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Charge order in the Pr substituted YBa$_2$Cu$_3$O$_7$ from high-field Hall effect measurements

T0 review · 3 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read Pr-substituted YBCO, a more disordered cousin of YBCO with a different doping route, shows the same low-temperature Hall-effect sign change that in pure YBCO signals Fermi-surface reconstruction by two-dimensional charge order—evidence that

desk verdict New high-field Hall data show a YBCO-like sign change in Pr-YBCO, but the charge-order attribution rests on an untested field-growth assumption; worth refereeing. read the letter →

arxiv 2512.16423 v1 pith:5ZYJ7WDT submitted 2025-12-18 cond-mat.supr-con cond-mat.str-el

C. M. Duffy , M. Altangerel , S. Badoux , D. Vignolles , T. Oustric , C. M. Moir , Keke Feng , A. Frano
show 3 more authors
M. B. Maple L. Taillefer C. Proust
This is my paper · ORCID
classification cond-mat.supr-concond-mat.str-el
keywords cupratesuperconductorschargeorderFermisurfacereconstructionHalleffectPr-YBCOhighmagneticfieldsunderdopedphasediagram
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

The paper tries to show that Pr-substituted YBCO, despite extra disorder and a different doping mechanism, hosts the same two-dimensional charge order and Fermi-surface reconstruction that are hallmarks of underdoped pure YBCO. It reports that the Hall coefficient of Pr-YBCO crystals changes sign at low temperature for higher-Tc samples (Pr content x = 0.2 and 0.35), with the sign-change temperature T0 falling as Tc falls, matching YBCO's behavior as hole doping varies. For lower-Tc samples (x = 0.4 and 0.45), the Hall coefficient stays positive, again like YBCO near the antiferromagnetic phase. The authors conclude that the phase diagrams of Pr-YBCO and YBCO are 'decidedly symmetric' and that the in-plane hole concentration, not the doping route, governs the electronic orders. A reader should care because the result extends charge-order physics to a more disordered, differently doped cuprate and sharpens the question of how much correlation length is needed to reconstruct a Fermi surface.

What carries the argument

The central observable is the Hall coefficient RH(T) measured in pulsed fields up to 65 T, and in particular the temperature T0 at which it changes sign. In the paper's interpretation, a sign change from positive to negative signals a Fermi-surface reconstruction in which a biaxial two-dimensional charge order with wavevectors (Qx,0) and (0,Qy) folds the large hole-like Fermi surface into small electron-like pockets at the nodes, giving a negative Hall response at low temperature. The comparison quantity is the same T0-versus-doping curve in pure YBCO, used as a fingerprint of charge-order-induced reconstruction. The short correlation length of the charge order in Pr-YBCO is the key tension

What would settle it

Measure quantum oscillations in a Pr-YBCO crystal with x = 0.2 or 0.35 at fields above the Hall sign change: observation of a low-frequency oscillation from a small electron pocket would support the charge-order-reconstruction claim, while its absence (or a hole-like pocket) would weaken it. Alternatively, resonant x-ray scattering on the same bulk crystals under high magnetic field could check whether the 2D charge-order correlation length grows from ~25-30 Å toward the ~80-100 Å scale that is associated with Fermi-surface reconstruction in YBCO.

Watch

Extended reading notes

Core claim

The central claim is that a temperature-dependent sign change in the Hall coefficient RH of Pr-YBCO at high magnetic fields (up to 65 T) is a signature of Fermi-surface reconstruction driven by two-dimensional charge order. For x = 0.2 and 0.35, RH falls sharply below ~100 K and crosses zero at a temperature T0 that decreases with increasing Pr content; for x = 0.4 and 0.45, RH remains positive. This pattern mirrors the doping dependence of RH in pure YBCO, where the negative low-temperature Hall effect is attributed to an electron pocket produced by biaxial charge order. The paper also finds that Pr-YBCO lacks the pronounced competition between charge order and superconductivity seen in YBC

Load-bearing premise

The argument rests on the assumption that the short-range two-dimensional charge correlations seen in Pr-YBCO thin films persist in the bulk crystals and grow enough under the 65 T field to reconstruct the Fermi surface; if they do not, the Hall sign change could have a different origin, such as antiferromagnetic reconstruction.

