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arxiv: 1906.10518 · v1 · pith:EQKOVAEZnew · submitted 2019-06-20 · ❄️ cond-mat.supr-con

Parabolic Scaling in Overdoped Cuprate Films

Yong Tao This is my paper

Pith reviewed 2026-05-25 18:56 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords parabolic scalingoverdoped cupratessuperfluid phase stiffnesstransition temperatureFermi energylattice constantquantum phase transitionLa2-xSrxCuO4
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The pith

Parabolic scaling Tc = γ √ρs(0) in overdoped La2-xSrxCuO4 films follows exactly from the Fermi energy and minimal lattice constant with no adjustable parameters.

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

The paper establishes that the observed parabolic relation between superconducting transition temperature Tc and zero-temperature superfluid phase stiffness ρs(0) can be derived directly from a quantum critical description of Cooper pairs. The prefactor γ in Tc = γ √ρs(0) is fixed solely by the material's Fermi energy εF and its smallest lattice constant a. For La2-xSrxCuO4 films this yields a numerical prediction of 4.29 K^{1/2} that lies inside the experimental uncertainty band of 4.2 ± 0.5 K^{1/2}. A sympathetic reader cares because the result supplies a parameter-free link between the quantum phase transition that ends the superconducting dome and ordinary band-structure quantities.

Core claim

Using the quantum critical model for zero-temperature Cooper pairs, parabolic scaling can be exactly derived, where γ=γ(εF,a) is uniquely determined by the Fermi energy εF and the minimal lattice constant a of superconducting materials. For single-crystal La_{2-x}Sr_xCuO_4 films, we calculate the theoretical value of γ, which yields 4.29 K^{1/2} and is in accordance with an experimental measure value (4.2 ± 0.5) K^{1/2} with high accuracy. Our formula for γ can be further tested by investigating other BCS-like materials.

What carries the argument

The quantum critical model for zero-temperature Cooper pairs, which fixes the scaling prefactor γ through the Fermi energy εF and the minimal lattice constant a.

If this is right

  • The scaling prefactor γ is material-specific and calculable from εF and a alone for any BCS-like superconductor.
  • Parabolic scaling is the signature of a quantum phase transition from superconductor to normal metal.
  • The same derivation applies to highly overdoped single-crystal films without post-hoc adjustments.
  • The explicit formula for γ supplies a testable prediction for other materials.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the relation holds, the zero-temperature superfluid stiffness directly encodes the distance to the quantum critical point through the Fermi energy.
  • Similar parabolic scaling may appear in other overdoped superconducting families once their Fermi energies and lattice constants are measured.
  • Independent spectroscopic determinations of εF in the same films would provide a cross-check on the numerical value of γ.
  • The approach could be used to forecast the location of the quantum critical point in engineered thin films whose lattice spacing is controlled by substrate choice.

Load-bearing premise

The quantum critical model for zero-temperature Cooper pairs must remain valid in these overdoped films and must permit an exact derivation of the scaling without extra adjustable parameters.

What would settle it

A precise measurement of γ in a second BCS-like material whose Fermi energy and minimal lattice constant are independently known, followed by a comparison showing a statistically significant mismatch with the experimental parabolic fit, would falsify the claimed derivation.

Figures

Figures reproduced from arXiv: 1906.10518 by Yong Tao.

Figure 1
Figure 1. Figure 1: The experimental data from [8] are plotted as black circles, which belong to the 𝑇𝑐 interval [5.1𝐾, 41.6𝐾]. The parabolic scaling (red line) 𝑇𝑐 = 4.29 𝐾 1⁄2 ∙ √𝜌𝑠 (0) perfectly fits the experimental data in [5.1𝐾, 𝑇𝑀], while the linear scaling (blue line) perfectly fits the experimental data in [𝑇𝑄, 41.6𝐾]. Both parabolic and linear scaling (yellow lines) fail to fit the experimental data in [𝑇𝑀,𝑇𝑄], where… view at source ↗
read the original abstract

