{"id":"322eb429-f89f-4c14-8fa3-e3ee531b4395","arxiv_id":"2506.01448","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"In trilayer Bi2223, the underdoped inner plane hosts charge order and a large pairing gap while staying as coherent as the overdoped outer planes, suggesting interlayer proximity boosts both pairing and phase coherence.","lead":"Using time-resolved photoemission, this study finds that the inner and outer copper-oxide planes of a trilayer superconductor behave very differently: the inner plane hosts short-range charge order and a large superconducting gap, yet remains unusually coherent. The authors propose that coupling between the differently doped planes boosts both pairing and coherence, offering a possible explanation for the record critical temperature of Bi2223.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central interlayer-coherence mechanism is not quantitatively supported: the paper's own CRISB calculation yields only a few percent enhancement in IP quasiparticle weight, far below the experimentally claimed exceptional coherence.","rationale":"The reader's weakest_assumption centers on the layer-specific assignment of the charge order, particularly the reliance on the tr-ARPES spectral-weight crossover and the lack of layer-resolved RXS. That is a legitimate concern, but I regard the quantitative insufficiency of the proposed interlayer mechanism as more load-bearing for the paper's central claim. The strongest_claim explicitly asserts that proximity between layers increases IP coherence and OP pairing, providing 'new microscopic insight into the record Tc.' The only direct theoretical support is the CRISB calculation, which the authors themselves describe as producing only a few percent effect and not aiming at quantitative description. Meanwhile, the experimental evidence for the coherence anomaly is a cross-compound comparison (Bi2223 IP vs. underdoped Bi2201/Bi2212) that is not controlled for disorder, surface termination, or matrix-element differences. The 'screened from inhomogeneities' statement in the Introduction offers a plausible non-proximity explanation. Thus the mechanism is speculative, and the abstract's claim to have 'revealed' it is too strong. This does not invalidate the experimental observations or the CO-detection work; it means the paper's interpretive layer should be conditioned. The reader's CONDITIONAL verdict remains appropriate, so I recommend UNCHANGED, with the caveat that the authors should soften the central mechanism claim and provide the missing controlled calculation or clearly label the mechanism as a hypothesis. My agreement is 'partial' because the reader and I identify different weak points, though both point to the need for revision.","tokens_in":13091,"tokens_out":10652,"duration_ms":122057,"concrete_test":"Re-run the CRISB (or cluster DMFT) calculation of the three-layer model with the same parameters as Fig. 5, sweeping the interlayer hopping t_perp from 0 (single-layer limit) to 0.4t, and compute the IP quasiparticle weight Z_IP at p_IP≈0.08 and the OP antinodal gap at p_OP≈0.22. If the increase in Z_IP relative to t_perp=0 remains only a few percent, then the interlayer-proximity mechanism cannot account for the experimentally observed IP coherence, and the abstract and discussion must be revised to present the mechanism as a conjecture rather than a finding.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's headline conclusion is that proximity between the underdoped inner plane (IP) and overdoped outer planes (OP) increases IP quasiparticle coherence and OP pairing, thereby explaining the record Tc of Bi2223. The only quantitative evidence for this mechanism is the three-layer Hubbard CRISB calculation of Fig. 5. Yet the authors explicitly state that the interlayer enhancement of the IP quasiparticle weight is 'small (a few percent) in our calculations' (Section 'Layer-resolved correlations and superconductivity'), and they defer a larger effect to future work with more accurate many-body coupling. Thus the quantitative model does not reproduce the experiment's central anomaly: an underdoped IP (p≈0.08) with a sharp, coherent quasiparticle peak comparable to the OP. The experimental comparison to underdoped Bi2201/Bi2212 (Fig. 4a,b) is not a controlled single-layer limit; the Bi2223 IP is structurally shielded from spacer-layer disorder, a known alternative source of enhanced coherence, and this alternative is not addressed. The theoretical limitation is self-acknowledged ('does not aim at a quantitative description'), so the abstract's 'reveal a unique interlayer mechanism' overstates what the evidence supports. This is a load-bearing gap in the central claim, not a peripheral concern.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript presents tr-ARPES and RXS measurements on trilayer Bi2223 and argues that the inner CuO2 plane (IP), at estimated doping p≈0.08, hosts short-range charge order at Q≈0.33 r.l.u., an underdoped-like d-wave gap (Δ0≈67 meV), and yet anomalously high quasiparticle coherence comparable to the overdoped outer planes (OP, p≈0.25). The pump-induced spectral-weight dynamics show a nodal increase and off-nodal decrease for the IP, interpreted as melting of CO, while the OP response is different. Complementary three-layer Hubbard calculations using CRISB reproduce the layer-resolved Fermi-surface and gap hierarchy and find a small interlayer enhancement of IP coherence and OP pairing. The authors conclude that interlayer proximity between underdoped and overdoped planes simultaneously optimizes pairing strength and phase coherence, providing a microscopic explanation for the record Tc of Bi2223.","tokens_in":13349,"tokens_out":6642,"duration_ms":73064,"significance":"If the layer-selective CO and