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This Perspective argues that an ideal disorder-free overdoped cuprate would be a Fermi liquid in the normal state and a weak-coupling BCS d-wave superconductor below T_c.

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load-bearing objection A candid, well-argued Perspective making the case that overdoped cuprates are FL/BCS once alloy disorder is accounted for, with the disorder attribution as the main unresolved pillar. the 5 major comments →

arxiv 2510.25767 v4 pith:XAOHQJ2S submitted 2025-10-29 cond-mat.supr-con cond-mat.str-el

Emergence of Fermi-liquid and BCS physics in overdoped cuprates

B.J. Ramshaw , Steven A. Kivelson This is my paper
classification cond-mat.supr-con cond-mat.str-el MSC 82D55 PACS 74.72.-h74.20.Fg
keywords cuprate superconductorsoverdoped regimeFermi liquidBCS d-wave superconductivityalloy disorderphase fluctuationssuperfluid stiffnessfalsifiable predictions
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This Perspective argues that the overdoped side of the cuprate superconducting dome is not exotic physics: in a hypothetical disorder-free cuprate, the normal state would be a conventional Fermi liquid and the superconducting state a weak-coupling BCS d-wave superconductor in which T_c is set by the pairing gap, not by phase stiffness. The paper's central move is to attribute every observed feature that contradicts this picture—T-linear resistivity when superconductivity is suppressed by a magnetic field, the 'boomerang' collapse of superfluid stiffness with overdoping, and superconducting gaps persisting far above T_c—to the unavoidable disorder of real samples, which are alloys with randomly positioned dopant atoms. Evidence is drawn from quantum oscillations in overdoped Tl2201 that follow the Fermi-liquid Lifshitz-Kosevich form, the approach of the gap/T_c ratio to the weak-coupling value 2.14, the purely d-wave gap shape that implies short-ranged pairing, and the exceptional behavior of stoichiometric YBa2Cu3O7, whose superfluid stiffness rises with overdoping. If the perspective is right, only the underdoped regime demands strong-correlation theory, the overdoped edge of the dome is a disorder-broadened exponential tail rather than a quantum-critical signature, and cleaner materials—most directly pressure-doped stoichiometric YBCO—will confirm the BCS/Fermi-liquid picture through a list of falsifiable predictions the paper spells out.

Core claim

The paper proposes a doping-controlled crossover inside the cuprate phase diagram: underdoped materials have the strong-coupling hierarchy |Δ0|/2 ≫ T_c ≈ T_θ, so T_c is set by phase fluctuations; overdoped materials have the BCS hierarchy T_θ ≫ T_c ≈ |Δ0|/2, so the normal state is a Fermi liquid and superconductivity is weak-coupling BCS mean-field below the gap scale. Every apparently contradictory observation in real overdoped samples—T-linear resistivity in a magnetic field, the boomerang drop of superfluid stiffness, gaps persisting well above T_c, large residual specific heat—is attributed to intrinsic alloy disorder, amplified because d-wave pairing with a two-lattice-constant coherenc

What carries the argument

The argument rests on three pieces: the two-scale hierarchy between the phase-ordering temperature T_θ (from the superfluid stiffness κ, k_B T_θ ≡ κc per plane) and the pairing scale |Δ0|/2, with BCS applying only when T_θ ≫ T_c ≈ |Δ0|/2; the real-space BCS gap equation Δ̃(r) = −Ṽ(r)φ̃(r), which makes the gap's momentum dependence image the interaction's range—so the measured purely d-wave gap Δ(k) = Δ0[cos k_x − cos k_y]/2 implies short-ranged (nearest-neighbor) pairing with strength Ṽ ≈ 0.6 eV; and the disorder amplifier: with coherence length ξ0 ≈ 2–3 lattice constants, comparable to the dopant spacing, alloy disorder creates mesoscopic superconducting puddles that explain the non-BCS a