Editorial extensions

If this is right

  • Underdoped Pr-YBCO should exhibit a small electron pocket in quantum oscillation experiments at high field, analogous to the pocket seen in YBCO and Hg-based cuprates.
  • The similarity of the T0(p) curves implies that the charge-order instability and the pseudogap scale in these cuprates are controlled by the plane hole density rather than by details of the charge reservoir.
  • Disorder and short correlation length suppress the competition between charge order and superconductivity, explaining the absence of a Tc plateau and an Hirr dip in Pr-YBCO.
  • The field may enhance the charge-order correlation length in Pr-YBCO, as it does in YBCO; this is a testable prediction.
  • The x >= 0.4 samples, with positive RH at all temperatures, are consistent with an antiferromagnetic reconstruction rather than charge-order reconstruction, preserving the YBCO analogy.

Reading between the lines

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

  • If the charge-order attribution holds, an immediate extension is that short-range correlations can reconstruct a Fermi surface in a bulk crystal once a magnetic field stiffens them; high-field x-ray scattering on bulk Pr-YBCO crystals would test this directly.
  • The claimed phase-diagram symmetry suggests that other isovalent or aliovalent substitutions that remove plane holes without changing the chain reservoir should reproduce the same T0(p) curve, giving a simple experimental fingerprint for future substitution studies.
  • The absence of an Hirr dip in Pr-YBCO could also be interpreted as the charge order being weaker or more fluctuating than in YBCO; if so, the lack of competition is not solely a disorder effect, a distinction that further transport or thermodynamic measurements on cleaner Pr-YBCO could resolve.
  • Should future ARPES on Pr-YBCO find the reconstructed electron pocket, that would confirm the Fermi-surface reconstruction mechanism directly rather than by Hall-effect analogy.
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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 / 4 minor

Summary. The paper reports high-field Hall-effect measurements on Pr_xY_{1-x}Ba2Cu3O7 crystals (x=0.2–0.45, Tc≈32–70 K). It finds a sign change of RH from positive to negative at low temperature for x=0.2 and 0.35, with T0 decreasing with decreasing Tc; for x=0.4 and 0.45 RH remains positive. By analogy with YBCO, the authors attribute this to a Fermi-surface reconstruction by 2D charge order and conclude the Pr-YBCO and YBCO phase diagrams are symmetric when disorder and different doping mechanisms are considered.

Significance. If the interpretation holds, the result extends charge-order-induced Fermi-surface reconstruction to a bulk cuprate with strongly suppressed correlation length and a distinct doping route, supporting the view that in-plane hole concentration controls electronic orders. The experimental core—two-polarity antisymmetrized Hall data across a doping series—is well executed, and the comparison with YBCO, Zn-YBCO, and Hg1201 is informative. The paper is transparent about its main assumption (field-induced growth of correlation length) and considers the AFM alternative. Its value lies in the dataset and the explicit formulation of a testable assumption, but the abstract's causal claim exceeds the direct evidence.

