Measurements of the doping effects on the in-plane paraconductivity in cuprate superconductors

Felix Vidal; Gonzalo Ferro; Jose Antonio Veira; Manuel V. Ramallo

REVIEW

Measurements of the doping effects on the in-plane paraconductivity in cuprate superconductors

Felix Vidal, Manuel V. Ramallo, Gonzalo Ferro, Jose Antonio Veira

Superconductivity · Submitted 3 Mar 2006 · 10 references

Pith's verdict: A transparent but largely derivative conference summary; the central doping-independence claim is plausible yet depends on background subtraction and on a BCS relaxation time put into the model by hand.

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arXiv IDcond-mat/0603074 (version 1)

Pith IDHMS65VMZ, Pith's permanent record of this paper and its review

CitationFelix Vidal, Gonzalo Ferro, Jose Antonio Veira, Manuel V. Ramallo. "Measurements of the doping effects on the in-plane paraconductivity in cuprate superconductors." arXiv:cond-mat/0603074 (2006). https://pith.science/paper/HMS65VMZ

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Editor's note

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Short version: this is a conference summary, not a new paper. The measurements and the fitted model come from the group's earlier PRB work (Ref. [2] and related); the only fresh element is Fig. 3, comparing T_C and T* from the literature. The conclusion that paraconductivity is doping independent and unrelated to the pseudogap is plausible but rests on two assumptions that the paper does not stress enough.

What deserves credit: the paper is transparent about where the data come from, the fits of Eq. (2) to the three doping levels look good, and the authors explicitly say the relaxation-time conclusion 'demands further studies.' That is honest. The comparison of T_C, T_C, and T* over doping (Fig. 3) is a useful way of stating the argument, and the lack of any correlation between T* and the fluctuation regime is visually clear.

The soft spots are real. First, the doping-independence claim is a difference of reciprocals built on an extrapolated normal-state resistivity. The stress-test note is right: in underdoped LSCO, T* moves strongly with x, and if the background extrapolation is even a few percent off inside the transition region, Δσ near T_C changes by a large relative amount, and the error will have a doping-dependent bias. No cross-check of that subtraction is given in this paper; one has to trust Ref. [2]. Second, the BCS relaxation time is put into Eq. (2) by hand, tau_0 = (πħ/8k_B T_C)ε^{-1}. That fixes both the value and the doping dependence through T_C. So the later conclusion that the relaxation time is doping independent and BCS-like is not a fit result; it is an input. The paper honestly labels that conclusion as requiring further study, but it should be clearer that the model cannot test it. Third, the fits use two free parameters per sample; with four samples and a model that already contains the conclusion, the good chi-squared does less work than it appears.

Citation pattern: mostly self-citations, but they point to refereed PRB/Europhys. Lett. papers, so it is not a problem here; it just means the present paper is a derivative summary.

Who is this for? Colleagues already in the cuprate-fluctuation business who want a compact statement of one group's position. A nonspecialist should not rely on it because the method is not self-contained.

Recommendation: if this is submitted as a new research paper, I would desk-reject it; the measurements and analysis are already published. For a proceedings volume that explicitly invites such summaries, a light referee check suffices, mainly to confirm the paper matches the prior published data and doesn't overstate the relaxation-time point.

Referee report

Significance

If the doping-independence result is robust, it is a useful experimental constraint on the role of superconducting fluctuations in cuprates. The direct comparison of Δσ across dopings is a strength, and the paper is commendably explicit about the assumption τ_0=(πħ/8k_BT_C)ε^{-1} and about the preliminary status of the relaxation-time conclusion. Nevertheless, the support for the theoretical claims is weaker than the text implies: the relaxation-time 'result' is an input to the fit, not a fit output, and the empirical doping-independence claim depends on a background subtraction that is not cross-checked across the doping series. Because the manuscript is a short proceedings contribution, these gaps can in principle be addressed by re-analysis and reframing, making the paper suitable for major revision rather than rejection.

