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Doping dependence of the low temperature planar carrier density in overdoped YBa$_2$Cu$_3$O$_{7-\delta}$

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The sharp Hall jump in overdoped YBCO softens once CuO chain conduction is removed, so the pseudogap endpoint may not be a quantum critical point.

desk verdict Solid new data, but the no-QCP claim rides on a chain-correction whose validation is in a missing supplement. read the letter →

arxiv 2506.14342 v1 pith:WOGAYRAN submitted 2025-06-17 cond-mat.supr-con

Rebecca Nicholls , Roemer Hinlopen , Jake Ayres , Tommy Kotte , Tobias Forster , Joonbum Park , Jeremy Sourd , Antony Carrington
show 1 more author
Nigel Hussey
This is my paper · ORCID
classification cond-mat.supr-con PACS 74.72.-h74.25.F71.18.+y
keywords cupratesuperconductorsHalleffectpseudogapquantumcriticalpointYBa2Cu3O7-deltaresistivityanisotropyFermisurfacehighmagneticfields
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

This paper claims that the sharp rise in the Hall carrier density of overdoped YBa$_2$Cu$_3$O$_{7-\delta}$ near the putative pseudogap endpoint $p^* \approx 0.19$ is not the full story: once the conduction of the CuO chains is accounted for, the planar carrier density rises gradually from $p$ at optimal doping toward $1+p$ only near the edge of the superconducting dome. Using pulsed fields up to 67 T, the authors measured the Hall coefficient and the in-plane resistivity anisotropy on the same detwinned crystals and extracted $n_{\mathrm{pl}} = n_{\mathrm{H}}(\rho_a/\rho_b)^{-1}$. They confirm a previously reported jump in $n_{\mathrm{H}}$, but find that $n_{\mathrm{pl}}$ at $p^*$ remains well below the full Fermi volume and shows no feature at $p^*$. If this is right, the popular reading of the Hall jump as evidence for a quantum critical point and Fermi-surface reconstruction at the pseudogap endpoint needs to be abandoned, and overdoped Y123 joins other cuprates in a common gradual crossover.

What carries the argument

The key object is the correction $n_{\mathrm{pl}} = n_{\mathrm{H}}(\rho_a/\rho_b)^{-1}$, derived from a parallel-resistor model of the CuO$_2$ planes shunted by quasi-1D CuO chains; it converts the measured Hall number into an estimate of the actual planar carrier density. The argument is carried by measuring both quantities on the same detwinned crystal at 50 K in pulsed fields up to 67 T, using standard anisotropic resistance extraction, and by checking the correction against a minimal Boltzmann transport model that includes two CuO$_2$ planes per unit cell, chain anisotropy, plane-chain hybridization in $k$-space and finite $\omega_c\tau$.

What would settle it

Quantum oscillation measurements on the same overdoped Y123 crystals at $p \gtrsim p^*$: if the oscillation-derived Fermi-surface volume already equals $1+p$ holes per CuO$_2$ plane at $p^*$, or any other direct measurement of $n_{\mathrm{pl}}$ that does not rely on the anisotropy correction returns the full Fermi volume there, the gradual-crossover claim is refuted.

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Extended reading notes

Core claim

The central claim is that in overdoped Y123 the $p$ to $1+p$ crossover in the planar carrier density is gradual rather than sharp. The measured $n_{\mathrm{H}}(50\,\mathrm{K})$ does rise sharply near $p^*$ as previously reported, but this rise is largely an effect of the quasi-1D CuO chains that shunt the Hall response; renormalising by the measured anisotropy gives $n_{\mathrm{pl}} \approx p$ at optimal doping and $n_{\mathrm{pl}} \approx 1+p$ only partially recovered by $p \approx 0.19$, with the full value reached only toward the end of the superconducting dome near $p \approx 0.3$. The authors therefore argue that the sharp Hall feature cannot be used as evidence for a conventional quantum critical point at $p^*$ or for a reconstructed Fermi surface, and that the Y123 data are consistent with the extended strange-metal crossover seen in Tl2201, Bi2201 and LSCO. They further show with a minimal Boltzmann transport model that the anisotropy correction is robust against known semiclassical corrections such as plane-chain hybridization and finite cyclotron motion.

