Common superconducting transition in under and overdoped cuprate superconductors

E. V. L. de Mello; H\'ercules H. Santana and

REVIEW 4 major objections 5 minor 43 references

Common superconducting transition in under and overdoped cuprate superconductors

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper claims that cuprates superconduct by one common mechanism on both sides of the doping dome: local amplitudes in charge-ordered domains act as Josephson-coupled grains, and Tc is set by the average coupling equalling kBT.

desk verdict Plausible granular-superconductivity explanation for overdoped cuprates, but the quantitative case rests on per-doping fits and missing parameters. read the letter →

arxiv 2507.01718 v1 pith:ZYTBNE67 submitted 2025-07-02 cond-mat.supr-con

Hércules H. Santana and , E. V. L. de Mello This is my paper

classification cond-mat.supr-con PACS 74.72.-h74.50.+r74.81.Bd

keywords cupratesuperconductorsoverdopedchargedensitywaveJosephsoncouplinggranularsuperconductivitypseudogapphasefluctuationsBogoliubov-deGennes

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

Underdoped cuprates are often described as phase-fluctuation-limited while overdoped ones are described as Fermi liquids that lose superconductivity when pairing weakens. This paper argues instead that both sides of the doping dome have the same granular phase-ordering transition: charge-ordered domains host local d-wave pairing amplitudes, the domains act as Josephson-coupled grains, and Tc is the temperature at which the plane-averaged Josephson coupling equals kBT. The authors reproduce the measured zero-temperature gaps, the diamagnetic onset temperatures, and the Tc values of overdoped LSCO from p=0.17 to p=0.29, including the persistence of local gaps beyond the superconducting dome. The result unifies the pseudogap and overdoped regimes and makes the disappearance of superconductivity at high doping a matter of puddle dilution rather than vanishing pairing.

What carries the argument

The central machinery is the mesoscopic granular-superconductor picture: a Cahn–Hilliard equation with a double-well Ginzburg–Landau potential $V_{GL}(u,T)$ generates the charge-ordered domain structure; self-consistent Bogoliubov–de Gennes calculations on this landscape produce local d-wave pairing amplitudes $\Delta_d(\mathbf{r},p,T)$; and the plane-averaged Ambegaokar–Baratoff Josephson coupling $\langle E_J(p,T)\rangle = \frac{\pi\hbar\langle\Delta_d\rangle}{4e^2R_n}\tanh\left(\frac{\langle\Delta_d\rangle}{2k_BT}\right)$ converts the local gap map into a global phase-ordering temperature. The transition condition $\langle E_J(p,T_c)\rangle=k_BT_c$ fixes Tc, while the vanishing of $\langle\Delta_d(p,T)\rangle$ fixes the higher onset temperature $T_c^{\mathrm{on}}$.

What would settle it

Measure the plane-averaged Josephson coupling and the local gap distribution on the same overdoped LSCO crystal and check whether the temperature where $\langle E_J\rangle$ crosses $k_BT$ matches the observed Tc, while $\langle\Delta_d\rangle$ vanishes at the higher $T_c^{\mathrm{on}}$; a mismatch between these two temperatures and the measured transitions would falsify the model.

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Extended reading notes

Core claim

The central claim is that superconducting long-range order in cuprates, across the entire doping range, is established by Josephson phase ordering between mesoscopic grains that form inside charge-ordered domains. The local pairing amplitude $\Delta_d(\mathbf{r},p,T)$ is computed self-consistently on a Cahn–Hilliard–generated charge landscape, and its plane average $\langle\Delta_d(p,T)\rangle$ controls both the onset of superconducting fluctuations and, through the average Ambegaokar–Baratoff coupling $\langle E_J(p,T)\rangle$, the critical temperature via $\langle E_J(p,T_c)\rangle=k_BT_c$. For overdoped La$_{2-x}$Sr$_x$CuO$_4$ with $x=p=0.17$, $0.21$, $0.25$, $0.26$, and $0.29$, the calculation reproduces the measured zero-temperature gaps, the diamagnetic onset temperatures, and the observed Tc values, including persistent local pairing beyond the nominal critical doping. The authors take this as evidence that underdoped and overdoped compounds have a common superconducting transition mechanism, contrary to the Fermi-liquid description of the overdoped side.

Load-bearing premise

The whole quantitative chain rests on the assumption that the attractive pairing potential is proportional to the phase-separation free-energy amplitude, with V0 tuned for each doping to match the measured zero-temperature gap to Kato et al., and on a normal-state resistance Rn(p) that the paper does not display.

