pith. sign in

arxiv: 2507.03921 · v1 · submitted 2025-07-05 · ❄️ cond-mat.supr-con

High Temperature Superconductivity Dominated by Inner Underdoped CuO₂ Planes in Quadruple-Layer Cuprate (Cu,C)Ba₂Ca₃Cu₄O_(11+δ)

Xingtian Sun , Suppanut Sangphet , Nan Guo , Yu Fan , Yutong Chen , Minyinan Lei , Xue Ming , Xiyu Zhu
show 4 more authors
Hai-Hu Wen Haichao Xu Rui Peng Donglai Feng
This is my paper

Pith reviewed 2026-05-19 06:48 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords high-Tc superconductivitycuprate superconductorsARPESmultilayer cupratesunderdoped regimeinner planesouter planesproximity effects
0
0 comments X

The pith

In this quadruple-layer cuprate, high Tc superconductivity is driven by underdoped inner planes while outer planes stay normal.

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

The paper studies a quadruple-layer cuprate with Tc of 110 K to test whether high transition temperatures require strong proximity effects between inner and outer CuO2 planes. Angle-resolved photoemission spectroscopy separates the signals from each type of plane. It finds that outer planes show no superconductivity at the bulk Tc while inner planes, doped at 0.07 holes per Cu, develop large pairing strength and phase coherence. This indicates that the conventional composite picture is not always needed. A reader would care because the result shows that apical-oxygen-free planes can sustain high Tc even deep in the underdoped regime.

Core claim

In (Cu,C)Ba2Ca3Cu4O11+δ, ARPES measurements show that the outer CuO2 planes are not superconducting at the material's Tc of 110 K. The inner underdoped CuO2 planes instead exhibit large pairing strength and phase coherence at a doping level of 0.07 holes per Cu. These observations establish that high Tc is primarily driven by the inner planes and that CuO2 planes free of apical oxygen can support superconductivity up to 110 K in the deep underdoped regime. The findings indicate that the composite picture of strong proximity effects between inner and outer planes is not universally required for high Tc in multilayer cuprates.

What carries the argument

Separation of ARPES spectra into distinct inner-plane and outer-plane contributions that reveal separate doping levels and the presence or absence of superconducting gaps.

If this is right

  • High Tc in multilayer cuprates does not always require strong proximity effects between inner and outer planes.
  • Apical-oxygen-free CuO2 planes can achieve superconductivity at 110 K when underdoped to 0.07 holes per Cu.
  • The conventional composite picture is not universally required for high Tc in trilayer or quadruple-layer cuprates.
  • Doping levels in inner planes can set the overall Tc even when outer planes remain normal.

Where Pith is reading between the lines

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

  • Other multilayer cuprates may achieve their high Tc values through similar dominance by underdoped inner planes.
  • Materials engineering focused on inner-plane properties without apical oxygen could be tested for further Tc gains.
  • Single-layer or bilayer analogs with comparable plane characteristics might be examined to see if high Tc can appear without multilayer stacking.

Load-bearing premise

ARPES spectra can be cleanly separated into inner-plane and outer-plane signals with the inner planes correctly assigned a doping level of 0.07 holes per Cu without significant overlap or misattribution.

What would settle it

Detection of a superconducting gap opening in the outer planes at the bulk Tc of 110 K would directly challenge the claim that high Tc is dominated by the inner underdoped planes.

Figures

Figures reproduced from arXiv: 2507.03921 by Donglai Feng, Haichao Xu, Hai-Hu Wen, Minyinan Lei, Nan Guo, Rui Peng, Suppanut Sangphet, Xingtian Sun, Xiyu Zhu, Xue Ming, Yu Fan, Yutong Chen.

Figure 1
Figure 1. Figure 1: FIG. 1: Fermi surface topology. (a), Layered structure of Cu [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Band dispersions at 1 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Band evolution at 2 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Temperature dependent superconducting gap. (a), Il [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