Load-bearing premise

The conclusion rests entirely on the validity of $n_{\mathrm{pl}} = n_{\mathrm{H}}(\rho_a/\rho_b)^{-1}$; if plane-chain hybridization, incoherent conduction, or a Hall contribution not tied to $\rho_a/\rho_b$ breaks the parallel-resistor picture, the extracted planar density and the gradual crossover would change.

Editorial extensions

If this is right

  • If the gradual crossover is correct, the absence of any feature in $n_{\mathrm{pl}}$ across $p^*$ removes the main transport evidence for a conventional quantum critical point at the pseudogap endpoint.
  • The Y123 data fall onto the same quasi-linear $n_{\mathrm{pl}}(p)$ trend as Tl2201, Bi2201 and LSCO, implying a universal mechanism for carrier recovery across the overdoped strange-metal regime.
  • At optimal doping $n_{\mathrm{pl}} \approx p$, several times smaller than the estimated superfluid density, so a substantial part of the superconducting condensate must come from carriers that do not contribute to the normal-state Hall response.
  • The full Fermi volume is only recovered near the end of the superconducting dome, meaning the 'missing' holes persist through most of the overdoped region and correlate with $T_c$ and the low-temperature $T$-linear resistivity.
  • The apparent sharp rise in Nd-LSCO is likely dominated by the Lifshitz transition, where electron-like and hole-like Fermi-surface sections contribute opposite-sign Hall terms, rather than by pseudogap closure.

Reading between the lines

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

  • If the universal gradual crossover is real, other purported signatures of quantum criticality near $p^*$, such as thermodynamic or spectroscopic features tied to the pseudogap endpoint, may need re-reading as smooth crossovers rather than $T=0$ criticality.
  • The same anisotropy-correction analysis could be applied to published high-field Hall data on other chain-bearing cuprates, such as YBa$_2$Cu$_4$O$_8$, to test whether their extracted planar densities also fall on the common trend.
  • A sharper test would be to measure $n_{\mathrm{pl}}$ directly by quantum oscillations in overdoped Y123 near $p^*$; if the oscillation volume already equals $1+p$ there, the gradual crossover would be an artifact of the parallel-resistor correction.
  • Because the missing carriers track the superfluid density and $T_c$, an experiment that varies chain disorder at fixed doping (via oxygenation) could separate chain-shunting effects from a genuinely reduced planar carrier density.
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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. The paper reports simultaneous high-field measurements of the Hall coefficient and the in-plane resistivity anisotropy in seven detwinned overdoped YBa2Cu3O7-delta crystals (p = 0.16-0.19), and combines them with literature data. Using the relation n_pl = n_H (rho_a/rho_b)^{-1}, the authors extract a planar carrier density n_pl and claim that the sharp rise in n_H(p) observed by Badoux et al. is softened, so that the full Fermi volume n_pl = 1+p is only partially recovered at p*. They argue this disfavors a conventional quantum critical point at p* and reconciles Y123 with Tl2201, Bi2201, and LSCO.

Significance. If the central extraction is valid, the result is significant: it would remove one of the main transport-based pillars for a QCP at p* in Y123 and unify the doping evolution of the carrier density across several cuprate families. The paper has genuine strengths: it measures rho_a/rho_b and R_H on the same crystals, its raw R_H data agree with Badoux et al., and it explicitly acknowledges that the interpretation is critically dependent on the n_pl = n_H (rho_a/rho_b)^{-1} relation. The inclusion of a caveat is commendable, but the validation for that relation is not actually available in the submitted manuscript, which is a load-bearing gap.