Editorial extensions

If this is right

The same Josephson phase-ordering mechanism determines Tc in both underdoped and overdoped cuprates; the difference is only the density of superconducting puddles.
The onset of diamagnetism and superconducting fluctuations at $T_c^{\mathrm{on}}$ is given by the vanishing of the average local pairing amplitude, not by phase order.
Beyond the nominal critical doping $p_c$, local pairing amplitudes can persist inside charge-ordered puddles, but they are too dilute to establish long-range order.
The model reconciles the conflicting STM, ARPES, and STS experiments: real-space probes see local gaps while k-space probes average over regions and see weaker pair amplitude.
The pseudogap temperature $T^*$ marks the onset of the charge inhomogeneity that seeds the local pairing, so the pseudogap and superconducting state share a common origin in the phase-separation free energy.

Reading between the lines

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

If the granular Josephson-ordering mechanism is universal, the same $\langle E_J\rangle=k_BT_c$ criterion could be tested in other cuprate families where charge order and pseudogap overlap, such as Bi- and Hg-based compounds.
The normal-state resistance $R_n(p)$ entering the Josephson formula is not shown in the paper; extracting it from transport data would provide an independent, falsifiable check of the predicted Tc values without any fitting of $V_0$.
The model suggests that the superconductor-to-metal crossover at $p_c$ is a percolation-like dilution of Josephson-coupled grains, which predicts a sharp boundary in the local gap distribution that real-space STS could map directly.
Because the local pairing amplitude scales with $T^*(p)$, the model implies that materials with a higher pseudogap temperature should retain local pairing to higher doping, a trend that could be checked across the cuprate family.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The paper extends the authors' earlier granular-superconductivity framework to overdoped LSCO and offers a sensible way to reconcile the ARPES result (pairing amplitude vanishes at pc) with the STM/STS result (local gaps survive beyond pc). That reconciliation is the genuinely new step, and it is a legitimate and useful one. The idea that charge-ordered puddles host local superconducting amplitudes and that the same phase-ordering mechanism sets Tc on both sides of the dome is worth taking seriously.

The soft spots are in the quantitative support. The zero-temperature average gap is fitted per doping: the paper says V0 is chosen "looking for agreement" with Kato et al. So the T=0 values in Fig. 3 are not predictions. The temperature dependence and the onset temperatures do follow from the model, which gives some real constraint, but the Tc values come from Eq. (2) and depend on Rn(p), the normal-state resistance, which is not shown anywhere in the main text. The supplemental material is promised but not present, so the numbers cannot be checked. The p=0.29 case is also a red flag: the model gives Tc around 1 K while the measured bulk response is near 5 K. That is a factor-of-five miss, and the stress-test point about the plane-averaged Ambegaokar-Baratoff formula is fair. In the dilute-puddle regime the global transition should be controlled by the percolating network of strong junctions, not by the spatial average, and averaging the gap first can overestimate the active coupling. The paper itself acknowledges the dilute limit, so this is not an internal contradiction, but it means the "same mechanism" conclusion is a plausible narrative rather than a quantitatively established one.

The paper is honest about what it does—it does not hide the calibration—and it engages the experiments seriously. It is not a desk-reject; it deserves a serious referee. The referee should insist on the missing parameter table, a clear separation between fitted inputs and predicted outputs, and an analysis of percolation or network effects in the dilute regime. If those are addressed, this could be a useful contribution for people working on overdoped cuprates and granular superconductivity.

Referee Report

4 major / 5 minor

Summary. The manuscript proposes that superconducting order in both underdoped and overdoped cuprates is established by the same granular mechanism: charge inhomogeneities generated by a Cahn–Hilliard phase-separation model create local d-wave superconducting amplitudes; these domains form a Josephson-coupled array; the plane-averaged Josephson energy <EJ(p,T)> from Eq. (2), compared with kBT, yields Tc; and the vanishing of the averaged local gap <Δd(p,T)> defines the onset temperature T_c^on of superconducting fluctuations. The authors apply this scheme to LSCO at p = 0.17, 0.21, 0.25, 0.26, and 0.29, reporting agreement with the susceptibility/STM data of Ref. [1] and with zero-temperature gap data of Ref. [36]. The central conclusion is that the doping dome, including the apparent superconductor–metal crossover near p_c ≈ 0.27, results from the same phase-ordering mechanism.