Major objections (3)

[§3, Eq. (2) and Conclusions] The statement that the SCF relaxation time is doping-independent and BCS-like is an input, not a fit output. The text reads: 'in calculating this expression for Δσ(ε)E we have assumed the BCS-like value for the SCF relaxation time, τ0=(πħ/8k_BT_C)ε^{-1}', and the fit varies only ξc(0) and ε_C. Therefore the fit cannot provide independent evidence that τ0 is doping-independent or BCS-like. Since the paper itself flags this conclusion as 'demanding further studies', I recommend moving it out of the conclusions, or refitting with τ0 (or at least its prefactor) as a free parameter to test it.
[§2, Fig. 1b, Eq. (1)] The model-independent claim of doping independence hinges on the background resistivity ρ_B(T), which is obtained by extrapolating the normal-state resistivity measured well above the transition through the transition region. The manuscript gives no cross-check of this extrapolation across the doping series. Because T* varies strongly with x in La_{2-x}Sr_xCuO_4 (Fig. 3) and the normal-state resistivity of underdoped LSCO is not simply linear below T*, a fixed extrapolation form can systematically misestimate ρ_B inside the transition region; since Δσ is the difference of reciprocals, even a few percent error in ρ_B(T_C) yields a large relative error in Δσ near T_C. The apparent collapse of the x=0.10, 0.12, and 0.15 curves in Fig. 2a could therefore be affected by this procedure. Please add a robustness check, e.g., by varying the extrapolation interval and functional form and showing that the Δσ curves remain unchanged.
[§3, Eq. (2)] The claim that the observed T_C is a 'good' mean-field critical temperature is based on the excellent agreement between Eq. (2) and the data, but Eq. (2) contains two free parameters per sample (ξc(0) and ε_C) and the paper reports no uncertainties for these parameters or for the fits. With two adjustable parameters, a visually good fit is a weak model test. Reporting the best-fit values with uncertainties, the correlation between the two parameters, and a fit-quality statistic (e.g., reduced χ²) would materially strengthen the conclusion.

Minor objections (4)

[Header] The published heading contains typographical artifacts ('S uperconductivity', 'Sp ringer'); these should be corrected if the manuscript is re-typeset.
[Fig. 1 and text] The notation TC (inflection point), T_C (where Δσ vanishes), and T* (pseudogap opening) is visually confusing because TC and T_C differ only by a subscript/superscript position. Renaming one of them, e.g., T_van for the vanishing of the paraconductivity, would improve readability.
[Fig. 2] No error bars or uncertainty bands are shown in Fig. 2, which makes the statement that the curves 'agree well within the experimental uncertainties' difficult to evaluate. A typical error bar or shaded band for at least one representative curve would help.
[§2] The background subtraction procedure is delegated to Ref. [2]; given its centrality to the doping-independence claim, a one-sentence summary of the functional form and extrapolation interval should be included here.

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The paper

The paper claims

Superconducting fluctuations in La2-xSrxCuO4 thin films are doping independent and disconnected from the pseudogap.

The reading

This paper measures the in-plane paraconductivity—the excess electrical conductivity from thermally created Cooper pairs above the superconducting transition—in thin films of the cuprate La2-xSrxCuO4 with strontium contents from underdoped to overdoped. It finds that the paraconductivity curves, plotted against the reduced temperature $\epsilon = \ln(T/T_C)$, are essentially the same for all dopings, and that they vanish above $\epsilon \simeq 0.7$, near twice the critical temperature. The authors conclude that these superconducting fluctuations are not related to the pseudogap, because the pseudogap temperature $T^*$ lies much higher and has a very different doping dependence. They also argue that the measured $T_C$ is a dependable mean-field critical temperature for an extended Gaussian–Ginzburg–Landau description of the fluctuations. If correct, this separates fluctuation physics from pseudogap physics and offers a straightforward route to the mean-field transition temperature in these materials.