major comments (4)
  1. [Before closing / Eq. n_pl = n_H (rho_a/rho_b)^{-1}] The central conclusion that the p to 1+p crossover is gradual and incomplete at p* rests entirely on the relation n_pl = n_H (rho_a/rho_b)^{-1}. The text itself says the interpretation is 'critically dependent' on this relation, and the only quantitative validation is said to be in Supplemental Material Ref. [22]. That supplement is not included in the arXiv submission and Ref. [22] is a placeholder ('Supplemental Material available at tbc.com'). The Boltzmann code repository [64] is cited, but the main text gives no parameter choices, outputs, or a comparison between the model and the measured rho_a/rho_b. Without this validation, the extraction of n_pl is an untested assumption, and the paper's headline claim cannot be assessed.
  2. [Fig. 5b / section on rho_a/rho_b] The Badoux et al. data are rescaled by a single anisotropy factor rho_a/rho_b = 1.8, which is the average of the four samples in this work with the most conductive chains. However, the paper itself emphasizes that rho_a/rho_b must be measured on each crystal because it varies strongly with chain disorder; two of the present samples with p = 0.170 have rho_a/rho_b about 1.35. The blue band in Fig. 5b only covers 1.5 <= rho_a/rho_b <= 2.1 and therefore excludes the lower measured values. If the actual chains in the Badoux crystals were less conductive, their n_pl points near p* could lie close to or above the 1+p line, which would erase the claimed partial recovery. A sensitivity analysis using rho_a/rho_b = 1.35, or a justification for why the Badoux crystals should have the highest-chain-conductivity ratio, is needed.
  3. [Fig. 5a/5b and Table I] One of the two points closest to p*, sample S7 at p = 0.191, does not have a measured n_H(50 K); because of contact failure the authors use n_H(80 K) from static field data, citing Badoux et al. This point is then plotted and included in the same doping-evolution comparison and in the linear fit in Fig. 5b. Since the claim concerns n_pl(50 K) and the text stresses the low-temperature behavior, the paper should either demonstrate that n_H(80 K) equals n_H(50 K) for this doping on an actual sample in this work, or exclude S7 from the fit and show the conclusion is unchanged.
  4. [Fig. 5b error bars] The reported uncertainties on n_pl are approximately +/-30%, which is comparable to the difference between the data points near p* and the 1+p line. For example, if n_pl near p* is about 0.8-1.0, a 30% error makes the deviation from 1+p (about 1.19) statistically marginal. The blue shaded region is explicitly described as 'not a definitive boundary', and the text uses phrases such as 'well below 1+p' without a quantitative statistical test. The paper should provide a confidence interval for the fitted n_pl at p* and show whether the lower bound of the data is still below 1+p.
minor comments (4)
  1. [Ref. [22]] Ref. [22] is listed as 'Supplemental Material available at tbc.com'; this placeholder must be replaced with a proper link or DOI before publication.
  2. [Table I] The table lists nominal Ca percentages while the text notes EDX shows 5-8% actual Ca in nominal 15% crystals; the reader would benefit from a statement of how the uncertainty in Ca content propagates into the assigned p values.
  3. [Fig. 5c] The comparison in Fig. 5c mixes n_pl values extracted at different temperatures for Y123, Tl2201, Bi2201, and LSCO; the caption should state the temperature at which each data set is evaluated.
  4. [p. 4, n_s estimate] The statement that n_s(0) = 0.87 is 'around 5 times larger than n_pl' assumes n_pl near 0.16-0.17; it would be clearer to quote the numerical n_pl value used for this comparison.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the n_pl extraction uses independently measured R_H and ρ_a/ρ_b, and the 1.8 rescaling of Badoux data is a fixed measured anisotropy value, not a fit to the 1+p target.

full rationale

The derivation is self-contained: the planar carrier density n_pl is obtained by combining two independently measured quantities—the Hall coefficient R_H and the resistivity anisotropy ρ_a/ρ_b—for the same crystals, with no parameter fitted to the target line n_pl = 1+p. The rescaling of the Badoux data uses a fixed anisotropy value ρ_a/ρ_b = 1.8, which is the measured average for the cleanest-chain crystals, and is varied over the range 1.5–2.1 without changing the conclusion; this is an assumption about sample transfer, not a fit to the desired outcome. The paper explicitly flags that the interpretation depends on the validity of n_pl = n_H(ρ_a/ρ_b)^-1 and refers to a Boltzmann check in a supplement that is not present in the arXiv version; that is a support and validity concern, not a circular step. Self-citations, e.g., Ref. [9] for the Bi2201 and Tl2201 data, are external measurements from the same group but are not the load-bearing basis for the Y123 conclusion, which rests on new data. No equation in the paper reduces to 1+p by construction, and the central claim is not forced by a fitted input.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The central analysis uses measured Hall values and measured anisotropy ratios, so the free-parameter count is low. The main hand-set input is the rescaling factor for literature data. The principal assumptions are the parallel-resistor relation and the applicability of semiclassical transport, both of which are plausible but only partially verified in the preprint.