Significance. If validated, the paper would replace the usual dichotomy of phase-fluctuation-limited underdoped behavior and mean-field-limited overdoped behavior with a single granular phase-ordering description supported by local-probe experiments. Its strengths are that it is a concrete computational pipeline combining Cahn–Hilliard charge-order simulations, BdG superconducting-amplitude calculations, and an Ambegaokar–Baratoff estimate of the Josephson coupling; it produces explicit values for T_c^on and Tc for each doping; and it addresses the puddle-dominated regime beyond p_c highlighted in recent STM/STS work. However, the current manuscript does not yet establish the quantitative claim: the zero-temperature gap data are used to calibrate V0 for each doping, the normal-state resistance entering Eq. (2) is not shown, and the use of a plane average rather than a percolation criterion is questionable in the dilute regime. These issues do not invalidate the framework, but they need to be addressed before the 'same mechanism' conclusion can be assessed.

major comments (4)

[Section III, Fig. 3] The zero-temperature gap agreement with Ref. [36] is obtained by choosing V0 for each doping 'looking for agreement', as stated in the paragraph beginning 'We repeat this procedure'. This means the T = 0 comparison does not test the model's pairing assumption or the asserted proportionality V0 ∝ ⟨VGL⟩ of Section II. The temperature-dependent gap and T_c^on are predictions only of the assumed form V(p,T) = V0[1 − T/T*]^2, so the paper should state explicitly which quantities are fitted and which are predictive, and should list the resulting V0 values for the five dopings.
[Eq. (2), Fig. 4] The plane-averaged Ambegaokar–Baratoff coupling ⟨EJ⟩ cannot determine global phase coherence in a dilute granular system. In the p = 0.29 and p = 0.35 regimes invoked in the paper, the relevant quantity is the stiffness of the percolating cluster of junctions with EJ above the thermal scale, not the spatial average over the whole plane. The paper's own Fig. 4 gives Tc ≈ 1 K for p = 0.29, whereas Ref. [1] reports a bulk-like response near 5 K; this factor-of-five discrepancy is consistent with the averaging problem and weakens the claim of quantitative agreement.
[Eq. (2), Section III] The normal-state resistance Rn(p) is essential input to Eq. (2), but its values are not given in the main text, and the paper refers only to a 'Supplemental Material at [URL will be inserted by publisher]'. Without the Rn(p) values, or a transparent derivation from measured resistivities, the Tc estimates in Fig. 4 cannot be checked. The values of α, ε, and T*(p) used in the Cahn–Hilliard and BdG calculations should likewise be tabulated or referenced in a way the reader can access.
[Section II] The identification of the attractive potential V(p,T) = V0[1 − T/T*]^2 with a single global V0, while the BdG calculation uses a spatially varying p(r), is not justified microscopically. At minimum, the authors should show how the results depend on the choice V0 ∝ ⟨VGL⟩ versus a local potential V(r) ∝ VGL(r), since the central 'same mechanism' claim rests on this proportionality.

minor comments (5)

[Title] The title has a typo: 'c uprate' should be 'cuprate'.
[Abstract] The sentence 'Underdoped cuprate superconductors are believed to be strongly correlated with electronic systems with small phase stiffness leading to a large phase fluctuation region is known as the pseudogap state' is ungrammatical and should be rewritten.
[Figs. 3–4] The figure labels contain the literal strings 'uni27E8' and 'uni27E9', which appear to be unrendered Unicode escapes; the figures should be regenerated with proper angle brackets.
[Section IV] In the Conclusion, 'according the recendt experiments' should read 'according to the recent experiments', and 'an interpretation to the conflicting' should be 'an interpretation of the conflicting'.
[Section III, Fig. 3] The text should specify whether the zero-temperature values compared with Ref. [36] are the spatial averages ⟨Δd(p,0)⟩ or the peak values of the gap distribution, since the two quantities differ in inhomogeneous systems.

Circularity Check

2 steps flagged · score 6.0 of 10

The paper's headline numbers are calibrated inputs: V0 is fit per doping to the zero-temperature gap of Kato et al., T_c^on is the vanishing of that fitted gap under an assumed (1-T/T*)^2 potential, and the central pairing interaction is imported from the authors' own prior model.

fitted input called prediction [Section III 'Results', V0-calibration paragraph and Fig. 3 discussion]
"The calculations follow up with the average ⟨VGL(p)⟩ giving an attractive potential V0 in such way that ⟨∆d(p = 0.25, T = 0)⟩ oscillates around ∼ 5.6 meV , that is shown in the right of Fig. 2, which is in agreement with the low temperature measurements of Kato et al [36]. ... We repeat this procedure to other overdoped compounds ... starting always with the zero temperature ⟨∆sc(p, 0)⟩ looking for agreement with the results of Ref. 36."

