamically generated particle–hole (charge-conjugation) symmetry. The result matters because it identifies a robust qualitative property of the normal state of cuprates with intertwined charge and spin stripes, and it sharply distinguishes these materials from other cuprates such as YBa2Cu3O6+x.

What carries the argument

The load-bearing probe is the Hall coefficient $R_H = \rho_{xy}/H$, obtained from the magnetic-field-antisymmetric part of the transverse voltage, used as a measure of the balance between electron-like and hole-like carriers: $R_H = 0$ means the Hall conductivity $\sigma_{xy}$ vanishes. The argument is carried by combining $R_H$ with the longitudinal resistivity $\rho_{xx}(T,H)$ and with previously established phase-diagram boundaries: $T_0(H)$ marks where the positive $R_H$ collapses to zero and coincides with the onset of phase fluctuations, where the normal-state sheet resistance per layer crosses the quantum resistance $R_Q = h/(2e)^2$; $H_{\rm peak}(T)$ marks the crossover from positive to negative magnetoresistance and is identified with the upper critical field; and the negative $R_H$ region at lower fields is identified as vortex motion through the scaling $\rho_{xx}^2/\rho_{xy} \propto H$. This combination lets the authors separate ordinary vortex-Hall physics from the normal-state zero and attribute $R_H = 0$ above $H_{\rm peak}$ to charge-conjugation symmetry.

What would settle it

Measure the Nernst coefficient, or the out-of-plane versus in-plane conductivity anisotropy, in the same samples at fields above $H_{\rm peak}$ and temperatures below $T_0$: a finite Nernst signal or a field-dependent anisotropy would reveal surviving superconducting-phase fluctuations, breaking the link between $R_H = 0$ and particle-hole symmetry. Conversely, resolving two compensated Fermi-surface pockets by quantum oscillations above $H_{\rm peak}$ would confirm the equal-electron/hole-pocket picture.

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Extended reading notes

Core claim

The central discovery is that $R_H = 0$ is a property of the entire normal-state phase, not a fine-tuned crossing point. In both materials, the positive, roughly field-independent Hall coefficient at high temperature drops to zero at $T_0(H)$; the drop does not depend on $H$, and $T_0(H)$ is almost flat, staying near $(2$–$3)T_c^0$ in the La-Eu compound and near $6T_c^0$ in the La-Nd compound. Below $T_0$, for fields above $H_{\rm peak}(T)$ — the boundary identified with the upper critical field by the companion transport studies and by the field-independence of the interlayer anisotropy — $R_H$ remains zero down to the lowest measured temperature, 0.019 K. At lower fields, inside the vortex-liquid regime, $R_H$ becomes negative and later returns to zero as vortex motion freezes; the vortex contribution is independently confirmed by the scaling $\rho_{xx}^2/\rho_{xy} \propto H$. Since the normal state shows no superconducting remnants, the zero Hall coefficient cannot be explained by Cooper pairs; the paper concludes that it must come from an approximate particle-hole symmetry that is dynamically generated, with equal electron and hole response, a property unique to stripe-ordered cuprates and not present in, for example, YBa2Cu3O6+x.

Load-bearing premise

The load-bearing premise is that the field $H_{\rm peak}(T)$ is indeed the upper critical field — the highest field at which superconductivity can survive — so that above it no superconducting correlations remain; if remnants persisted, the zero Hall coefficient could be produced by Cooper pairs rather than by particle-hole symmetry.

Editorial extensions

If this is right

  • A correct theory of the cuprate normal state must reproduce a phase in which $\sigma_{xy} = 0$ over a wide range of $T$ and $H$ while $\sigma_{xx}$ remains nonzero and weakly insulating-like.
  • The zero-$R_H$ state is a phase property: it persists from onset temperatures a few times $T_c^0$ down to 0.019 K in two compounds, ruling out fine-tuned band-structure cancellations.
  • Superconducting pairs are ruled out as the cause of the zero in the normal state, because no vortex, Cooper-pair, or pair-density-wave signal survives above $H_{\rm peak}$; particle-hole symmetry is the remaining explanation.
  • The pair-density-wave model, which attributes a zero Hall effect to pairs surviving inside charge stripes, applies to compounds such as La1.875Ba0.125CuO4 but not to the materials studied here, where no pairs survive.
  • The difference from YBa2Cu3O6+x and YBa2Cu4O8 shows that the emergent particle-hole symmetry is tied to static spin and charge stripes rather than to cuprate superconductivity generally.