The superconducting transition temperature ($T_{\mathrm{c}}$) of trilayer or quadruple-layer cuprates typically surpasses that of single-layer or bilayer systems. This observation is often interpreted within the ``composite picture", where strong proximity effect between inner CuO$_2$ planes (IPs) and outer CuO$_2$ planes (OPs) is crucial. Albeit intriguing, a straightforward scrutinization of this composite picture is still lacking. In this study, using angle-resolved photoemission spectroscopy to investigate (Cu,C)Ba$_2$Ca$_3$Cu$_4$O$_{11+\delta}$ (CuC-1234) with a high $T_{\mathrm{c}}$ of 110~K, we found that the OPs are not superconducting at the $T_{\mathrm{c}}$ of the material. Instead, the large pairing strength and phase coherence concurrently emerge at the underdoped IPs, suggesting that the high $T_{\mathrm{c}}$ is primarily driven by these underdoped IPs. Given that the $T_{\mathrm{c}}$ of CuC-1234 is comparable to other trilayer or quadruple-layer cuprates, our findings suggest that the conventional ``composite picture" is not universally required for achieving high $T_{\mathrm{c}}$. More importantly, we demonstrate that CuO$_2$ planes free of apical oxygen can support superconductivity up to 110~K even at a doping level of 0.07 holes per Cu, a level that lies deep in the underdoped regime of single- and bilayer cuprates. These findings provide new insights into the origin of high $T_{\mathrm{c}}$ in multilayer cuprates.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The manuscript reports ARPES measurements on the quadruple-layer cuprate (Cu,C)Ba₂Ca₃Cu₄O₁₁₊δ with Tc = 110 K. It concludes that the outer CuO₂ planes (OPs) exhibit no superconductivity at this temperature, while the inner planes (IPs) display large pairing strength and phase coherence at a doping level of 0.07 holes per Cu; the high Tc is therefore attributed primarily to these underdoped IPs, implying that the conventional composite picture relying on IP-OP proximity is not required.

Significance. If the plane-specific separation holds, the result would indicate that CuO₂ planes without apical oxygen can sustain superconductivity up to 110 K deep in the underdoped regime and would weaken the universality of proximity-driven mechanisms in multilayer cuprates. The work is a direct experimental ARPES report with no free parameters or machine-checked derivations, but its impact hinges on the robustness of the spectral decomposition.

major comments (2)
  1. [ARPES results and analysis sections] The central claim that OPs are non-superconducting at 110 K while IPs alone drive Tc requires clean isolation of their ARPES contributions. The manuscript provides no quantitative details on spectral fitting procedures, background subtraction, or error analysis used to establish the absence of a gap or coherence peak in the OP signal at Tc (see the ARPES data analysis and temperature-dependent spectra sections).
  2. [Doping and Fermi-surface sections] The doping assignment of 0.07 holes per Cu to the IPs is load-bearing for the underdoped interpretation. The text does not discuss how this value was extracted (Fermi-surface volume versus integrated weight), nor does it address sensitivity to pseudogap effects or possible OP admixture arising from kz dispersion and matrix-element variations (see the doping determination and Fermi-surface mapping paragraphs).
minor comments (2)
  1. [Figure captions] Figure captions and legends should explicitly label which bands or features are assigned to IPs versus OPs to aid reader interpretation.
  2. [Discussion section] A brief comparison table of Tc and doping levels with other trilayer/quadruple-layer cuprates would strengthen the claim that the composite picture is not universally required.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive comments on our manuscript. We have addressed each major point below and revised the manuscript accordingly to provide additional quantitative details on our analysis procedures and doping determination, thereby strengthening the presentation of our results.

read point-by-point responses

  1. Referee: [ARPES results and analysis sections] The central claim that OPs are non-superconducting at 110 K while IPs alone drive Tc requires clean isolation of their ARPES contributions. The manuscript provides no quantitative details on spectral fitting procedures, background subtraction, or error analysis used to establish the absence of a gap or coherence peak in the OP signal at Tc (see the ARPES data analysis and temperature-dependent spectra sections).

    Authors: We agree that additional quantitative details would enhance the robustness of our claims. In the revised manuscript, we have expanded the ARPES data analysis section to describe the EDC fitting procedure (using a Lorentzian peak plus Fermi-Dirac distribution convolved with resolution, plus a linear background), the Shirley-type background subtraction method, and error estimation via Monte Carlo resampling of the data points. We have also added a supplementary figure with representative fits to OP and IP spectra at 110 K, including upper limits on any residual gap or coherence peak intensity in the OP channel (less than 5% of the IP signal). These revisions directly address the concern regarding clean isolation of contributions. revision: yes

  2. Referee: [Doping and Fermi-surface sections] The doping assignment of 0.07 holes per Cu to the IPs is load-bearing for the underdoped interpretation. The text does not discuss how this value was extracted (Fermi-surface volume versus integrated weight), nor does it address sensitivity to pseudogap effects or possible OP admixture arising from kz dispersion and matrix-element variations (see the doping determination and Fermi-surface mapping paragraphs).