The zero-temperature average gap is not predicted; V0 is adjusted per doping so that ⟨∆d(p,0)⟩ matches Kato et al. The onset T_c^on is then read off as the temperature at which this fitted average gap vanishes, using V(p,T)=V0[1−T/T*]^2 with T* taken from the literature. Since the pairing potential is constructed to vanish at T*, the disappearance of the average gap—and hence the derived T_c^on—is a consequence of the fitted zero-T scale and the assumed T*, not an independent outcome. The paper explicitly says it 'starts always with the zero temperature ⟨∆sc(p,0)⟩ looking for agreement with Ref. 36,' so the subsequent 'derivation' of the fluctuation onset is a fitted-input-called-prediction.
ansatz smuggled in via citation [Section II 'The Model', after Eq. (1) and before Fig. 1]
"We have already argued[17, 21] that this inhomogeneous charge unbalance, favors pairing attraction inside the charge domains, which is proportional to the mean VGL(u(r)) amplitude of oscillations ⟨VGL⟩ ... ⟨VGL⟩ is proportional to the T ∗(p) and weakens with doping[17–19] ... Using the GL phase separation theory, we write the attractive Hubbard potential as[19] V (p, T ) = V0 × [1 − T /T ∗]2, where V0 ∝ ⟨ VGL⟩ is a parameter used to derive the low-temperature average superconducting amplitude ⟨∆sc(p, 0)⟩."

The central input of the calculation—that the local pairing attraction is proportional to the phase-separation potential VGL and has the temperature factor (1−T/T*)^2—is not derived in this paper but is imported from the authors' own Refs. [17,19,21] via 'we have already argued.' This is a load-bearing ansatz: every subsequent quantity (local gap map, ⟨∆d(T)⟩, T_c^on, and Tc) inherits it. The paper presents the resulting 'same mechanism' conclusion as a unified explanation, but the mechanism's key interaction term is a self-cited modeling assumption rather than an independently established result.

full rationale

The paper contains no machine-checked or parameter-free derivation of its central assumptions. The zero-temperature average gap is explicitly calibrated: V0 is chosen per doping so that ⟨∆d(p,0)⟩ matches Kato et al., and T_c^on is then identified as the temperature at which this fitted average gap vanishes under the assumed V(p,T)=V0[1−T/T*]^2. Because V is forced to zero at T*, the onset temperature is essentially a restatement of the fitted amplitude and the literature T*; calling it a prediction is circular in the fitted-input-called-prediction sense. The Josephson criterion Tc from ⟨EJ⟩=kBT retains some independent content—it is a standard Ambegaokar-Baratoff formula and is compared with measured Tc values—but its input ⟨∆(T)⟩ is already calibrated, and the values of Rn(p) entering Eq. (2) are not tabulated, so the Tc curve is not a from-scratch prediction. In addition, the core premise that local pairing is proportional to the phase-separation potential VGL and has the temperature factor (1−T/T*)^2 is imported from the authors' own Refs. [17,19,21] ('we have already argued'), making the self-citation load-bearing. The paper is not entirely tautological: the granular-Josephson mechanism is a physical model with external experimental comparisons, and the Tc(criterion) has independent conceptual content. Nevertheless, several of the headline numerical 'results' (zero-T gaps, T_c^on, and the resulting fluctuation interval) reduce to calibrated inputs, so a partial circularity score of 6 is appropriate.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central calculation rests on a series of model assumptions: electronic phase separation described by CH/GL, pairing proportional to the phase-separation potential, Josephson coupling via a plane-averaged AB expression, and T* from Hall-effect measurements. No new particles, forces, or conserved quantities are introduced; the Josephson-coupled grain array is an interpretation of known CDW/CO domains, not a new entity.

free parameters (3)

V0 (pairing potential scale) = not stated numerically; set per doping to match Kato et al. zero-T gap values (about 5.6 meV at p=0.25)
Section III: V0 is adjusted so the average zero-temperature BdG gap matches Ref. 36 for each doping. This is a fit, not a prediction.
Rn(p) (normal-state resistance in Eq. 2) = not given in main text
Eq. 2 requires Rn(p); the paper only says it is proportional to the normal-state resistance just above Tc. Without these values, Tc cannot be reproduced from the text.
Cahn-Hilliard coefficients alpha and epsilon = not given in main text
Section II: alpha sets the temperature scale of the double-well potential and epsilon controls the domain spacing; both are model inputs tied to experimental wavelength, but their values are not shown.