It was recently reported that, in the highly overdoped side of single-crystal $La_{2-x}Sr_xCuO_4$ films, the transition temperature $T_c$ and zero-temperature superfluid phase stiffness $\rho_s(0)$ will obey a parabolic scaling $T_c=\gamma \cdot \sqrt{\rho_s(0)}$. Parabolic scaling indicates a quantum phase transition from a superconductor to a normal metal, for which there has been scant understanding [Nature 536, 309-311 (2016)]. The current study shows that, using the quantum critical model for zero-temperature Cooper pairs [EPL 118, 57007 (2017)], parabolic scaling can be exactly derived, where $\gamma=\gamma(\varepsilon_F,a)$ is uniquely determined by the Fermi energy $\varepsilon_F$ and the minimal lattice constant $a$ of superconducting materials. For single-crystal $La_{2-x}Sr_xCuO_4$ films, we calculate the theoretical value of $\gamma$, which yields $4.29 K^{1/2}$ and is in accordance with an experimental measure value $(4.2 \pm 0.5) K^{1/2} $ with high accuracy. Our formula for $\gamma$ can be further tested by investigating other BCS-like materials.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The paper claims that the parabolic scaling relation Tc = γ √ρs(0) observed in highly overdoped single-crystal La_{2-x}Sr_xCuO4 films can be exactly derived from the quantum critical model for zero-temperature Cooper pairs (EPL 118, 57007, 2017), where γ is uniquely fixed by the Fermi energy εF and minimal lattice constant a. For LSCO the model yields γ = 4.29 K^{1/2}, stated to agree with the experimental value 4.2 ± 0.5 K^{1/2}. The result is presented as supporting a superconductor-to-normal-metal quantum phase transition and as testable in other BCS-like materials.

Significance. If the derivation and applicability hold, the work supplies a concrete theoretical origin for the parabolic scaling that signals the quantum phase transition in overdoped cuprates, together with a material-parameter formula for the prefactor γ that can be checked experimentally in additional systems. The reported numerical match would then constitute independent support rather than a consistency check.

major comments (3)
  1. [Derivation of parabolic scaling (near Eq. for γ)] The manuscript states that parabolic scaling 'can be exactly derived' from the 2017 EPL model but supplies no self-contained steps, intermediate equations, or explicit mapping from the model's pair-wavefunction or critical scaling relations to Tc ∝ √ρs(0) and to the functional form γ(εF, a). Without these, the claims of exactness and absence of adjustable parameters cannot be verified for the overdoped regime.
  2. [Application to LSCO films and discussion of QPT] Application of the 2017 zero-temperature Cooper-pair quantum critical model to the highly overdoped LSCO films (where the QPT to normal metal occurs) is asserted without regime-specific justification or independent checks that the model's assumptions remain valid. If those assumptions (e.g., form of the pair wavefunction or critical exponents) do not hold precisely here, both the exact parabolic form and the parameter-free status of γ are compromised.
  3. [Calculation of γ for LSCO] The numerical agreement (4.29 vs. 4.2 ± 0.5) is presented as high accuracy, yet the manuscript gives no error propagation or sensitivity analysis on the input values of εF and a, nor states how they were extracted for the specific films. This leaves open whether the match is robust or sensitive to plausible variations in those parameters.
minor comments (1)
  1. Notation for the superfluid stiffness ρs(0) and the experimental data source should be cross-referenced explicitly to the cited Nature 2016 paper to clarify whether new measurements or re-analysis are involved.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major point below and will revise the manuscript to incorporate additional details on the derivation, applicability, and parameter extraction as suggested.

read point-by-point responses

  1. Referee: [Derivation of parabolic scaling (near Eq. for γ)] The manuscript states that parabolic scaling 'can be exactly derived' from the 2017 EPL model but supplies no self-contained steps, intermediate equations, or explicit mapping from the model's pair-wavefunction or critical scaling relations to Tc ∝ √ρs(0) and to the functional form γ(εF, a). Without these, the claims of exactness and absence of adjustable parameters cannot be verified for the overdoped regime.

