Multilayer Effects in Bi2Sr2Ca2Cu3O10+z Superconductors

Giulio Vincini; Kiyohisa Tanaka; Setsuko Tajima; Shigeki Miyasaka

REVIEW

Multilayer Effects in Bi2Sr2Ca2Cu3O10+z Superconductors

Giulio Vincini, Setsuko Tajima, Shigeki Miyasaka, Kiyohisa Tanaka

Superconductivity · Submitted 2 Sep 2019 · 49 references

Pith's verdict: A genuine but limited Kubo-formula consistency check added to a review of the authors' own Bi2223 results; the collapse of all B1g gaps onto one doping line rests on an unverified constant doping imbalance.

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arXiv ID1909.00602 (version 2)

Pith IDF3JTYM46, Pith's permanent record of this paper and its review

CitationGiulio Vincini, Kiyohisa Tanaka, Setsuko Tajima, Shigeki Miyasaka. "Multilayer Effects in Bi2Sr2Ca2Cu3O10+z Superconductors." arXiv:1909.00602 (2019). https://pith.science/paper/F3JTYM46

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Editor's note

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First thing you should know: this is a review article, not a new experimental paper. The ARPES and Raman data were published before, mostly by the same group. What's new here is a Kubo-formula calculation that takes the ARPES bands and gaps as input and reproduces the two B1g Raman peaks in the optimally doped compound. That calculation is a genuine consistency check, and it helps anchor the assignment of the low-energy peak to the outer planes and the high-energy peak to the inner planes. The paper also lays out the NMR evidence for doping imbalance clearly and is candid about what is speculative, especially the idea that the large gap ratio comes from the bulk Tc being suppressed by the proximity effect from the pseudo-gapped inner plane.

The soft spot is where the stress-test note points. Figure 16, the paper's central synthesis, plots B1g pair-breaking energies against layer-specific doping levels p(IP) and p(OP). Those p-values are not measured for the four crystals. They come from assuming p(OP)-p(IP)=0.076 for all samples, fixed by one NMR measurement on an optimally doped crystal. If the charge imbalance changes with oxygen content, as the paper's own Tc-plateau discussion hints it might, then every point in Figure 16 shifts by an unknown amount and the single-line collapse could be an artifact. The authors acknowledge the assumption, but they build a lot on it. A partial cross-check is that the IP of the most underdoped sample gets p=0.079 and no B1g pair-breaking peak, which is consistent with established doping dependence. That reassures me the two-gap picture is right, but it does not pin down the line.

Minor soft spots: the overdoped sample's average doping comes from a linear extrapolation of three c-axis points, and footnote 36 concedes part of that crystal contains a lower-Tc phase. The Raman peak energies have no error bars, which makes the straight-line fit less robust than it looks.

All that said, the two-gap assignment is solid: ARPES, NMR, and the Kubo calculation agree. This paper deserves a serious referee, but a referee should push for a quantitative model of the Tc suppression and for an explicit sensitivity analysis of the constant-doping-imbalance assumption. I'd bring it to a reading group to discuss how much conclusion can rest on one fixed parameter. I wouldn't cite it as the primary source for the experimental facts, but the calculation is worth citing.

Referee report

Significance

If the central claims hold, the paper provides a coherent explanation of the double Raman peak in Bi2223 and identifies a generic property of triple-layer cuprates: a large gap ratio that does not scale with Tc. The Kubo-formula calculation from ARPES bands to Raman spectra is a strong and relatively independent check of the two-gap assignment, and the agreement with experiment (OP peak within about 65 cm^-1, IP peak within about 23 cm^-1) is a notable achievement. The paper also honestly discusses the limitations of the B2g analysis and the possibility of artifacts in the IP contribution. However, the universality of the PE(p) line and the large-ratio conclusion rest on an assumption about the doping dependence of the IP-OP charge imbalance that is not independently verified; this is the main weakness.