Load-bearing premise

The load-bearing premise (announced in Section I, argued rather than modeled in Section IV) is that the anomalous overdoped features—T-linear resistivity in a field, the boomerang stiffness drop, gaps above T_c, residual uncondensed carriers—are caused by randomly placed dopant atoms and would vanish in an ideal crystal. If any one of them is intrinsic, the central claim fails; the authors themselves concede (Section V) that their extracted pairing interaction at optimal dopi

What would settle it

Follow the paper's own recipe: measure the low-energy properties of a genuinely low-disorder overdoped cuprate, most directly stoichiometric YBa2Cu3O7 driven further overdoped by pressure. If the T-linear resistivity persists when superconductivity is quenched by a magnetic field, if the superfluid stiffness still 'boomerangs' downward, or if the dome edge stays sharp rather than rounding, the claim fails. Likewise, any measurable deviation from the single-mass Lifshitz-Kosevich form in quantum oscillations of the cleanest overdoped material would falsify the Fermi-liquid premise. A quantitati

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • An ideal disorder-free overdoped cuprate would have T_θ ≫ T_c ≈ |Δ0|/2, so T_c is set by pair-breaking and the normal state is a Fermi liquid; the deviations seen in real samples should shrink as disorder is reduced.
  • The overdoped edge of the dome should be a rounded, convex tail with T_c ~ exp(−α/(p_max − p)) as the effective pairing interaction Ṽ passes through zero—not a sharp cutoff—and p_max should move to higher doping in cleaner materials.
  • The T-linear resistivity observed in overdoped LSCO and Tl2201 when superconductivity is killed by a magnetic field is predicted to vanish in less disordered materials, most directly in pressure-doped stoichiometric YBa2Cu3O7.
  • Because the gap retains the pure d-wave form f(k) ≈ 1 from slightly underdoped to the highest overdoping measured, the pairing interaction is short-ranged, which rules out the exchange of a quantum-critical collective mode as the primary pairing mechanism at optimal doping.
  • The search for new high-temperature superconductors should aim for the cuprate band-structure motif—a large density of states near (0,π) and (π,0) connected by wavevector (π,π) with short-range antiferromagnetic correlations—rather than trying to reproduce the local chemistry.

Where Pith is reading between the lines

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

  • Beyond the paper: if the disorder attribution is right, the anomalies should track a disorder proxy such as the NQR linewidth, not the superconducting T_c—a quantitative dome-shape-versus-linewidth correlation across cuprate families would be a cheap, sharp test of the whole framework.
  • Beyond the paper: the puddle picture implies that the 'clean enough' threshold is set by the coherence length itself, so even state-of-the-art overdoped samples sit in the granular regime near the dome edge; the deciding experiments require synthesis of stoichiometric overdoped crystals or pressure-tuned fully ordered compounds.
  • Beyond the paper: the same logic applied to electron-doped cuprates—where antiferromagnetic correlations persist to optimal doping and the gap shows hints of non-monotonic structure—would classify those as genuine strong-correlation physics, since the disorder mechanism alone has no reason to be weaker there.
  • Beyond the paper: the inverted-gap-equation analysis gives a reusable recipe: measure Δ(k) and the dispersion, invert the BCS self-consistency condition, and read off the range and sign of the pairing interaction—importable directly to other unconventional superconductors with short coherence lengths.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 5 minor

Summary. This Perspective argues that in overdoped cuprates, below an intermediate energy scale of order 0.1 eV, the normal state is a Fermi liquid and superconductivity is d-wave BCS mean-field, with the observed non-FL/non-BCS phenomena (T-linear resistivity in field, the boomerang superfluid stiffness, persistent gaps above Tc, and residual specific heat) attributed to intrinsic alloy disorder and nanoscale superconducting puddles. The paper defines BCS as a weak-coupling instability from a Fermi liquid independent of the pairing glue, reviews quantum oscillations, superfluid stiffness and gap-ratio data across YBCO, LSCO, Tl2201 and Bi2212, inverts the BCS gap equation to infer the effective pairing interaction V(p), and lists falsifiable predictions for cleaner materials. The argument is explicitly conditional: the authors acknowledge that key observed features contradict the framework if taken at face value, and they assign those contradictions to disorder.