major comments (3)
  1. [§V.2, §V.4, Abstract] The attribution of the negative low-T RH to 2D charge-order-induced FSR rests on an explicit, untested assumption. §V.2 states 'we cannot exclude that it increases under a strong magnetic field' and §V.4 says 'If we assume that the correlation length grows...'. The only CO evidence is thin-film REXS/GIXD with ξ ≈ 25–30 Å (refs [12,13]); no x-ray or QO data exist for the bulk crystals measured here. If ξ does not grow under field, the sign change could reflect the AFM-type FSR invoked for x ≥ 0.4 (§IV). The abstract's 'indicating the presence of 2D charge order' is therefore not supported; the conclusion should be softened or supplemented with a quantitative estimate.
  2. [§II, Fig. 6, §VI] The 'decidedly symmetric' phase-diagram claim is partly built into the comparison because Pr-YBCO samples are not assigned a hole doping p. §II says 'it is not possible to label our samples with a specific hole doping p', yet Fig. 6 plots T0 versus 'doping p' without explaining the Tc-to-p conversion. Since Pr suppresses Tc through pair-breaking and disorder as well as carrier depletion, equal Tc does not imply equal p. The conclusion should be supported by an explicit calibration or restricted to a Tc-based qualitative comparison.
  3. [§IV, Fig. 5, §V.4] The absence of canonical CO–SC competition is acknowledged in §IV, and Fig. 5 shows no Tc plateau or Hc2 dip. The response that disorder smears the competition is plausible but not demonstrated; Hg1201 with similar ξ still shows a Tc anomaly. The pressure evidence (ref [63]) is indirect. This part should be framed as a prediction for future x-ray/thermodynamic tests, not as an established consequence.
minor comments (4)
  1. [Fig. 2/3] T0 values lack uncertainties; add estimates from duplicate samples and field/temperature resolution.
  2. [§I vs §V.2] 2D CO correlation length in YBCO is given as 'up to 60 Å' and later '80–100 Å'; reconcile.
  3. [Table I] Text says six crystals but figures show four; clarify that duplicates gave identical results.
  4. [Title/Abstract] Wording suggests direct charge-order measurement; suggest 'signatures of charge-order-induced Fermi-surface reconstruction'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Hall measurements are new data compared against external benchmarks, and the acknowledged correlation-length assumption is a validity caveat, not an input-by-construction.

full rationale

The derivation chain is: (i) measure R_H(T,B) in Pr-YBCO crystals; (ii) observe a low-temperature sign change with a doping-dependent T0; (iii) compare with R_H data in YBCO, Hg1201, and Zn-YBCO from published experiments; (iv) attribute the sign change to Fermi-surface reconstruction by 2D charge order, citing prior thin-film REXS evidence for short-range 2D CO in Pr-YBCO; and (v) interpret the resulting phase-diagram similarity. None of these steps defines its conclusion as its input. The Hall sign change is a directly measured observable, not a parameter fitted to the conclusion. The comparisons to YBCO and other cuprates are external experimental datasets, including prior work by the same groups, but those datasets are independently reproducible measurements and are not assumed to already contain the present result. The paper explicitly flags its main vulnerability: the 25–30 Å correlation length is three times smaller than in YBCO, and the inference requires that the correlation length grow under high magnetic field (§V.2: 'we cannot exclude that it increases under a strong magnetic field'; §V.4: 'If we assume that the correlation length grows at high magnetic field in order to reconstruct the FS'). This is a stated physical assumption that weakens the inference, but it is not circular: the assumption is not derived from the Hall data, nor is the Hall data used to prove the assumption. The use of Tc as a doping proxy is also stated explicitly (§II: 'not possible to label our samples with a specific hole doping p... We therefore use Tc as a measure of sample doping'), and while it shapes the comparison, the observed trend is not forced—the data could have shown no sign change, a different T0(x) relation, or a different ordering. No equation or construction in the paper reduces a predicted quantity to its fitted input, and no load-bearing conclusion rests solely on a self-citation chain. Accordingly, no circular step is identified.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The paper fits no numerical model, so free_parameters is empty; the closest items to parameters are the assumed Tc→p mapping (listed as an axiom) and the linear extrapolation of RH from 30 T to 65 T above 100 K (§III), a data-treatment choice rather than a fitted value. The load-bearing premises are: (i) identity of the Tc(p) relation between YBCO and Pr-YBCO; (ii) the field-standard Hall-sign-change→electron-pocket→FSR interpretation; (iii) the causal attribution to 2D charge order from thin-film REXS rather than from these crystals; (iv) the assumed high-field growth of the correlation length — speculative; (v) chain oxygen near y=7. No new entities are postulated.