assumptions (6)

domain assumption The pseudogap temperature T*(p) marks the onset of electronic phase separation and can be identified with the temperature-independent Hall coefficient up to p about 0.35.
Used in Section II to set TPS=T* and in the expression V(p,T)=V0[1-T/T*]^2; extends T* beyond the superconducting dome based on Ref. 23.
ad hoc to paper The pairing attraction is proportional to the amplitude of the phase-separation GL potential, V0 proportional to the average VGL.
Introduced in Section II as the bridge between charge order and the BdG pairing potential; no microscopic derivation is given.
ad hoc to paper The superconducting state can be modeled as a plane-averaged granular array with a single Ambegaokar-Baratoff Josephson coupling (Eq. 2), and phase order sets in when the average Josephson energy equals kBTc.
Used in Section III to convert average gap and normal-state resistance into Tc; the averaging over the plane is a model assumption.
domain assumption The Cahn-Hilliard equation with a double-well GL free energy describes intrinsic electronic phase separation and CDW/CO in cuprates.
Section II uses CH dynamics to generate the charge pattern on which all later calculations run; the relevance to cuprates is inferred from prior self-cited work.
domain assumption BdG calculations on a frozen low-temperature CO structure, with the local chemical potential adjusted self-consistently, give the local pairing amplitudes.
Section II: the BdG method keeps a given CO structure constant while varying the local chemical potential at each self-consistent interaction.
domain assumption Hubbard and tight-binding parameters are taken from Ref. 31 (Table 1 of the supplemental material) without re-derivation.
Section II states parameters derived for overdoped LSCO from Ref. 31 are listed in the missing supplemental table.

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Cite this review

Pith. "Pith review of Common superconducting transition in under and overdoped cuprate superconductors." pith.science (2026). https://pith.science/paper/ZYTBNE67

@misc{pith2026250701718,
  author       = {Pith},
  title        = {Pith review of: Common superconducting transition in under and overdoped cuprate superconductors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZYTBNE67}},
  note         = {Machine review of arXiv:2507.01718}
}

abstract

Underdoped cuprate superconductors are believed to be strongly correlated with electronic systems with small phase stiffness leading to a large phase fluctuation region is known as the pseudogap state. With increasing doping it is generally agree that they become Fermi liquid, rendering the end of the superconductivity due to the sufficiently large electronic screening. However, this scenario does not stand against a recent experiment\cite{OverJJ2022} that combined magnetic susceptibility and Scanning Tunnelling Microscopy (STM) which measured superconducting gaps and amplitudes amid charge inhomogeneity far beyond the critical doping $p_{\rm c} \approx 0.27$. We reproduced these results by calculating the localized superconducting amplitudes that emerge out of charge inhomogeneities, which forms a mesoscopic granular superconductor with an array of Josephson junctions, whose average couplings determine the critical temperature $T_{\rm c}$. The calculations agree with the experiments and both yield that underdoped and overdoped compounds have superconducting long-range order by the same mechanism.

Figures

Figures reproduced from arXiv: 2507.01718 by the authors.

**Figure 2.** In the left we show the local variations [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** The average d-wave superconducting amplitude h∆sc(p, T )i as function of temperature for some overdoped compounds. The zero temperature results match the experimental values[36] and we derive the onset of superconducting fluctuations T on c (p) when h∆sc(p, T )i → 0 that coincides with the onset of susceptibility signal of Ref. 1 and the Nernst effect[8–10]. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 [PITH_F… view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: The average Josephson coupling as function of temp [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

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Works this paper leans on

43 extracted references · 42 canonical work pages

[1]

Y . Li, A. Sapkota, P . M. Lozano, Z. Du, H. Li, Z. Wu, A. K. Kundu, R. J. Koch, L. Wu, B. L. Winn, S. Chi, M. Matsuda, M. Frontzek, E. S. Boˇ zin, Y . Zhu, I. Boˇ zovi´ c, A. N. Pasupa- thy, I. K. Drozdov, K. Fujita, G. D. Gu, I. A. Zaliznyak, Q. Li, and J. M. Tranquada, Strongly overdoped La 2−xSrxCuO4: Ev- idence for josephson-coupled grains of strongl...

work page 2022
[36]

T. Kato, T. Maruyama, S. Okitsu, and H. Sakata, Doping dependence of two energy scales in the tun- neling spectra of superconducting La 2−xSrxCuO4, Journal of the Physical Society of Japan 77, 054710 (2008)

work page 2008
[2]

H¨ ufner, M

S. H¨ ufner, M. A. Hossain, A. Damascelli, and G. A. Sawatzky, Two gaps make a high-temperature superconductor?, Reports on Progress in Physics 71, 062501 (2008)

work page 2008
[3]

Keimer, S

B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida, and J. Z a- anen, From quantum matter to high-temperature superconduc - tivity in copper oxides, Nature 518, 179–186 (2015)

work page 2015
[4]