What carries the argument

The load-bearing object is the extended Gaussian–Ginzburg–Landau (GGL) paraconductivity expression with a “total-energy” cutoff that encodes the uncertainty-principle limit on the shrinkage of the superconducting wave function above $T_C$. In the single-layer form used for La2-xSrxCuO4, with $s$ the CuO2 layer spacing, $B_{LD}=[2\xi_c(0)/s]^2$ the interlayer coupling parameter, and $\epsilon_C$ the reduced temperature at which the paraconductivity vanishes, the expression is $\Delta\sigma(\epsilon)^E = (e^2/16\hbar s)[\epsilon^{-1}(1+B_{LD}/\epsilon)^{-1/2} - \epsilon_C^{-1}(2-(\epsilon+B_{LD}/2)/\epsilon_C)]$. Fitting this expression to the measured curves fixes $\xi_c(0)$ and $\epsilon_C$; these two fitted quantities carry the paper's main claims, namely a doping-independent $\epsilon_C \simeq 0.7$, BCS-like fluctuation relaxation, and a 2D–3D crossover in the underdoped and optimally doped films that is absent in the overdoped ones.

Extended reading notes

Core claim

The central discovery is that the in-plane paraconductivity in La2-xSrxCuO4 thin films, expressed as a function of the reduced temperature $\epsilon = \ln(T/T_C)$, is essentially doping independent over the measured range $10^{-2} \lesssim \epsilon \lesssim 1$: the underdoped $x=0.1$ and $x=0.12$ data agree within uncertainties with the optimally doped $x=0.15$ data, and only the overdoped samples show a change in slope at small $\epsilon$ that is attributed to a change in fluctuation dimensionality. Fitted with the GGL expression extended by a total-energy cutoff, the same data give a reduced cutoff temperature $\epsilon_C \simeq 0.7$ that is independent of doping and close to the BCS uncertainty-principle estimate, together with a doping-independent relaxation time close to the BCS value. Because in the underdoped compounds this cutoff lies well below the pseudogap-opening temperature $T^*$, the paper concludes that these superconducting fluctuations are unconnected to the pseudogap.

Load-bearing premise

The load-bearing premise is that the normal-state resistivity measured well above the transition, extrapolated down through the transition, gives the correct background for every doping level; if that extrapolation is inaccurate or varies with doping, the apparent doping independence of the paraconductivity could be an artifact.

Editorial extensions

If this is right

In underdoped La2-xSrxCuO4 films, the superconductivity-induced fluctuation signal disappears near twice $T_C$, far below the pseudogap temperature $T^*$, so the pseudogap does not appear to be a precursor of these fluctuations.
The measured resistivity inflection temperature $T_C$ can serve as a mean-field critical temperature for fluctuation analyses, even up to the temperature where the paraconductivity vanishes.
The reduced cutoff temperature $\epsilon_C \simeq 0.7$ and the fluctuation relaxation time are doping independent and close to BCS values, implying a universal fluctuation regime when measured in reduced temperature.
The fluctuation dimensionality changes with doping: underdoped and optimally doped films show a 2D–3D crossover near $\epsilon \simeq 7 \times 10^{-2}$, while overdoped films remain essentially two-dimensional.

Reading between the lines

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

Editorial inference: if the paraconductivity is doping independent while $T^*$ varies strongly with doping, the pseudogap and the paraconductivity channel are likely governed by separate physics in this material.
Editorial inference: a direct extension would be to compare paraconductivity in other cuprate families with controlled pseudogap modifications, predicting the same reduced-temperature universality if the claim is generic.
Editorial inference: the same data could be reinterpreted as evidence that the pairing amplitude itself is doping independent when measured in units of $T_C$, which would constrain theories that tie pairing strength to pseudogap formation.

Original abstract

We will summarize here some of our measurements of the superconducting fluctuations effects on the in-plane electrical resistivity (the so-called in-plane paraconductivity) in La_{2-x}Sr_xCuO_4 thin films with different Sr content. Our results suggest that these superconducting fluctuations effects are not related to the opening of a pseudogap in the normal-state of underdoped compounds.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,362 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.12 · human participants 0.02 · controlled comparison 0.14 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.11 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We will summarize here some of our measurements of the superconducting fluctuations effects on the in-plane electrical resistivity (the so-called in-plane paraconductivity) in La_{2-x}Sr_xCuO_4 thin films with different Sr content. Our results suggest that these superconducting fluctuations effects are not related to the opening of a pseudogap in the normal-state of underdoped compounds.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We will summarize here some of our measurements of the superconducting fluctuations effects on the in-plane electrical resistivity (the so-called in-plane paraconductivity) in La_{2-x}Sr_xCuO_4 thin films with different Sr content.	contribution 1.00	0.96	0.04	asserted 0.92
s1	Our results suggest that these superconducting fluctuations effects are not related to the opening of a pseudogap in the normal-state of underdoped compounds.	interpretation 0.93	0.90	0.78	hedged possibility 1.00