Major objections (4)

[Sec. 5, Fig. 16] The central universal PE(p) line is derived under the assumption that the charge imbalance between IP and OP is constant, p(OP)-p(IP)=0.076, for all doping levels. This value is taken from a single NMR measurement on the optimally doped crystal. If the imbalance varies with oxygen content—an effect the paper itself invokes in Sec. 3 when discussing the Tc plateau ('redistribution of holes between IP and OP with oxygen incorporation')—then the horizontal positions of all data points in Fig. 16 shift by unknown amounts. The collapse onto a single line and the conclusion that 'no other factor' distinguishes IP from OP would then be an artifact of the assumed x-axis. The manuscript acknowledges the approximation but does not provide a robustness test, such as showing how the line spread changes for a plausible doping-dependent imbalance. This is load-bearing for the paper's most distinctive conclusion and should be addressed with additional analysis or a clear statement of the uncertainty.
[Sec. 3, Fig. 7, footnote [36]] The overdoped point (OvD109) is assigned pav=0.17 by linear extrapolation of the c-axis lattice parameter using only three other samples. Footnote [36] further states that a part of OvD109 contains a lower-Tc phase and that Raman spectroscopy probes the well-oxygenated surface, which is expected to be more overdoped than the bulk. Thus the horizontal coordinate of the OvD109 OP point in Fig. 16 is uncertain in a systematic way that is not captured by the plotted symbols. This weakens the support that the OvD109 point provides for the universal line, and the authors should either provide a direct measure of the surface doping or explicitly mark the additional uncertainty on the figure.
[Eq. (1)] Equation (1) as printed, Tc/Tc,max = 1 - 1.82(pav - 0.16)^2, is inconsistent with the standard Presland-Tallon relation, which has coefficient 82.6. The numerical pav values in Table I (0.14 and 0.11 for Tc=105 K and 88 K) are consistent only with the standard 82.6 coefficient, not with the printed 1.82. Since Eq. (1) is the basis for assigning pav for UnD105 and UnD88, the printed equation is misleading and must be corrected to 82.6 (or the analysis must be re-derived if another form was intended).
[Sec. 6, Fig. 16] The claim that the Hg1223 data point 'sits on the same B1g line' is not fully verifiable because the manuscript does not specify how the doping coordinate for Hg1223 was determined. If it is placed using an assumed p(OP) or pav without a documented procedure, the apparent agreement may be coincidental. The authors should state the source of the doping value for Hg1223 and, if possible, show the sensitivity of the placement to the assumed doping.

Minor objections (4)

[Sec. 6] The text 'which is shown on the right axis of Fig.14' should refer to Fig. 16, which is the figure with the right axis for PE/kBTc,max.
[Sec. 4.3] The statement 'Here we assumed that the matrix element Mk is constant' followed by 'As the matrix element has only a small momentum dependence' is slightly redundant or contradictory; the reader would benefit from a single clear statement of the assumption and its justification.
[Sec. 5] The phrase 'Despite such a rough approximation, these values seem reasonable' could be strengthened by adding error bars to the data points in Fig. 16 that reflect the uncertainty in the p assignment, not just in the peak energies.
[Sec. 4.1] The text says the OP is assigned to the Fermi surface closer to the Gamma point; it would be helpful to remind the reader that this assignment is initially an assumption and later supported by the doping-dependent gap behavior.

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The paper

The paper claims

The paper argues that the two superconducting gaps in triple-layer Bi2Sr2Ca2Cu3O10+z are just the gaps of its inner and outer CuO2 planes, which hold different hole counts and follow a single pairing-energy-versus-doping line; the notable…

The reading

This review argues that the two superconducting gaps observed in triple-layer Bi2Sr2Ca2Cu3O10+z are the gaps of its two inequivalent copper-oxide planes, which carry different hole counts: the inner plane is underdoped and the outer plane is overdoped. The pair-breaking energies of both planes fall on a single line when plotted against each plane's own doping, so the double Raman peak is a doping split, not evidence of a second pairing mechanism. The authors stress that what is special about triple-layer cuprates is not the size of the gap but the ratio of pairing energy to the maximum $T_c$, which is roughly twice the BCS value and much larger than in single- and double-layer cuprates. They propose that this large ratio arises because the pseudo-gapped inner plane boosts pairing energy while suppressing the bulk $T_c$ through interlayer coupling.