Reading between the lines

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

  • A natural extension, not developed in the paper: if $R_H = 0$ arises from equal electron and hole populations, the Seebeck and Nernst coefficients should show systematic sign and cancellation behavior in the same $T$–$H$ region, offering a transport-level check.
  • The weakly field-dependent $T_0(H)$ suggests that $R_H = 0$ is a property of the zero-field ground state, so one could search for quantum oscillations from two compensated Fermi-surface pockets at fields well above $H_{\rm peak}$; detecting a single hole pocket would speak against the equal-population picture.
  • Whether static stripe order is the essential ingredient could be tested by measuring the same Hall protocol in La-214 compounds where stripe correlations are weakened by pressure or by moving doping away from $x = 1/8$; the zero-$R_H$ plateau should weaken or disappear if stripes are causal.
  • The combination of $\ln(1/T)$ resistivity and zero Hall response suggests that a useful next step is a theory in which charge-conjugation symmetry is emergent yet the longitudinal conductivity remains anomalous, a direction the paper points to only briefly.
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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

3 major / 5 minor

Summary. This paper reports Hall-effect measurements on two stripe-ordered cuprate families, La1.7Eu0.2Sr0.1CuO4 and La1.48Nd0.4Sr0.12CuO4, over an extended range of temperature (down to 0.019 K) and perpendicular magnetic field (up to 31 T). The authors find that the Hall coefficient RH is positive and nearly field-independent at high temperature, drops to zero at a weakly field-dependent temperature T0(H) ~ (2–6)Tc0, and remains zero for all T < T0(H) in the high-field regime H > Hpeak, which they identify with the upper critical field Hc2. At lower fields, RH becomes negative in a regime attributed to vortex motion, and the data are used to construct a T–H phase diagram. The central claim is that RH = 0 is a robust property of the field-revealed normal state of stripe-ordered cuprates and that it implies a dynamically generated charge-conjugation (particle-hole) symmetry, in contrast to other cuprates such as YBa2Cu3O6+x.

Significance. If the experimental observation is correct, it is a striking and potentially important result: it identifies a new property of the normal state of stripe-ordered cuprates, distinguishes these materials from other cuprate families, and provides a strong constraint on theories of intertwined orders. The measurements appear careful: the authors use multiple magnets and cryostats, check consistency between runs, ensure linear response by comparing excitation currents, and extract RH from antisymmetrized Hall voltages. The paper also gives a useful phase diagram for two closely related compounds. The strongest part is the direct observation of RH consistent with zero over a wide T–H region; the weakest part is the inference from that observation to a dynamically generated particle-hole symmetry, which is not uniquely required by the data.

major comments (3)
  1. [Main text, 'The remaining, most intriguing question…' (p. 8–9) and Fig. 1] The conclusion that RH = 0 in the field-revealed normal state is uncontaminated by superconducting correlations depends on identifying Hpeak(T) with Hc2(T) and on the assertion that no vortices, Cooper pairs, or pair-density wave survive for H > Hpeak. This boundary is imported from the authors' companion preprints (refs 12 and 13) via non-Ohmic transport and interlayer-anisotropy measurements on the same samples; it is not independently established in the present manuscript. The Hall data alone cannot exclude pair contributions above Hpeak; indeed, RH = 0 is also observed in the viscous vortex-liquid regime H < Hpeak (Fig. S1B), so the interpretation hinges entirely on the imported boundary. If superconducting remnants persist above Hpeak, the zero Hall response could be explained by the same pair-related mechanism invoked for La1.875Ba0.125CuO4 (ref. 33), and no normal-state particle-hole symmetry follows. The authors should either reproduce the relevant control measurements or state explicitly that the normal-state designation is inherited from refs 12 and 13 and discuss how the central claim would be affected if that identification fails.
  2. [Abstract and p. 10, concluding paragraph] The claim that RH = 0 'has to imply that charge conjugation symmetry is dynamically generated' overreaches what the transport data can establish. A compensated two-band Fermi surface with equal electron and hole densities, which is a natural consequence of stripe-induced Fermi-surface reconstruction, gives RH = 0 identically without any dynamical symmetry. The paper itself acknowledges that electron pockets would imply n_e = n_h. To sustain the stronger conclusion, the authors would need to rule out this conventional two-band compensation and other kinematic mechanisms, or reframe the conclusion as an interpretive possibility rather than a logical necessity. As written, the phrase 'In standard models, RH can only vanish accidentally' is an assertion that conflicts with the paper's own two-band discussion.
  3. [Fig. 2, Fig. S2, and Fig. 3] At the lowest temperatures, the error bars on RH are large, as the Fig. 2 caption attributes to the extremely small excitation currents needed to remain in the linear-response regime. The data are consistent with RH = 0 but also with a small nonzero value. The paper would be strengthened by a quantitative upper bound on |RH| (or, equivalently, on the apparent carrier density) in the normal-state region H > Hpeak for T < T0, with statistical and systematic uncertainties. Without such a bound, 'remains zero' should be softened to 'is zero within experimental resolution'.
minor comments (5)
  1. [Title and abstract] The title uses 'zero Hall response' while the abstract says 'vanishing Hall response'; please use one formulation consistently.
  2. [p. 3, first paragraph] 'unprecendented' should be 'unprecedented'.
  3. [References 12 and 13] Refs 12 and 13 are cited as preprints; if published versions are now available, they should be cited instead.
  4. [Fig. 1 and main text, 'h/4e2' notation] Fig. 1 is dense; the numerous boundary curves and shaded regions are hard to distinguish, especially in grayscale; consider distinct line styles and a legend. Also, 'h/4e2' should be defined at first use as h/(2e)^2.
  5. [p. 10, 'In standard models…'] The sentence 'In standard models, RH can only vanish accidentally' needs a supporting reference or a derivation; as written it is an unsupported assertion.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central Hall measurement is direct, and the normal-state boundary is an empirical input from companion work, not a fitted prediction.