interlayer-coherence mechanism are correct, the paper provides a new experimental window into why trilayer cuprates have the highest Tc: it would reconcile a strongly paired underdoped inner plane with a phase-coherent, overdoped outer plane. The strengths are the combination of layer-resolved tr-ARPES with RXS confirmation of a CO-like wavevector, the systematic extraction of quasiparticle weight and scattering rates, and the transparent theoretical comparison. The CRISB calculation is not fitted to the measured Z or gap values, so the comparison is not circular; it independently yields the correct layer-resolved Fermi-surface and gap hierarchy, and it openly states its quantitative limitations. The main value of the paper is the formulation of a precise, falsifiable scenario rather than a completed quantitative proof of the mechanism.","major_comments":[{"comment":"The central mechanistic claim—interlayer proximity increases IP coherence and OP pairing—rests on the CRISB results in Fig. 5, but the quantitative support is acknowledged to be small: the IP Z enhancement is \"small (a few percent)\", the OP gap enhancement is \"quantitatively small\", and the Methods state that the model \"does not aim at a quantitative description of the experimental results\". The experimental anomaly is large: the IP and OP HWHM are equivalent in Fig. 4(c), and the IP Z rises toward the OP value with temperature in Fig. 4(d). A few-percent effect in a model that explicitly disclaims quantitative accuracy does not demonstrate that interlayer coupling is the origin of the observed exceptional IP coherence. The authors need either a calculation capable of producing a larger effect (for example, including interlayer correlations beyond the present static embedding) or a quantitative bound on the enhancement from interlayer coupling, and the abstract and Discussion must be moderated to the level of the presented evidence.","section":"Layer-resolved correlations and superconductivity: theoretical perspective"},{"comment":"The comparison in Fig. 4(a–c) of the Bi2223 IP with underdoped Bi2201 and Bi2212 is not a controlled test of interlayer proximity. As the paper notes in the introduction, the IP is \"screened from inhomogeneities in the spacer layers\", while the Fermi-surface sheets measured in Bi2201 and Bi2212 are associated with CuO2 planes in direct contact with the (BiO)2 spacer layers. Spacer-layer disorder is a known source of quasiparticle broadening and incoherence in underdoped cuprates, so the higher coherence of the Bi2223 IP could reflect reduced structural disorder rather than proximity to the overdoped OP. This alternative is not addressed or excluded in the manuscript. The central claim that \"it is the proximity of the IP to the OP that is responsible for its sharp spectral features\" therefore needs either a control experiment or a quantitative disorder model before it can be regarded as established.","section":"Layer-dependent quasiparticle weight and pairing gap"},{"comment":"The layer attribution of the charge order is underdetermined. The RXS signal at Q≈0.33 r.l.u. in Fig. 3(c) is not layer-resolved; it demonstrates that the sample contains short-range CO with that wavevector, but it cannot show that the order resides on the IP. The assignment rests on the interpretation of the momentum-dependent tr-ARPES spectral-weight crossover around the node as the signature of a reconstructed IP Fermi surface (Fig. 3(b)), an interpretation that is plausible but not directly verified. Moreover, no temperature-dependent CO measurement is shown; the claim that the pump-induced Z increase is due to CO melting would be strongly supported by temperature-dependent RXS (for example, peak intensity versus T) or by a pump-probe RXS experiment. Without such evidence, the \"layer-selective\" charge-order narrative and the inference that CO fluctuations suppress IP coherence are not uniquely established.","section":"Observation of layer-selective charge order by tr-ARPES and RXS"}],"minor_comments":[{"comment":"The normalization of the EDCs in Fig. 4(a,b) is not fully transparent: the overdoped spectra are scaled to the QP peak height and the underdoped backgrounds are \"scaled to match\". This procedure can exaggerate or suppress apparent linewidth differences; the raw spectra, or an explicit statement of the scaling factors, should be provided.","section":"Layer-dependent quasiparticle weight and pairing gap"},{"comment":"The definition Z=∫_{−0.025}^{∞} I(k_F,ω)dω / ∫_{−∞}^{∞}I(k_F,ω)dω in Fig. 4(d) depends on the choice of integration window lower bound; the sensitivity of the extracted Z values and of the temperature trend to this bound should be reported or cited from the Supplementary Material.","section":"Layer-dependent quasiparticle weight and pairing gap"},{"comment":"There is a typo in the text: \"upong including\" should read \"upon including\".","section":"Layer-resolved correlations and superconductivity: theoretical perspective"},{"comment":"The doping values p=0.08±0.02 and p=0.25±0.02 and the gap amplitudes Δ0=67 meV and 36 meV are quoted in the main text without specifying the extraction procedure; a short pointer to the relevant Supplementary Material sections for each quantity would improve reproducibility.","section":"Layer-dependent quasiparticle weight and pairing gap"}],"recommendation":"major_revision","confidential_remarks":"This is a strong experimental paper whose main risk is inferential rather than technical. The tr-ARPES and RXS data are of high quality, and the qualitative picture is attractive, but the quantitative theory support for the central interlayer mechanism is small and explicitly non-quantitative, and the layer assignment of the charge order has no independent layer-resolved confirmation. I do not see grounds for rejection; a major revision that moderates the claims to match the evidence, adds the requested controls or explicit uncertainty, and strengthens the theoretical case would make it acceptable. I also see no citation-pattern concerns; the self-citations are standard for this line of work."