    Authors: We agree that the manuscript would benefit from including the explicit derivation steps to make the mapping self-contained. In the revised version we will add a concise section (or appendix) that starts from the zero-temperature pair wavefunction and critical scaling relations of the 2017 EPL model, derives Tc ∝ √ρs(0), and shows how γ is fixed solely by εF and a with no free parameters. This will allow direct verification of the exact parabolic form. revision: yes

  2. Referee: [Application to LSCO films and discussion of QPT] Application of the 2017 zero-temperature Cooper-pair quantum critical model to the highly overdoped LSCO films (where the QPT to normal metal occurs) is asserted without regime-specific justification or independent checks that the model's assumptions remain valid. If those assumptions (e.g., form of the pair wavefunction or critical exponents) do not hold precisely here, both the exact parabolic form and the parameter-free status of γ are compromised.

    Authors: The 2017 model was constructed precisely for the superconductor-to-normal-metal quantum phase transition driven by the disappearance of zero-temperature Cooper pairs, which matches the regime of the highly overdoped LSCO films. We will expand the discussion section to provide regime-specific justification, citing experimental signatures of the QPT in overdoped LSCO and confirming that the model's pair-wavefunction form and critical exponents remain applicable in this doping range. revision: yes

  3. Referee: [Calculation of γ for LSCO] The numerical agreement (4.29 vs. 4.2 ± 0.5) is presented as high accuracy, yet the manuscript gives no error propagation or sensitivity analysis on the input values of εF and a, nor states how they were extracted for the specific films. This leaves open whether the match is robust or sensitive to plausible variations in those parameters.

    Authors: We acknowledge the absence of these details. The values of εF and a are taken from established literature (ARPES for εF and crystallographic data for a in LSCO). In the revision we will explicitly state the sources, show the calculation of γ, and add a sensitivity analysis demonstrating how γ responds to small variations in the input parameters, thereby confirming the robustness of the reported agreement. revision: yes

Circularity Check

1 steps flagged

Exact parabolic scaling derived solely by applying author's unverified 2017 self-cited quantum critical model

specific steps
  1. self citation load bearing [Abstract]
    "using the quantum critical model for zero-temperature Cooper pairs [EPL 118, 57007 (2017)], parabolic scaling can be exactly derived, where γ=γ(εF,a) is uniquely determined by the Fermi energy εF and the minimal lattice constant a of superconducting materials. For single-crystal La_{2-x}Sr_xCuO_4 films, we calculate the theoretical value of γ, which yields 4.29 K^{1/2}"

    The exactness of the derivation and the parameter-free uniqueness of γ(εF,a) reduce directly to the assumptions of the cited 2017 model by the same author; the present manuscript supplies neither a self-contained derivation nor independent checks that the model's pair-wavefunction or critical scaling relations hold in the overdoped regime, rendering the claimed prediction a consequence of the prior self-citation.

full rationale

The paper's central result—that parabolic scaling Tc = γ √ρs(0) with γ uniquely fixed by εF and a follows exactly from the zero-temperature Cooper-pair model—is obtained by direct invocation of the 2017 EPL paper by the same author. No independent re-derivation, regime validation for overdoped LSCO, or external falsifiability is supplied in the present work; the numerical agreement (4.29 vs 4.2 ± 0.5) is therefore a consistency check internal to the prior model's assumptions rather than new grounding. This matches self-citation load-bearing (pattern 3) and uniqueness imported from authors (pattern 4).

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim depends on the validity of the 2017 quantum critical model, which is imported without re-derivation or new falsifiable tests in this work.

axioms (1)
  • domain assumption The quantum critical model for zero-temperature Cooper pairs accurately describes overdoped cuprate films and yields the parabolic scaling without further assumptions.
    Invoked directly from the 2017 EPL reference to enable the exact derivation.

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Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages · 1 internal anchor

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    work page 2004

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    [16]. K. G. Wilson and J. B. Kogut, The renormalization group and the epsilon expansion. Physics Reports 12, 75-200 (1974) [17]. H. Sonoda, Wilson’s Renormalization Group and Its Applications in Perturbation Theory. arXiv:hep-th/0603151 [18]. K. G. Wilson, The renormalization group and critical phenomena. Rev. Mod. Phys. 55, 583 (1983) [19]. H. Kamimura a...

    work page internal anchor Pith review Pith/arXiv arXiv 1974