W. S. Lee, I. M. Vishik, K. Tanaka, D. H. Lu, T. Sasagawa, T. P . Nagaosa, N.and Devereaux, Z. Hussain, and Z.-X. Shen, Abrupt onset of a second energy gap at the superconducting transiti on of underdoped Bi2212, Nature 450, 81 (2007). 5

work page 2007
[5]

Kanigel, U

A. Kanigel, U. Chatterjee, M. Randeria, M. R. Norman, G. K o- ren, K. Kadowaki, and J. C. Campuzano, Evidence for pair- ing above the transition temperature of cuprate supercondu c- tors from the electronic dispersion in the pseudogap phase, Phys. Rev. Lett. 101, 137002 (2008)

work page 2008
[6]

Vignolle, A

B. Vignolle, A. Carrington, R. A. Cooper, M. M. J. French, A. P . Mackenzie, C. Jaudet, D. Vignolles, C. Proust, and N. E. Hussey, Quantum oscillations in an overdoped high-tc super - conductor, Nature 455, 952 (2008)

work page 2008
[7]

V . J. Emery and S. A. Kivelson, Importance of phase ﬂuc- tuations in superconductors with small superﬂuid density, Nature 374, 434 (1995)

work page 1995

Show all 43 references

[8]

L. Li, Y . Wang, S. Komiya, S. Ono, Y . Ando, G. D. Gu, and N. P . Ong, Diamagnetism and cooper pairing above Tc in cuprates, Phys. Rev. B 81, 054510 (2010)

2010
[9]

P . M. C. Rourke, I. Mouzopoulou, X. Xu, C. Panagopoulos, Y . Wang, B. Vignolle, C. Proust, E. V . Kurganova, U. Zeitler, Y . Tanabe, T. Adachi, Y . Koike, and N. E. Hussey, Phase- ﬂuctuating superconductivity in overdoped La 2−xSrxCuO4, Nature Physics 7, 455 (2011)

2011
[10]

Cyr-Choini` ere, R

O. Cyr-Choini` ere, R. Daou, F. Lalibert´ e, C. Colligno n, S. Badoux, D. LeBoeuf, J. Chang, B. J. Ramshaw, D. A. Bonn, W. N. Hardy, R. Liang, J.-Q. Yan, J.-G. Cheng, J.- S. Zhou, J. B. Goodenough, S. Pyon, T. Takayama, H. Tak- agi, N. Doiron-Leyraud, and L. Taillefer, Pseudog...

2018
[11]

K. K. Gomes, A. N. Pasupathy, A. Pushp, S. Ono, Y . Ando, and A. Yazdani, Visualizing pair formation on the atomic scale in the High-t c superconductor Bi2Sr2CaCu2O8+δ, Nature 447, 569 (2007)

2007
[12]

Z. L. Mahyari, A. Cannell, E. V . L. de Mello, M. Ishikado, H. Eisaki, R. Liang, D. A. Bonn, and J. E. Sonier, Universal inhomogeneous magnetic-ﬁeld response in the normal state of cuprate High- Tc superconductors, Phys. Rev. B 88, 144504 (2013)

2013
[13]

Spivak, P

B. Spivak, P . Oreto, and S. A. Kivelson, Theory of quantu m metal to superconductor transitions in highly conducting s ys- tems, Phys. Rev. B 77, 214523 (2008)

2008
[14]

V alla, I

T. V alla, I. K. Drozdov, and G. D. Gu, Disappearance of su - perconductivity due to vanishing coupling in the overdoped Bi2Sr2CaCu2O8+δ, Nature Communications 11, 569 (2020)

2020
[15]

W. O. Tromp, T. Benschop, J.-F. Ge, I. Battisti, K. M. Bastiaans, D. Chatzopoulos, A. H. M. V ervloet, S. Smit, E. van Heumen, M. S. Golden, Y . Huang, T. Kondo, T. Takeuchi, Y . Yin, J. E. Hoffman, M. A. Sulangi, J. Zaanen, and M. P . Allan, Puddle formation and persistent ga...

2023
[16]

J. C. Anjos, H. S. Santana, and E. V . L. de Mello, Uniﬁed model of the Hall effect from insulator to overdoped compounds in cuprate superconductors, Phys. Rev. B 111, 115109 (2025)

2025
[17]

E. V . L. de Mello, Description and connection between th e oxygen order evolution and the superconducting transition in La2CuO4+y, Europhysics Letters 98, 57008 (2012)

2012
[18]

de Mello and J

E. de Mello and J. Sonier, Superconducting correlation s in- duced by charge ordering in cuprate superconductors and fermi- arc formation, Phys. Rev. B 95, 184520 (2017)

2017
[19]