What carries the argument

The argument is carried by a comparison plot: pair-breaking peak energy (PE) from $B_{1g}$ Raman spectra versus the per-layer hole doping $p$ for each plane. Building that plot requires three inputs: the NMR result that the inner plane sits 0.076 holes below the outer plane, an empirical $T_c(p)$ relation used to fix the average doping of each crystal, and the assignment of the lower-energy $B_{1g}$ peak to the OP and the higher-energy one to the IP, which is verified by calculating Raman spectra from ARPES data through the Kubo formula. The plot's collapse of all IP and OP points onto one line is what converts the double peak from an anomaly into a layer-doping effect, and the same line, extended to Hg1223, supports the claim that a large PE/$k_BT_{c,\max}$ ratio is generic to triple-layer cuprates.

Extended reading notes

Core claim

The paper's central claim is that the inner (IP) and outer (OP) CuO2 planes of Bi2223 behave as two electronically independent layers with different doping, yet are coupled enough to share one bulk $T_c$ and one common relation between pair-breaking energy and doping. The two $B_{1g}$ Raman pair-breaking peaks—roughly 560 and 800 cm$^{-1}$ in the optimally doped crystal—are assigned to the OP and IP, respectively; an ARPES-based Kubo-formula calculation reproduces both peaks, confirming this assignment. Across four doping levels, all $B_{1g}$ peak energies collapse onto a single PE($p$) line once each plane's doping is estimated, meaning the double peak is simply the consequence of $p(\mathrm{OP})-p(\mathrm{IP})=0.076$. The authors emphasize that the important finding is the large normalized gap ratio PE/$k_BT_{c,\max}$ ($\sim$7–11 for $B_{1g}$), which is a common property of triple-layer cuprates; they attribute it to the underdoped IP, whose pseudogap enhances the antinodal pairing energy but, through proximity coupling, suppresses the bulk $T_c$ below what the pairing energy alone would allow.

Load-bearing premise

The load-bearing premise is that the doping gap between the inner and outer planes stays fixed at 0.076 holes per copper for all four oxygen levels, even though it was measured on only the optimally doped crystal; if that imbalance changes with doping, the single-line collapse and the large-gap-ratio conclusion are not uniquely determined.

Editorial extensions

If this is right

The double $B_{1g}$ pair-breaking peak of Bi2223 should be interpreted as two ordinary single-layer gaps at different dopings, so future work should not invoke a separate pairing mechanism for each peak.
The common PE($p$) line predicts that any triple-layer cuprate with a comparable IP–OP charge imbalance will reproduce the same normalized gap energy, as the authors show for Hg1223.
Because the IP and OP share one bulk $T_c$ even though their individual $T_c$ values would differ, the bulk $T_c$ is an interlayer average; this explains why overdoping Bi2223 leaves $T_c$ nearly constant.
The large PE/$k_BT_{c,\max}$ ratio is a separate scale from the gap energy: it arises from pseudogap-enhanced pairing energy on the IP combined with proximity suppression of bulk $T_c$.

Reading between the lines

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

Beyond the paper: if the single-line collapse is real, the antinodal pairing energy in cuprates is controlled by local hole content and the pseudogap rather than by the coherent condensate, so reports of 'large gaps' should be normalized by $T_{c,\max}$ rather than by the actual $T_c$.
Beyond the paper: the fixed charge-imbalance assumption, drawn from one optimally doped crystal, could be checked directly with site-selective NMR on the underdoped and overdoped crystals; a doping-dependent imbalance would shift the x-coordinates and could break the line.
Beyond the paper: a natural extension is to four- and five-layer cuprates, where more inner planes should amplify both the pseudogap pairing-energy contribution and the proximity suppression, predicting even larger normalized gap ratios if the mechanism is right.
Beyond the paper: on the materials side, the paper implies that raising $T_c$ in triple-layer cuprates means reducing the IP–OP charge imbalance or weakening the proximity coupling, so that the pseudogap-enhanced pairing energy is not cancelled by a suppressed bulk $T_c$.