What kind of paper the classifier reports this is: empirical study 1.00 · evidence from observation or experiment 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** Temperature dependence of the resistivity of (a) a polycrystalline sample of the underdoped cuprate La1.9Sr0.1CuO4, taken from [1], and (b) a film of the same composition and thickness ∼ 150 nm, taken from [2]. In (b), the measurements correspond to the in-plane direction (parallel to the CuO2 layers). The temperatures T ∗ , T C and TC correspond, respectively, to the pseudogap opening temperature, to the temperature where the SCF effects become indistinguishable, and to the (inflexion-point) observed normal-superconducting transition temperature. well above the superconducting tra

**Figure 2.** In-plane paraconductivity versus reduced temperature measured in Ref.[2], in La2−xSrxCuO4 films with thickness ∼ 150 nm and Sr contents covering the underdoped (x < 0.15), optimally-doped (x = 0.15) and overdoped (x > 0.15) compositions. The solid lines correspond to the best fit to those data using the GGL approach with a total-energy cutoff (Eq. (2)). See main text for details. related to the coherent Cooper pairs created above the superconducting transition by thermal fluctuations. 3 Is the observed TC(x) a “good” mean–field superconducting–normal transition temperature? This…

**Figure 3.** Comparison for La2−xSrxCuO4 between the temperatures of the pseudogap opening (T ∗ ), of the vanishing of the in-plane paraconductivity (T C), and of the normal-superconducting transition as observed in the resistivity measurements (TC). The T ∗ values are taken from the compilation in Ref. [9], and correspond to resistivity measurements (ρ), Hall coefficient measurements (RH ), infrared measurements (τ ), and static susceptibility measurements (χ0) A model-independent conclusion: The general behaviour of the inplane paraconductivity is not affected, even up to T C, by doping. The…

Figures reproduced from arXiv:cond-mat/0603074 by the authors.

References

Works cited (10)

[2]

S.R. Curr´ as, G. Ferro, M.T. Gonz´ alez, M.V. Ramallo, M. Ruibal, J.A. Veira, P. Wagner, and F. Vidal, Phys. Rev. B 68, 094501 (2003)

View on Pith 2003
[1]

B. Batlogg, H.Y. Hwang, H. Takagi, R.J. Cava, H.L. Kao, an d J. Kwo, Physica C 235-240, 130 (1994)

View on Pith 1994
[3]

F. Vidal, C. Carballeira, S.R. Curr´ as, J. Mosqueira, M.V. Ramallo, J.A. Veira, and J. Vi˜ na, Europhys. Lett. 59, 754 (2002)

View on Pith 2002
[4]

See, e.g., J. Orenstein and A.J. Millis, Science 288, 468 (2000). See also, B. Batlogg and C.M. Varma, Physics World, February 2000, p. 3 3

View on Pith 2000
[5]

M. Suzuki and M. Hikita, Phys. Rev. B 44, 249 (1991); 47, 2913 (1993)

View on Pith 1991
[6]

E. Silva, S. Sarti, R. Fastampa, and M. Giura, Phys. Rev. B 64, 144508 (2001)

View on Pith 2001
[7]

B. Leridon, A. Defossez, J. Dumont, J. Lesueur, and J.P. C ontour, Phys. Rev. Lett. 87, 197007 (2001); 90, 179704 (2003). See also C.W. Luo, J.Y. Juang, J.-Y. Lin, K.H. Wu, T.M. Uen, and Y.S. Gou, Ph ys. Rev. Lett. 90, 179703 (2003)

View on Pith 2001
[8]

C. Carballeira, S.R. Curr´ as, J. Vi˜ na, J.A. Veira, M.V.Ramallo, and F. Vidal, Phys. Rev. B 63, 144515 (2001)

View on Pith 2001
[9]

T. Timusk and B. Statt, Rep. Prog. Phys. 62, 61 (1999)

View on Pith 1999
[10]

M.V. Ramallo, C. Carballeira, J. Vi˜ na, J.A. Veira, T. M ishonov, D. Pavuna, and F. Vidal, Europhys. Lett. 48, 79 (1999). 7

View on Pith 1999

How the literature uses it

1 arXiv paper cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States a conflicting result 3 papers

Together with this, the presence of a SC pseudogap region T_0-T_{c0} increasing with underdoping is found to be the origin of the Nernst coefficient becoming anomalously smaller and the in-plane coherence length {\it apparently} increasing with underdoping.