full rationale

The paper's central claim is an experimental observation: the Hall coefficient vanishes in the field-revealed normal state of two stripe-ordered cuprates over a wide range of temperature and field. No model parameters are fitted to the Hall data, and no equation is defined in terms of the conclusion. The only potentially load-bearing external input is the identification of the normal state with H > Hpeak ≈ Hc2, which is taken from the authors' companion preprints (refs 12 and 13) based on magnetoresistance, non-Ohmic transport, and interlayer anisotropy measurements on the same samples. That identification is an empirical input, not a quantity derived from or equivalent to the Hall result; the Hall data themselves are not used to define Hpeak. If the companion work were incorrect, the interpretation would be weakened, but that is a correctness or verification risk rather than a circular reduction. Similarly, the inference that RH = 0 'has to imply' dynamically generated charge-conjugation symmetry is an interpretive step made because the authors argue that standard accidental mechanisms are excluded; it is not a derivation of the measured transport from that symmetry. No uniqueness theorem is invoked, no ansatz is smuggled in via self-citation, and no known result is merely renamed. Therefore no circular step can be exhibited, and the honest finding is no significant circularity.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No free parameters are fitted in this experimental paper; T0(H), Hpeak, and R_H are measured quantities. No new entities are introduced; the interpretation invokes the existing concept of particle-hole symmetry. The main load-bearing axioms are the normal-state boundary from companion papers and the vortex scaling attribution.

assumptions (4)
  • domain assumption For H > Hpeak(T), the system is in the normal state with no superconducting correlations (no vortices, no Cooper pairs, no PDW).
    Central to excluding a superconducting origin of R_H=0; established by companion papers (refs 12,13) on the same samples, not independently reproduced here.
  • domain assumption The vortex contribution to Hall resistivity in the vortex liquid regime follows the scaling rho_xx^2/rho_xy proportional to H (Vinokur et al., ref 40).
    Used to attribute the negative R_H at H < Hpeak to vortex motion (Supplementary Text, Fig. S4).
  • standard math The Hall coefficient in the high-field normal state can be interpreted via R_H = rho_xy/H and single-band Hall number n_H = 1/(e R_H).
    Standard definition used throughout; the paper discusses its limitations and uses it only qualitatively.
  • ad hoc to paper If R_H=0 over a wide T-H range and superconductivity is absent, then charge conjugation (particle-hole) symmetry is dynamically generated.
    This is the paper's interpretive conclusion, not a proven theorem; the paper itself notes R_H can vanish accidentally in standard models.

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Pith. "Pith review of Magnetic field reveals vanishing Hall response in the normal state of stripe-ordered cuprates." pith.science (2026). https://pith.science/paper/7QK5VIOC

@misc{pith2026190902491,
  author       = {Pith},
  title        = {Pith review of: Magnetic field reveals vanishing Hall response in the normal state of stripe-ordered cuprates},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7QK5VIOC}},
  note         = {Machine review of arXiv:1909.02491}
}
abstract

The origin of the weak insulating behavior of the resistivity, i.e. $\rho_{xx}\propto\ln(1/T)$, revealed when magnetic fields ($H$) suppress superconductivity in underdoped cuprates has been a longtime mystery. Surprisingly, the high-field behavior of the resistivity observed recently in charge- and spin-stripe-ordered La-214 cuprates suggests a metallic, as opposed to insulating, high-field normal state. Here we report the vanishing of the Hall coefficient in this field-revealed normal state for all $T<(2-6)T_{\mathrm{c}}^{0}$, where $T_{\mathrm{c}}^{0}$ is the zero-field superconducting transition temperature. Our measurements demonstrate that this is a robust fundamental property of the normal state of cuprates with intertwined orders, exhibited in the previously unexplored regime of $T$ and $H$. The behavior of the high-field Hall coefficient is fundamentally different from that in other cuprates such as YBa$_2$Cu$_3$O$_{6+x}$ and YBa$_2$Cu$_4$O$_{8}$, and may imply an approximate particle-hole symmetry that is unique to stripe-ordered cuprates. Our results highlight the important role of the competing orders in determining the normal state of cuprates.

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    V. M. Vinokur, V. B. Geshkenbein, M. V. Feigel’man, G. Blatter, Scaling of the Hall resistivity in high-Tc superconductors. Phys. Rev. Lett. 71, 1242–1245 (1993). Acknowledgments We thank G. Saraswat for experimental assistance. Funding: This work was supported by NSF Grants N...

    1993

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.