Original abstract

We discuss the characteristic features of triple Cu-O2 layer cuprates superconductors, by comparing those of single and double layer cuprates superconductors. After a brief introduction to multilayer cuprates and their characteristic properties such as the doping imbalance between the inner and outer Cu-O2 planes (IP and OP, respectively) revealed by nuclear magnetic resonance, we present the experimental results of angle resolved photoemission and Raman scattering spectroscopy for the triple layer Bi2Sr2Ca2Cu3O10+z which showed two different superconducting gaps opening on the IP and OP. The doping dependence of the double peak structure in Raman spectra was found to be qualitatively consistent with that of single and double layer cuprates, if each layer doping for the IP and OP is taken into account. The fact that the IP and OP share the same electronic phase diagram and the same transition temperature (Tc) hints to a coupling between the IP and OP. Moreover, the energies of IP and OP Raman peaks were found to be very large, not scaling with Tc, which can be attributed to the strong influence of the pseudogap of the underdoped IP in triple layer cuprates. These findings suggest that the high Tc and the large gap ratio of triple layer cuprates are realized through a combination of the interlayer coupling between the OP and IP and the interaction between superconductivity and the pseudogap.

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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,241 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.09 · human participants 0.02 · controlled comparison 0.48 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.92 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We discuss the characteristic features of triple Cu-O2 layer cuprates superconductors, by comparing those of single and double layer cuprates superconductors. After a brief introduction to multilayer cuprates and their characteristic properties such as the doping imbalance between the inner and outer Cu-O2 planes (IP and OP, respectively) revealed by nuclear magnetic resonance, we present the experimental results of angle resolved photoemission and Raman scattering spectroscopy for the triple layer Bi2Sr2Ca2Cu3O10+z which showed two different superconducting gaps opening on the IP and OP. The doping dependence of the double peak structure in Raman spectra was found to be qualitatively consistent with that of single and double layer cuprates, if each layer doping for the IP and OP is taken into account. The fact that the IP and OP share the same electronic phase diagram and the same transition temperature (Tc) hints to a coupling between the IP and OP. Moreover, the energies of IP and OP Raman peaks were found to be very large, not scaling with Tc, which can be attributed to the strong influence of the pseudogap of the underdoped IP in triple layer cuprates. These findings suggest that the high Tc and the large gap ratio of triple layer cuprates are realized through a combination of the interlayer coupling between the OP and IP and the interaction between superconductivity and the pseudogap.

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 discuss the characteristic features of triple Cu-O2 layer cuprates superconductors, by comparing those of single and double layer cuprates superconductors.	contribution 0.86	0.47	0.04	asserted 0.63
s1	After a brief introduction to multilayer cuprates and their characteristic properties such as the doping imbalance between the inner and outer Cu-O2 planes (IP and OP, respectively) revealed by nuclear magnetic resonance, we present the experimental results of angle resolved photoemission and Raman scattering spectroscopy for the triple layer Bi2Sr2Ca2Cu3O10+z which showed two different superconducting gaps opening on the IP and OP.	contribution 0.89	0.89	0.05	asserted 1.00
s2	The doping dependence of the double peak structure in Raman spectra was found to be qualitatively consistent with that of single and double layer cuprates, if each layer doping for the IP and OP is taken into account.	result 0.97	0.90	0.07	hedged possibility 0.55
s3	The fact that the IP and OP share the same electronic phase diagram and the same transition temperature (Tc) hints to a coupling between the IP and OP.	interpretation 0.75	0.61	0.10	hedged possibility 0.82
s4	Moreover, the energies of IP and OP Raman peaks were found to be very large, not scaling with Tc, which can be attributed to the strong influence of the pseudogap of the underdoped IP in triple layer cuprates.	result 0.57	0.93	0.08	asserted 0.71
s5	These findings suggest that the high Tc and the large gap ratio of triple layer cuprates are realized through a combination of the interlayer coupling between the OP and IP and the interaction between superconductivity and the pseudogap.	interpretation 1.00	0.45	0.88	hedged possibility 0.99

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 v2

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 3.** 63Cu-NMR spectra of Bi2223 single crystal and Hg1223 polycrystal. Here, a resonance field Bres for 63Cu at B⊥c is 15.55T for Bi2223 and 10.95T for Hg1223. [24]

**Figure 8.** (a) and (b) Intensity plots of ARPES spectra with

**Figure 9.** Momentum dependence of energy gaps for Bi2223. In the OP, the gap has a

**Figure 12.** Extraction of IP and OP intensity from the raw ARPES data

Showing 4 of the paper's 12 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:1909.00602 by the authors.