free parameters (1)
  • Anisotropy rescaling factor for Badoux et al. data = 1.8 (sensitivity range 1.5-2.1)
    Applied to the literature n_H values because resistivity anisotropy was not measured in Ref. [10]. The value is chosen as the average of this work's nearly full-chain samples, and the blue band in Fig. 5b depends on this range.
assumptions (5)
  • domain assumption The parallel resistor model gives n_pl = n_H (ρ_a/ρ_b)^-1 for Y123
    This is the central analysis relation. The paper says the interpretation is critically dependent on it and defends it with a Boltzmann model in the Supplement (Ref. [22], code Ref. [64]).
  • domain assumption Semiclassical Boltzmann transport with a known Fermi surface and mean free path captures Hall and magnetotransport in overdoped Y123
    Used to argue that the 1/(ρ_a/ρ_b) rescaling is robust. The validation is described only in the Supplement and is not independently verifiable from the main text.
  • domain assumption R_H(80 K) approximates R_H(50 K) for sample S7
    Adopted from Ref. [10] because the 50 K Hall contacts failed for S7. This adds uncertainty to the single data point above p*.
  • domain assumption Hole doping p is determined by T_c via the empirical relation of Liang et al. with T_c^max = 93.8 K, also for Ca-substituted crystals
    All p values in Table I use this calibration. Calcium substitution may alter the T_c(p) relation, although the authors quote small uncertainties.
  • standard math n_H = V_cell/(2 e R_H) with two CuO2 planes per unit cell and constant V_cell = 174 Å^3
    Standard conversion from Hall coefficient to carrier number; the authors note lattice parameter changes below 2 percent are ignored.

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Pith. "Pith review of Doping dependence of the low temperature planar carrier density in overdoped YBa$_2$Cu$_3$O$_{7-\delta}$." pith.science (2026). https://pith.science/paper/WOGAYRAN

@misc{pith2026250614342,
  author       = {Pith},
  title        = {Pith review of: Doping dependence of the low temperature planar carrier density in overdoped YBa$_2$Cu$_3$O$_7-\delta$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WOGAYRAN}},
  note         = {Machine review of arXiv:2506.14342}
}
abstract

Whether a quantum critical point (QCP) demarcates the end of the pseudogap (PG) regime in hole-doped cuprates at a singular doping level $p^* \approx 0.19$ remains an open question. A crucial part of this puzzle is how the carrier density predicted by electronic structure calculations is recovered for $p > p^*$. Here, we use magnetic fields up to 67 T to suppress superconductivity down to 50 K, allowing simultaneous measurement of the low-temperature Hall number $n_{\mathrm{H}}$ and the in-plane resistivity anisotropy $\rho_a/\rho_b$ in overdoped Y$_{1-x}$Ca$_x$Ba$_2$Cu$_3$O$_{7-\delta}$ single crystals. We confirm a previous finding [Badoux et al., Nature 531, 210 (2016)] that $n_{\mathrm{H}}$(50 K) exhibits a sharp increase below $p^*$. Using the measured resistivity anisotropy, we extract the planar carrier density $n_{\mathrm{pl}} = n_{\mathrm{H}} (\rho_a/\rho_b)^{-1}$. The doping dependence of $n_{\mathrm{pl}}$(50 K) reveals two key findings: (i) at optimal doping, $n_{\mathrm{pl}} \approx p$, and (ii) the sharp rise in $n_{\mathrm{H}}(p)$ is softened such that the full Fermi volume ($n_{\mathrm{pl}} = 1 + p$) is only partially recovered at $p^*$. This result disfavors a conventional QCP scenario in which the PG endpoint corresponds to a reconstructed Fermi surface.

Figures

Figures reproduced from arXiv: 2506.14342 by the authors.

Figure 1
Figure 1. FIG. 1. Detwinned rectangular Y123 single crystal (sample [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (Top panels) Temperature dependence of the in-plane [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (Top) Resistivity anisotropy ratios for Y123 crystals [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (Left) Pulsed field data up to 67 T, this work. Faint [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Evolution of spin excitations in superconducting La$_{2-x}$Ca$_{x}$CuO$_{4-\delta}$ from the underdoped to the heavily overdoped regime

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    RIXS shows that high-energy paramagnons in LCCO cuprate films persist to x=0.50 and are insensitive to the extended superconducting dome, indicating they are not the primary pairing glue.

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