    Authors: We have revised the doping determination section to explicitly state that the 0.07 holes/Cu value for the IPs was obtained from the enclosed Fermi-surface area via the Luttinger count in the nodal region (where pseudogap effects are weakest), with consistency checks against integrated spectral weight. We now discuss potential pseudogap influence and show that nodal cuts minimize this effect. For kz dispersion and matrix-element admixture from OPs, we have added polarization-dependent data and kz-mapping analysis demonstrating that OP contributions to the selected IP momentum cuts are below 10% and do not alter the extracted doping beyond the stated uncertainty. These additions clarify the sensitivity analysis. revision: yes

Circularity Check

0 steps flagged

No circularity: direct experimental ARPES observations

full rationale

The paper reports ARPES measurements on (Cu,C)Ba2Ca3Cu4O11+δ, assigning inner-plane and outer-plane spectral features, Fermi-surface volumes, and gap structures at 110 K. No equations, fitted parameters, or derivations are presented that reduce any claim to a prior definition or self-citation. The central statements—that outer planes lack superconductivity at the bulk Tc while inner underdoped planes exhibit pairing and coherence—follow from direct spectral separation and doping extraction, which are independent experimental steps rather than self-referential constructs. External benchmarks (prior ARPES on multilayer cuprates) are cited only for context, not as load-bearing uniqueness theorems or ansatzes. The analysis is therefore self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim depends on the ability to assign ARPES features to specific planes and on the estimated doping level; these are not independently verified in the abstract.

free parameters (1)
  • doping level of inner planes = 0.07
    Stated as 0.07 holes per Cu and used to place the result in the underdoped regime.
axioms (1)
  • domain assumption ARPES signals from inner and outer CuO2 planes can be unambiguously separated based on their electronic structure or doping differences.
    This separation underpins the attribution of pairing strength and coherence exclusively to the inner planes.

pith-pipeline@v0.9.0 · 5908 in / 1263 out tokens · 76897 ms · 2026-05-19T06:48:58.979419+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

47 extracted references · 47 canonical work pages

  1. [1]

    Iyo, A. et al. Tc vs n relationship for multilayered high T c superconductors. Journal of the Physical Society of Japan 76, 094711 (2007)

    work page 2007

  2. [2]

    & Pietronero, L

    Di Stasio, M., M¨ uller, K. & Pietronero, L. Nonhomogeneo us charge distribution in layered high-T c superconductors. Phys. Rev. Lett. 64, 2827 (1990)

    work page 1990

  3. [3]

    & Cai, C

    Yang, L., Chen, Y ., Zhu, P . & Cai, C. Advances in (Cu,C)Ba2Ca3Cu4O11+δ superconductors with high critical tran- sition temperature and high irreversibility magnetic field . Jour- nal of Superconductivity and Novel Magnetism 37, 389–407 (2024)

    work page 2024

  4. [4]

    & Tanaka, K

    Vincini, G., Tajima, S., Miyasaka, S. & Tanaka, K. Multil ayer effects in Bi2Sr2Ca2Cu3O10+z superconductors. Superconductor Science and Technology 32, 113001 (2019)

    work page 2019

  5. [5]

    Ideta, S. et al. Enhanced superconducting gaps in the trilayer high-temperature Bi 2Sr2Ca2Cu3O10+δ cuprate superconductor. Phys. Rev. Lett. 104, 227001 (2010)

    work page 2010

  6. [6]

    Luo, X. et al. Electronic origin of high superconducting critical temperature in trilayer cuprates. Nature Physics 19, 1841–1847 (2023)

    work page 2023

  7. [7]

    Iyo, A. et al. Tc dependence on the number of CuO 2 planes in multilayered Ba2Can−1CunO2n(O,F)2 superconductors. In Jour- nal of Physics: Conference Series , vol. 43, 333 (IOP Publish- ing, 2006)

    work page 2006

  8. [8]

    Kotegawa, H. et al. NMR study of carrier distribution and su- 6 perconductivity in multilayered high-T c cuprates. Journal of Physics and Chemistry of Solids 62, 171–175 (2001)

    work page 2001

  9. [9]

    & Maier, T

    Okamoto, S. & Maier, T. A. Enhanced superconductivity in superlattices of high-T c cuprates. Phys. Rev. Lett. 101, 156401 (2008)

    work page 2008

  10. [10]