Significance. If correct, the paper would reframe overdoped cuprates as conventional at low energy, with the exotic physics located in disorder-induced puddles rather than in intrinsic strong-correlation physics. This is a significant counterpoint to quantum-critical and non-Fermi-liquid narratives. The paper's strengths are its unusually candid treatment of contradictory evidence, its reliance on high-quality experimental probes such as quantum oscillations and Lifshitz-Kosevich analysis, and its explicit falsifiable predictions. Its current weakness is that the disorder attribution is largely qualitative: no quantitative model with a single set of disorder parameters is shown to reproduce the boomerang Tθ(p), the T-linear resistivity in field, the residual C/T, and the persistent gaps. The paper is therefore a thoughtful and potentially influential Perspective, but the central claim is not yet backed by a demonstrated microscopic mechanism for the anomalies.

major comments (5)
  1. [Section IV, 'Reconciling a Fermi liquid ground state'] The T-linear resistivity observed when superconductivity is suppressed by magnetic field is the strongest evidence against a Fermi-liquid normal state. The only mechanism offered here is scattering from quantum phase fluctuations of superconducting puddles, citing Ref. [49] (arXiv:2502.08699), a preprint co-authored by one of the present authors. No calculation or quantitative comparison is shown to demonstrate that this mechanism reproduces the magnitude, doping range, or temperature/field dependence of the data of Cooper et al. [16] or Proust et al. [17]. Because the abstract's central claim requires reconciling this anomaly, this is currently a promissory note rather than an established result.
  2. [Section IV, 'Evidence that the large phase fluctuations are extrinsic'] The boomerang effect—Tθ decreasing with doping on the overdoped side—is one of the principal apparent violations of the BCS picture. The paper argues that mesoscopic inhomogeneity is dominant, citing NQR broadening, STM puddles, and the YBCO comparison. However, no quantitative disorder model is fit to the measured Tθ(p) of LSCO or Tl2201, nor to the residual C/T and √H specific-heat data of Wang et al. [83]. Without a quantitative calculation showing that realistic dopant disorder produces the observed magnitude and doping dependence, the attribution of the boomerang to extrinsic disorder remains an assertion rather than a demonstrated mechanism.
  3. [Section V, Fig. 3 and Eqs. (7)–(8)] The inference of the pairing interaction V from measured gap values by inverting Eq. (7), followed by a linear fit to V as a function of doping (Eq. (8)), and then the use of that fitted line to 'predict' Δ0 at higher doping, is an in-sample fit-and-extrapolate construction. The purple 'predicted' Δ points inherit the same data and the same assumed linear form. The extrapolated pmax is sensitive to the choice of fitting function and to the free parameters V0 and pmax. The paper should provide error bands that propagate uncertainties in the ARPES gap, the tight-binding parameters in Eq. (10), and the choice F(ε)=1, and should discuss sensitivity to excluding near-optimal points from the fit.
  4. [Section V, 'Additional Considerations'; Section II] The paper defines a BCS superconductor as a weak-coupling instability from a Fermi liquid, but the inferred coupling at optimal doping is Vρ(E_F) ~ 1. This is not weak coupling in the usual BCS sense. The comparison to Pb with λ~1 in Migdal-Eliashberg theory does not fully resolve the tension, because in Pb the Migdal parameter is controlled by the small ratio of phonon to Fermi energies, whereas the present effective interaction is a static electronic interaction with no such control parameter. The authors should clarify what 'weak-coupling' means in this context and why a mean-field treatment is quantitatively justified despite Vρ ~ 1.
  5. [Section VI, falsifiable predictions] The predictions are qualitatively useful, but they lack an operational metric for disorder. Statements such as 'the T-linear term should become increasingly small with decreasing disorder' require a quantitative definition of disorder strength—for example, RMS local doping variation or a distribution of local Tc values—and a predicted scaling. The NQR linewidth comparison and the stoichiometric YBCO example provide a start, but they do not yet make the central claim quantitatively falsifiable.
minor comments (5)
  1. [Section III] Typo: 'emersed' should be 'immersed'.
  2. [Section IV heading] Typo: 'Tl1201' should be 'Tl2201'.
  3. [Section IV, 'Absence of intertwined orders'] Typo: 'inlelastic' should be 'inelastic'.
  4. [Fig. 3] The label 'Δextrap.' is used without defining the fitting procedure or the uncertainty in the extrapolation; consider adding a figure caption explanation and error bands.
  5. [Throughout] The paper repeatedly invokes 'the expected effects of material disorder' without a precise definition of what 'expected' means; a short subsection formalizing the disorder parameter and the relevant length scales would improve readability.