assumptions (6)
  • domain assumption Tc is a valid measure of in-plane hole doping in Pr-YBCO, with the same Tc(p) relation as YBCO.
    Section II: 'not possible to label our samples with a specific hole doping p... We therefore use Tc as a measure of sample doping and to facilitate comparison with YBCO.' Underlies Fig. 6 and the 'phase diagrams decidedly symmetric' conclusion.
  • domain assumption A low-temperature sign change of RH in underdoped cuprates is a reliable fingerprint of Fermi-surface reconstruction with an electron pocket.
    Section IV: 'The sign reversal of the Hall effect is a signature of the presence of charge order and of an electron pocket in the reconstructed FS', following the standard interpretation used for YBCO (ref. [30]) and Hg cuprates (refs [20, 31]).
  • domain assumption The FSR in Pr-YBCO is caused specifically by 2D charge order rather than by AFM order or another order.
    Section V.2: 'it is natural to conclude by comparison that the FSR reported here is a consequence of such 2D charge order.' Grounded only in thin-film REXS (refs [12,13]); these crystals are not x-rayed, and the paper invokes AFM-type reconstruction for x≥0.4 (§IV).
  • ad hoc to paper The 2D charge-order correlation length in Pr-YBCO grows under high magnetic field sufficiently to reconstruct the Fermi surface.
    Section V.2: 'we cannot exclude that it increases under a strong magnetic field'; Section V.4: 'If we assume that the correlation length grows at high magnetic field in order to reconstruct the FS...' — an unverified premise needed to reconcile ξ≈25–30 Å with the observed reconstruction.
  • domain assumption The chains are fully oxygen-loaded (y≈7) in all measured crystals; small deviations do not affect the results.
    Section II: 'To isolate the effect of Pr only, the chains were fully loaded with oxygen (y=7). Small deviations from optimal oxygen doping are possible, but are not responsible for the results reported herein.'
  • domain assumption Two-field-polarity symmetrization/antisymmetrization correctly isolates the Hall signal from c-axis contamination in ρxx.
    Section II: 'c-axis contamination was observed in the resistivity ρxx measurement but does not alter the Hall measurements due to the antisymmetrization' — a standard but load-bearing data-treatment premise.

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Cite this review

Pith. "Pith review of Charge order in the Pr substituted YBa$_2$Cu$_3$O$_7$ from high-field Hall effect measurements." pith.science (2026). https://pith.science/paper/5ZYJ7WDT

@misc{pith2026251216423,
  author       = {Pith},
  title        = {Pith review of: Charge order in the Pr substituted YBa$_2$Cu$_3$O$_7$ from high-field Hall effect measurements},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5ZYJ7WDT}},
  note         = {Machine review of arXiv:2512.16423}
}
abstract

The mechanism of doping in the composite Pr$_x$Y$_{1-x}$Ba$_2$Cu$_3$O$_{7-\delta}$ (Pr-YBCO) system is distinct from that of pure YBCO, offering a means to explore the requirements for the numerous electronic orders appearing in the phase diagram. One such example is the ubiquitous 2D charge order and concomitant Fermi surface reconstruction in underdoped YBCO. Here, using magnetotransport and Hall effect measurements, we find signatures of a Fermi surface reconstruction similar to that in pure YBCO indicating the presence of 2D charge order in Pr-YBCO. Additionally, we find that the phase diagrams of Pr-YBCO and YBCO are decidedly symmetric despite the additional disorder in the former and the distinction between hole depletion through Pr substitution and through O reduction. This indicates that while the mechanism of doping differs, the amount of charge carriers in the planes is the most important factor governing the electronic orders in these systems.

Figures

Figures reproduced from arXiv: 2512.16423 by the authors.

Figure 1
Figure 1. FIG. 1. The phase diagram of Pr-YBCO. The yellow region [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Comparison of the temperature of the sign rever [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

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