E. V . de Mello, A framework for the description of charge order, pseudo and superconducting gap, critical temper- ature and pairing interaction in cuprate superconductors, J. Phys.: Condens. Matter 32, 40LT02 (2020)

2020
[20]

Santana and E

H. Santana and E. V . L. de Mello, Generalization of inter layer tunneling models to cuprate superconductors with charge de n- sity waves, Phys. Rev. B 107, 184514 (2023)

2023
[21]

E. V . L. de Mello and R. B. Kasal, The disordered induced interaction and the phase diagram of cuprates, Physica C: Superconductivity 472, 60 (2012)

2012
[22]

E. V . L. de Mello, Disordered-based theory of pseudo- gap, superconducting gap, and Fermi arc of cuprates, Europhys. Lett. 99, 37003 (2012)

2012
[23]

H. Y . Hwang, B. Batlogg, H. Takagi, H. L. Kao, J. Kwo, R. J. Cava, J. J. Krajewski, and W. F. Peck, Scaling of the temperature dependent Hall effect in La 2−xSrxCuO4, Phys. Rev. Lett. 72, 2636 (1994)

1994
[24]

H. Zhao, Z. Ren, B. Rachmilowitz, J. Schneeloch, R. Zhon g, G. Gu, Z. Wang, and I. Zeljkovic, Charge-stripe crystal phas e in an insulating cuprate, Nature Materials 18, 103 (2019)

2019
[25]

M. Kang, C. C. Zhang, E. Schierle, S. McCoy, J. Li, R. Su- tarto, A. Suter, T. Prokscha, Z. Salman, E. Weschke, S. Cy- bart, J. Y . T. Wei, and R. Comin, Discovery of charge order in a cuprate mott insulator, PNAS 120, e2302099120 (2023), https://www.pnas.org/doi/pdf/10.1073/p...

2023 doi
[26]

Y . Fei, Y . Zheng, K. Bu, W. Zhang, Y . Ding, X. Zhou, and Y . Yin, Visualizing the charge order and topological de- fects in an overdoped (Bi,Pb) 2Sr2CuO6+x superconductor, Science China Physics, M. & A. 63, 227411 (2019)

2019
[27]

H. Miao, G. Fabbris, R. J. Koch, D. G. Mazzone, C. S. Nelson, R. Acevedo-Esteves, G. D. Gu, Y . Li, T. Yili- maz, K. Kaznatcheev, E. V escovo, M. Oda, T. Kurosawa, N. Momono, T. Assefa, I. K. Robinson, E. S. Bozin, J. M. Tranquada, P . D. Johnson, and M. P . M. Dean, Charge de...

2021
[28]

J. W. Cahn and J. E. Hilliard, Free Energy of a Nonuniform Sys- tem. I. Interfacial Free Energy, J. Chem. Phys. 28, 258 (1958)

1958
[29]

H. S. Santana and E. de Mello, Evidence that cuprate supe r- conductors form an array of nanoscopic josephson junctions , Phys. Rev. B 105, 134513 (2022)

2022
[30]

Comin and A

R. Comin and A. Damascelli, Resonant X-Ray Scattering Studies of Charge Order in Cuprates, Ann. Rev. of Cond. Mat. Phys. 7, 369 (2016)

2016
[31]

Zhong, Z

Y . Zhong, Z. Chen, S.-D. Chen, K.-J. Xu, M. Hashimoto, Y .He, S. ichi Uchida, D. Lu, S.-K. Mo, and Z.-X. Shen, Differentiat ed roles of lifshitz transition on thermodynamics and superconduc- tivity in La 2−xSrxCuO4, PNAS 119, e2204630119 (2022)

2022
[32]

B. I. Spivak and S. A. Kivelson, Negative local superﬂui d den- sities: The difference between dirty superconductors and d irty Bose liquids, Phys. Rev. B 43, 3740 (1991)

1991
[33]

E. V . L. de Mello, The charge-density-wave signature on the superﬂuid density of cuprate superconductors, J. of Phys.: Cond. Matter 33, 145503 (2021)

2021
[34]

Bruder, A

C. Bruder, A. van Otterlo, and G. T. Zimanyi, Tun- nel junctions of unconventional superconductors, Phys. Rev. B 51, 12904 (1995)

1995
[35]

Ambegaokar and A

V . Ambegaokar and A. Baratoff, Tunneling between super con- ductors, Phys. Rev. Lett. 10, 486 (1963)

1963
[37]

Y . Li, R. Zhong, M. B. Stone, A. I. Kolesnikov, G. D. Gu, I. A. Zaliznyak, and J. M. Tranquada, Low-energy antiferro- magnetic spin ﬂuctuations limit the coherent superconduct ing gap in cuprates, Phys. Rev. B 98, 224508 (2018)