Circularity Check

0 steps flagged

No significant circularity: the FL/BCS claim is supported by independent data, and the disorder attribution is a falsifiable hypothesis; the Fig. 3 extrapolation and Ref [49] self-citation are transparent caveats rather than reductions.

full rationale

This is a perspective paper, not a derivation: it proposes that overdoped cuprates can be described by Fermi-liquid plus BCS physics once alloy disorder is accounted for, and it makes falsifiable predictions for cleaner materials. The main supporting evidence is independent of the proposal: quantum oscillations fitting the Lifshitz-Kosevich form, ARPES Fermi-surface and mass-renormalization data, the measured gap ratio approaching 2.14 k_B T_c, and the contrasting doping dependence of the superfluid stiffness in stoichiometric YBCO versus more disordered LSCO/Tl2201. The disorder attribution is not built into the definitions; it is defended by separate observations (NQR linewidth inhomogeneity, STM-visible puddles, irradiation studies, the YBCO comparison) and is explicitly couched as a testable hypothesis. The Fig. 3 construction is the closest thing to a fit-and-extrapolate: the pairing interaction is inferred by inverting Eq. 7 from measured gaps, a line is fit, and the purple dots are the gaps that would follow from that fitted line. But the paper labels these as 'simple fits' and 'smoothly extrapolated' values, and the central falsifiable claim in that context is the independent BCS relation Delta0 ≈ 2T_c, not the purple-dot extrapolation. The resolution of the T-linear resistivity anomaly does cite a non-peer-reviewed preprint coauthored by one of the present authors (Ref. [49]), which is a legitimate verification caveat; however, the paper also cites independent alternative mechanisms (Refs. [50-54]) and makes a specific falsifiable prediction that the T-linear term should vanish in cleaner overdoped materials. The argument therefore does not reduce by construction to its own inputs, and no circular step meets the standard required by the review rules.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The paper's conclusions rest mainly on three kinds of inputs: a low-energy Fermi-liquid/BCS ansatz with short-ranged interactions; analytic smoothness of effective parameters in doping; and the claim that intrinsic alloy disorder produces the observed deviations. The quantitative Fig. 3 analysis additionally uses ARPES-fitted band parameters and an inferred pairing interaction. No new microscopic entity is introduced.