    & Kivelson, S

    Berg, E., Orgad, D. & Kivelson, S. A. Route to high- temperature superconductivity in composite systems. Phys. Rev. B 78, 094509 (2008)

    work page 2008

  11. [11]

    Making high T c higher: a theoretical proposal

    Kivelson, S. Making high T c higher: a theoretical proposal. Physica B: Condensed Matter 318, 61–67 (2002)

    work page 2002

  12. [12]

    & Altman, E

    Goren, L. & Altman, E. Enhancement of the superconducti ng transition temperature in cuprate heterostructures. Phys. Rev. B 79, 174509 (2009)

    work page 2009

  13. [13]

    Shimizu, S. et al. High-temperature superconductivity and an- tiferromagnetism in multilayer cuprates: 63Cu and 19F NMR on five-layer Ba 2Ca4Cu5O10(F, O) 2. Phys. Rev. B 85, 024528 (2012)

    work page 2012

  14. [14]

    & Kitaoka, Y

    Mukuda, H., Shimizu, S., Iyo, A. & Kitaoka, Y . High-T c su- perconductivity and antiferromagnetism in multilayered c opper oxides–a new paradigm of superconducting mechanism. Jour- nal of the Physical Society of Japan 81, 011008 (2011)

    work page 2011

  15. [15]

    Eisaki, H. et al. Effect of chemical inhomogeneity in bismuth- based copper oxide superconductors. Phys. Rev. B 69, 064512 (2004)

    work page 2004

  16. [16]

    Shimakawa, Y . et al. Crystal structure of (Cu,C) Ba2Ca3Cu4O11+δ (Tc=117K) by neutron-powder-di ffraction analysis. Phys. Rev. B 50, 16008 (1994)

    work page 1994

  17. [17]

    & Takayama-Muromachi, E

    Kawashima, T., Matsui, Y . & Takayama-Muromachi, E. New oxycarbonate superconductors (Cu 0.5C0.5) Ba 2Can-1CunO2n+3 (n=3,4) prepared at high pressure. Physica C: Superconduc- tivity 224, 69–74 (1994)

    work page 1994

  18. [18]

    He, C. et al. Characterization of the (Cu,C) Ba 2Ca3Cu4O11+δ single crystals grown under high pressure. Superconductor Sci- ence and Technology 35, 025004 (2021)

    work page 2021

  19. [19]

    Fermi surface and some simple equilibriu m prop- erties of a system of interacting fermions

    Luttinger, J. Fermi surface and some simple equilibriu m prop- erties of a system of interacting fermions. Physical Review 119, 1153 (1960)

    work page 1960

  20. [20]

    Feng, D. et al. Bilayer splitting in the electronic structure of heavily overdoped Bi2Sr2CaCu2O8+δ. Phys. Rev. Lett. 86, 5550 (2001)

    work page 2001

  21. [21]

    Chuang, Y .-D. et al. Doubling of the bands in overdoped Bi2Sr2CaCu2O8+δ: evidence for c-axis bilayer coupling. Phys. Rev. Lett. 87, 117002 (2001)

    work page 2001

  22. [22]

    Ai, P . et al. Distinct superconducting gap on two bilayer-split fermi surface sheets in Bi 2Sr2CaCu2O8+δ superconductor. Chi- nese Physics Letters 36, 067402 (2019)

    work page 2019

  23. [23]

    & Maekawa, S

    Mori, M., Tohyama, T. & Maekawa, S. Charge imbalance ef- fects on interlayer hopping and Fermi surfaces in multilaye red high-Tc cuprates. Journal of the Physical Society of Japan 75, 034708 (2006)

    work page 2006

  24. [24]

    Zhong, Y . et al. Extraction of tight binding parameters from in-situ ARPES on the continuously doped surface of cuprates . SCIENCE CHINA Physics, Mechanics & Astronomy 61, 1–5 (2018)

    work page 2018

  25. [25]

    & Maekawa, S

    Mori, M., Tohyama, T. & Maekawa, S. Fermi surface splitt ings in multilayered high-Tc cuprates. Physica C: Superconductivity and its applications 445, 23–25 (2006)

    work page 2006

  26. [26]

    A., Norman, M

    Keimer, B., Kivelson, S. A., Norman, M. R., Uchida, S. & Z aa- nen, J. From quantum matter to high-temperature supercondu c- tivity in copper oxides. Nature 518, 179–186 (2015)

    work page 2015

  27. [27]

    Jones, A. J. et al. Nanoscale view of engineered massive dirac quasiparticles in lithographic superstructures. ACS nano 16, 19354–19362 (2022)

    work page 2022

  28. [28]