2018
[38]

M. Hoek, F. Coneri, X. R. Wang, and H. Hilgenkamp, Ramp-edge junctions between superconduct- ing Nd 1.85Ce0.15CuO4 and La 1.85Sr0.15CuO4, 6 Superconductor Science and Technology 29, 035001 (2016)

2016
[39]

T. Kato, S. Okitsu, and H. Sakata, Inhomogeneous electr onic states of La 2−xSrxCuO4 probed by scanning tunneling spec- troscopy, Phys. Rev. B 72, 144518 (2005)

2005
[40]

T. Kato, T. Noguchi, R. Saito, T. Machida, and H. Sakata, Gap distribution in overdoped La 2−xSrxCuO44 observed by scanning tunneling spectroscopy, Physica C: Superconductivity 460-462, 880 (2007), pro- ceedings of the 8th International Conference on Materials and Mechanisms o...

2007
[41]

J. S. Kim, B. H. Kim, D. C. Kim, and Y . W. Park, Two pseudo- gap behavior in La 2−xSrxCuO4: Thermoelectric power at high temperature, Journal of Superconductivity 17, 151 (2004)

2004
[42]

Fujimori, A

A. Fujimori, A. Ino, T. Mizokawa, C. Kim, Z.-X. Shen, T. Sasagawa, T. Kimura, K. Kishio, M. Tak- aba, K. Tamasaku, H. Eisaki, and S. Uchidau, Chem- ical potential shift, density of states and fermi sur- faces in overdoped and underdoped La 2−xSrxCuO4, Journal of Physics and Ch...

1998
[43]

Loret, N

B. Loret, N. Auvray, Y . Gallais, M. Cazayous, A. For- get, D. Colson, M.-H. Julien, I. Paul, M. Civelli, and A. Sacuto, Intimate link between charge density wave, pseudogap and superconducting energy scales in cuprates, Nature Physics 15, 771 (2019)

2019

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Y . Li, A. Sapkota, P . M. Lozano, Z. Du, H. Li, Z. Wu, A. K. Kundu, R. J. Koch, L. Wu, B. L. Winn, S. Chi, M. Matsuda, M. Frontzek, E. S. Boˇ zin, Y . Zhu, I. Boˇ zovi´ c, A. N. Pasupa- thy, I. K. Drozdov, K. Fujita, G. D. Gu, I. A. Zaliznyak, Q. Li, and J. M. Tranquada, Strongly overdoped La 2−xSrxCuO4: Ev- idence for josephson-coupled grains of strongl...

work page 2022

[2] [36]

T. Kato, T. Maruyama, S. Okitsu, and H. Sakata, Doping dependence of two energy scales in the tun- neling spectra of superconducting La 2−xSrxCuO4, Journal of the Physical Society of Japan 77, 054710 (2008)

work page 2008

[3] [2]

H¨ ufner, M

S. H¨ ufner, M. A. Hossain, A. Damascelli, and G. A. Sawatzky, Two gaps make a high-temperature superconductor?, Reports on Progress in Physics 71, 062501 (2008)

work page 2008

[4] [3]

Keimer, S

B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida, and J. Z a- anen, From quantum matter to high-temperature superconduc - tivity in copper oxides, Nature 518, 179–186 (2015)

work page 2015

[5] [4]

W. S. Lee, I. M. Vishik, K. Tanaka, D. H. Lu, T. Sasagawa, T. P . Nagaosa, N.and Devereaux, Z. Hussain, and Z.-X. Shen, Abrupt onset of a second energy gap at the superconducting transiti on of underdoped Bi2212, Nature 450, 81 (2007). 5

work page 2007

[6] [5]

Kanigel, U

A. Kanigel, U. Chatterjee, M. Randeria, M. R. Norman, G. K o- ren, K. Kadowaki, and J. C. Campuzano, Evidence for pair- ing above the transition temperature of cuprate supercondu c- tors from the electronic dispersion in the pseudogap phase, Phys. Rev. Lett. 101, 137002 (2008)

work page 2008

[7] [6]

Vignolle, A

B. Vignolle, A. Carrington, R. A. Cooper, M. M. J. French, A. P . Mackenzie, C. Jaudet, D. Vignolles, C. Proust, and N. E. Hussey, Quantum oscillations in an overdoped high-tc super - conductor, Nature 455, 952 (2008)

work page 2008

[8] [7]

V . J. Emery and S. A. Kivelson, Importance of phase ﬂuc- tuations in superconductors with small superﬂuid density, Nature 374, 434 (1995)

work page 1995