Fluctuation Effects in Underdoped Cuprate Superconductors under Magnetic Field · 0.95
We reconsider transport experiments in strongly anisotropic superconducting cuprates and we find that universal Aslamazov-Larkin (AL) paraconductivity in two dimensions is surprisingly robust even in the underdoped regime below the pseudogap crossover temperature T^*.

Extended paraconductivity regime in underdoped cuprates · 0.90
This allows to address the nature of the pseudogap in favour of incoherent pairing.

Conductivity of underdoped YBa2Cu3O7-d : evidence for incoherent pair correlations in the pseudogap regime · 0.80

Papers citing it · 1 sentence without a confident label

Cites it as support 1 paper

This result further confirms, at least for dopings above 0.1 hole/, [ref] the conventional nature of the superconducting fluctuations in cuprates (GGL-like, associated with fluctuating superconducting pairs above the mean-field critical temperature), independently of their doping and of the temperature region above , as also earlier concluded by Currás and coworkers [ref] by analyzing the in-plane excess conductivity in other cuprates (see also Refs. [ref] to [ref] and [ref] to [ref] ).

Comment on "High Field Studies of Superconducting Fluctuations in High-Tc Cuprates. Evidence for a Small Gap distinct from the Large Pseudogap" · Introduction · 0.97

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [2]

S.R. Curr´ as, G. Ferro, M.T. Gonz´ alez, M.V. Ramallo, M. Ruibal, J.A. Veira, P. Wagner, and F. Vidal, Phys. Rev. B 68, 094501 (2003)

View on Pith 2003

[2] [1]

B. Batlogg, H.Y. Hwang, H. Takagi, R.J. Cava, H.L. Kao, an d J. Kwo, Physica C 235-240, 130 (1994)

View on Pith 1994

[3] [3]

F. Vidal, C. Carballeira, S.R. Curr´ as, J. Mosqueira, M.V. Ramallo, J.A. Veira, and J. Vi˜ na, Europhys. Lett. 59, 754 (2002)

View on Pith 2002

[4] [4]

See, e.g., J. Orenstein and A.J. Millis, Science 288, 468 (2000). See also, B. Batlogg and C.M. Varma, Physics World, February 2000, p. 3 3

View on Pith 2000

[5] [5]

M. Suzuki and M. Hikita, Phys. Rev. B 44, 249 (1991); 47, 2913 (1993)

View on Pith 1991

[6] [6]

E. Silva, S. Sarti, R. Fastampa, and M. Giura, Phys. Rev. B 64, 144508 (2001)

View on Pith 2001

[7] [7]

B. Leridon, A. Defossez, J. Dumont, J. Lesueur, and J.P. C ontour, Phys. Rev. Lett. 87, 197007 (2001); 90, 179704 (2003). See also C.W. Luo, J.Y. Juang, J.-Y. Lin, K.H. Wu, T.M. Uen, and Y.S. Gou, Ph ys. Rev. Lett. 90, 179703 (2003)

View on Pith 2001

[8] [8]

C. Carballeira, S.R. Curr´ as, J. Vi˜ na, J.A. Veira, M.V.Ramallo, and F. Vidal, Phys. Rev. B 63, 144515 (2001)

View on Pith 2001

[9] [9]

T. Timusk and B. Statt, Rep. Prog. Phys. 62, 61 (1999)

View on Pith 1999

[10] [10]

M.V. Ramallo, C. Carballeira, J. Vi˜ na, J.A. Veira, T. M ishonov, D. Pavuna, and F. Vidal, Europhys. Lett. 48, 79 (1999). 7

View on Pith 1999