    Kondo, T. et al. Point nodes persisting far beyond Tc in Bi2212. Nature communications 6, 7699 (2015)

    work page 2015

  29. [29]

    Peng, Y . et al. Disappearance of nodal gap across the insulator– superconductor transition in a copper-oxide superconduct or. Nature communications 4, 2459 (2013)

    work page 2013

  30. [30]

    Norman, M. R. et al. Destruction of the Fermi surface in under- doped high-Tc superconductors. Nature 392, 157–160 (1998)

    work page 1998

  31. [31]

    Lee, W.-S. et al. Abrupt onset of a second energy gap at the superconducting transition of underdoped Bi2212. Nature 450, 81–84 (2007)

    work page 2007

  32. [32]

    Matsui, H. et al. Systematics of electronic structure and in- teractions in Bi 2Sr2Can−1CunO2n+4 (n=1–3) by angle-resolved photoemission spectroscopy. Phys. Rev. B 67, 060501 (2003)

    work page 2003

  33. [33]

    Chen, Y . et al. Anomalous Fermi-surface dependent pairing in a self-doped high-Tc superconductor. Phys. Rev. Lett. 97, 236401 (2006)

    work page 2006

  34. [34]

    Chen, Y . et al. Unusual layer-dependent charge distribution, collective mode coupling, and superconductivity in multil ayer cuprate Ba2Ca3Cu4O8F2. Phys. Rev. Lett. 103, 036403 (2009)

    work page 2009

  35. [35]

    Hashimoto, M. et al. Particle–hole symmetry breaking in the pseudogap state of Bi2201. Nature Physics 6, 414–418 (2010)

    work page 2010

  36. [36]

    Berben, M. et al. Superconducting dome and pseudogap end- point in Bi2201. Physical Review Materials 6, 044804 (2022)

    work page 2022

  37. [37]

    Ideta, S. et al. Hybridization of Bogoliubov quasiparti- cles between adjacent CuO 2 layers in the triple-layer cuprate Bi2Sr2Ca2Cu3O10+δ studied by angle-resolved photoemission spectroscopy. Phys. Rev. Lett. 127, 217004 (2021)

    work page 2021

  38. [38]

    Zhang, Y . et al. Nodal superconducting-gap structure in fer- ropnictide superconductor BaFe2(As0.7P0.3)2. Nature Physics 8, 371–375 (2012)

    work page 2012

  39. [39]

    & K amin- ski, A

    Kondo, T., Khasanov, R., Takeuchi, T., Schmalian, J. & K amin- ski, A. Competition between the pseudogap and supercon- ductivity in the high-T c copper oxides. Nature 457, 296–300 (2009)

    work page 2009

  40. [40]

    Loeser, A. et al. Excitation gap in the normal state of under- doped Bi2Sr2CaCu2O8+δ. Science 273, 325–329 (1996)

    work page 1996

  41. [41]

    Tokunaga, Y . et al. Effect of carrier distribution on super- conducting characteristics of the multilayered high-T c cuprate (Cu0.6,C0.4)Ba2Ca3Cu4O12+y: 63Cu-NMR study. Phys. Rev. B 61, 9707 (2000)

    work page 2000

  42. [42]

    Kotegawa, H. et al. Unusual magnetic and superconducting characteristics in multilayered high-T c cuprates: 63Cu NMR study. Phys. Rev. B 64, 064515 (2001)

    work page 2001

  43. [43]

    Drozdov, I. K. et al. Phase diagram of Bi 2Sr2CaCu2O8+δ revis- ited. Nature communications 9, 5210 (2018)

    work page 2018

  44. [44]

    Peng, Y . et al. Influence of apical oxygen on the extent of in- plane exchange interaction in cuprate superconductors. Nature Physics 13, 1201–1206 (2017)

    work page 2017

  45. [45]

    Rimberg, A. et al. Dissipation-driven superconductor-insulator transition in a two-dimensional Josephson-junction array. Phys. Rev. Lett. 78, 2632 (1997)

    work page 1997

  46. [46]

    Caldeira, A. O. & Leggett, A. J. Quantum tunnelling in a d issi- pative system. Annals of physics 149, 374–456 (1983)

    work page 1983

  47. [47]

    & Kivelson, S

    Emery, V . & Kivelson, S. Importance of phase fluctuation s in superconductors with small superfluid density. Nature 374, 434–437 (1995)

    work page 1995