free parameters (4)
  • Effective nearest-neighbor pairing interaction V(p) = about -0.6 eV near optimal doping, decreasing in magnitude with overdoping (Fig. 3)
    Obtained by inverting the BCS gap equation (Eq. 7) using measured gap values and the ARPES dispersion in Bi2212. It is the central fitted coupling used for the mechanism discussion and dome-tail prediction.
  • Linear-fit parameters V0 and p_max in Eq. (8) = Red/grey fit lines in Fig. 3; p_max near where extrapolated V changes sign, roughly p ~ 0.28-0.30
    Eq. (8) assumes V = -V0 (p_max - p); the line is fit to the inferred V(p) values and is used to predict the exponentially rounded Tc tail and the end of the superconducting dome.
  • Tight-binding parameters t, t', t'', t_perp in Eq. (10) = t = 166 meV, t' = -0.33t, t'' = 0, t_perp = 0.21t
    Taken from ARPES fits in refs. [101,102] and used in the gap-equation inversion; the inferred pairing interaction depends on these inputs.
  • Intermediate energy scale defining the low-energy regime = about 0.1 eV, i.e. of order J
    Chosen 'somewhat arbitrarily' in Section IV to restrict attention to low-energy properties; the central claim is explicitly about energies of order the superconducting gap and below, so this scale choice matters for which data are considered.
axioms (5)
  • domain assumption Existence of a low-energy effective description with well-defined quasiparticles and short-ranged residual interactions below an intermediate scale (of order J) in overdoped cuprates.
    Section III: 'we assume that there exists an intermediate energy scale ... below which the electronic properties can be understood on the basis of an effective model of well defined quasi-particles with relatively weak residual interactions.' This is the core ansatz of the paper.
  • domain assumption Effective parameters are analytic functions of doping, leading to V = -V0(p_max - p) near the edge of the dome.
    Section III: 'Since the dependence of the effective parameters on microscopic parameters is analytic by assumption...' This is used to derive the exponential Tc tail and the rounded dome edge; it is a smoothness assumption, not derived.
  • domain assumption The BCS gap-equation inversion can be done with no additional high-energy cutoff, F(epsilon) = 1.
    Section V: 'inverting Eq. 6, (without introducing any additional high-energy cutoff, i.e. taking F(epsilon)=1)'. This assumes the BCS integral converges with the bare band model and directly affects the extracted values of V.
  • domain assumption Intrinsic alloy disorder produces mesoscopic electronic inhomogeneity on the coherence-length scale in all doped cuprates, and this inhomogeneity is responsible for the non-BCS anomalies in overdoped materials.
    Section IV: 'we argue that the latter [mesoscopic inhomogeneity] is dominant', and Section I: 'features that are inconsistent with this approach can in fact be attributed to the expected effects of material disorder.' This is the key interpretive premise, supported by STM, NQR, and irradiation evidence but not by a quantitative model of all anomalies.
  • standard math Abrikosov-Gor'kov pair-breaking and the phase-fluctuation criterion T_theta/Tc apply as stated to d-wave superconductors with short coherence length.
    Section III uses AG effective-medium theory and Eqs. (2) and (9). These are established results, though their application to cuprates where the coherence length is comparable to the disorder correlation length is an extrapolation.

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read the original abstract

Cuprates are the paradigmatic `unconventional' superconductors: their critical temperature is much higher than can be expected from phonon-mediated pairing; the superconducting gap has $d$-wave symmetry; and the normal-metallic state appears to be far from a conventional Fermi liquid. These and numerous other experimental facts have led to a consensus that the conventional theory --- the Fermi-liquid-based Bardeen--Cooper--Schrieffer (BCS) theory --- is the wrong starting point for understanding superconductivity in the cuprates. In this Perspective, we propose that, although underdoped cuprates do indeed require a different theoretical framework, there is a crossover with increasing doping to an overdoped regime in which a BCS-like approach is warranted (at energy scales of the order of the superconducting gap and below), provided that the various forms of disorder are accounted for. We summarize key experimental studies of the low-energy properties of overdoped cuprates, identify properties that are and are not compatible with this proposal --- and argue that features that are inconsistent with this approach can in fact be attributed to the expected effects of material disorder. Finally, we provide falsifiable predictions for the behaviour of an `ideal' (disorder-free) overdoped cuprate through which our approach can be tested.

Figures

Figures reproduced from arXiv: 2510.25767 by B.J. Ramshaw, Steven A. Kivelson.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Doping dependence of [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Effective pairing interaction inferred from ARPES [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

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Cited by 1 Pith paper

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