References

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Although a part of the OvD109 sample seems to contain a lower Tc phase, we think that it is due to the imperfect oxygenation of the inner part of crystal. It is expected that the crystal surface is well oxygenated, namely, well overdoped, which is probed by Raman scattering

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View on Pith 2001

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] [36]

Although a part of the OvD109 sample seems to contain a lower Tc phase, we think that it is due to the imperfect oxygenation of the inner part of crystal. It is expected that the crystal surface is well oxygenated, namely, well overdoped, which is probed by Raman scattering

View on Pith

[2] [1]

Bednorz J G and Müller A 1986 Z. Phys. B 64 189

View on Pith 1986

[3] [2]

Anderson P W and Zou Z 1988 Phys. Rev. Lett. 60 132

View on Pith 1988

[4] [3]

Chakravarty S and Anderson P W 1994 Phys. Rev. Lett. 72 3859

View on Pith 1994

[5] [4]

Tajima S, Schützmann J, Miyamoto S, Terasaki I, Sato Y and Hauff R 1997 Phys. Rev. B 55 6051

View on Pith 1997

[6] [5]

Tranquada J, Sternlieb B J, Axe, J D, Nakamura Y and Uchida S, 1995 Nature 375 561. 15

View on Pith 1995

[7] [6]

For a review, 2012 Physica C (special issue) 481 edited by Uchida S, Tranquada J, Fink J, Kivelson S and Tajima S

View on Pith 2012

[8] [7]

For a review, Timusk T and Statt B, 1999 Rep. Prog. Phys. 62 61

View on Pith 1999

[9] [8]

Wang Y, Li L and Ong N P 2006 Phys. Rev. B 73 024510

View on Pith 2006

[10] [9]

Li L, Wang Y, Komiya S, Ono S, Ando Y, Gu G D and Ong N P 2010 Phys. Rev. B 81 054510

View on Pith 2010

[11] [10]

Dubroka A et al. 2011 Phys. Rev. Lett. 106 047006

View on Pith 2011

[12] [11]

Uykur E, Tanaka K, Masui T, Miyasaka S and Tajima S 2014 Phys. Rev. Lett. 112 127003, and references therein

View on Pith 2014

[13] [12]

Iyo A et al. 2007 J. Phys. Soc. Jpn. 76 094711

View on Pith 2007

[14] [13]

Eisaki H et al. 2004 Phys. Rev. B 69 064512

View on Pith 2004

[15] [14]

Fujita K et al. 2006 Phys. Rev. Lett 96 097006

View on Pith 2006

[16] [15]

Wheatley J M, Hsu T C and Anderson P W 1988 Nature (London) 333 121

View on Pith 1988

[17] [16]

Chakravarty S, Kee H and Volker K 2004 Nature (London) 428 53

View on Pith 2004

[18] [17]

Kivelson S A 2002 Physica B 318 61

View on Pith 2002

[19] [18]

For a review, Cooper S L and Grey K E 1994 in Physical Properties of the High Temperature Superconductors IV edited by Ginsberg D M (World Scientific, Singapore,

View on Pith 1994

[20] [19]

Kleiner R, Steinmeyer F, Kunkel G and Mueller P, 1992 Phys. Rev. Lett. 68 2394

View on Pith 1992

[21] [20]

Terasaki I, Sayo Y, Miyamoto S, Tajima S and Koshizuka N 1995 Phys. Rev. B 52 16246

View on Pith 1995

[22] [21]

Mukuda H, Shimuzu S, Iyo A and Kitaoka Y 2012 J. Phys. Soc. Jpn. 81 011008

View on Pith 2012

[23] [22]

Presland M R, Tallon J L, Buckley R G, Liu R S and Flower N E 1991 Physica C 176 95

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