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know this paper for the experiment, not for the theory. The tr-ARPES measurements resolve clear, layer-dependent behavior in Bi2223: the inner plane is underdoped with a large gap and, unexpectedly, high quasiparticle coherence; the outer planes are overdoped with a smaller gap that is still larger than comparable Bi2212. The momentum-dependent spectral weight dynamics around the node, plus the RXS peak at Q≈0.33 r.l.u., is the first ARPES-style detection of charge order in a trilayer cuprate. That is a genuine advance, and the data seem carefully taken and analyzed. Credit is due for the layer-resolved comparison and for the explicit statement that the theory is only qualitative.\n\nNow the soft spots. First, the RXS is not layer-resolved, so the claim that the charge order lives specifically on the inner plane rests entirely on the tr-ARPES angular crossover. That crossover is consistent with IP charge order, but it is an indirect inference—other explanations for the momentum-dependent pump response are not ruled out. Second, the link between CO melting and the measured coherence increase is asserted but not directly shown: no temperature-dependent CO measurement is presented. Third, the CRISB calculation is honest about its quantitative limits, but the few-percent enhancement it finds is orders of magnitude short of the experimentally claimed exceptional coherence. Calling this a 'unique interlayer mechanism' in the abstract overshoots what the evidence supports. Fourth, the comparison to underdoped Bi2201/Bi2212 is not controlled; the IP is structurally screened from spacer disorder, which could independently explain its sharper coherence.\n\nThese are not fatal flaws. The experimental facts are new and interesting on their own, and the authors identify most of the caveats themselves. But the paper would be stronger if the central narrative were framed as a hypothesis rather than a demonstrated mechanism. The missing error bars and lack of a data availability statement are small problems but should be fixed.\n\nVerdict: send this to peer review. A good referee should push on the layer attribution of the CO and on the overreach in the abstract, but the experimental core deserves publication. I would not cite the interlayer mechanism as established, but I would cite the tr-ARPES result if I worked on multilayer cuprates.","headline":"A striking experimental paper with a plausible but not proven interlayer mechanism; the tr-ARPES evidence for layer-selective charge order is the real advance, while the theoretical support is too weak to carry the full weight of the abstract's claims.","tokens_in":14038,"tokens_out":1539,"would_cite":true,"duration_ms":20893,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that the trilayer cuprate Bi2223 reaches record $T_c$ because its underdoped inner CuO$_2$ plane gains quasiparticle coherence from overdoped outer planes while sharing its strong pairing with them.","keywords":["trilayer cuprate","Bi2223","charge order","quasiparticle coherence","time-resolved ARPES","resonant X-ray scattering","interlayer coupling","Hubbard model"],"falsifier":"Measure the charge-order reflection with layer sensitivity — for example by resonant scattering tuned to the inner-plane environment — while repeating the pump-probe coherence measurement; if the $Q \\simeq 0.33$ r.l.u. signal survives at electronic temperatures where the inner-plane coherence has already risen, or vanishes while the coherence gain remains, the proposed mechanism fails. A simpler first check is a temperature sweep of the RXS intensity through the same electronic temperatures used in the time-resolved experiment, which would show whether charge-order melting actually tracks the coherence enhancement.","tokens_in":12894,"feed_emoji":"⚡","tokens_out":9842,"duration_ms":101489,"temperature":0.7,"pith_summary":"This paper argues that the record superconducting temperature of the trilayer cuprate Bi2223 comes from a division of labor between the three copper-oxide planes in each unit cell. Using time- and angle-resolved photoemission, it identifies the inner plane as a strongly underdoped layer — hole concentration $p \\approx 0.08$, short-range charge order at $Q \\simeq 0.33$ r.l.u., and a d-wave gap of about 67 meV — yet finds that this plane carries sharp, long-lived quasiparticles instead of the incoherent spectral weight typical of underdoped cuprates. The two outer planes are overdoped ($p \\approx 0.25$) with a smaller gap of about 36 meV, which is nevertheless larger than in comparably doped bilayer compounds. The paper proposes that proximity between the two kinds of planes transfers pairing strength to the outer layers and phase coherence to the inner layer, so that strong pairing and phase rigidity are optimized at the same time. If this is right, it would explain why multilayer cuprates outperform single- and bilayer ones, and would push theories of cuprate superconductivity toward interlayer, rather than purely intralayer, physics.","feed_headline":"Differently doped CuO2 layers cooperate to lift cuprate Tc","feed_subtitle":"A strongly paired inner plane stays coherent thanks to overdoped neighbors, pointing to why trilayers hold the record.","key_machinery":"The central object is the trilayer block itself: three CuO$_2$ planes with deliberately imbalanced hole content (inner $p \\approx 0.08$, outer $p \\approx 0.25$), addressed separately by time- and angle-resolved photoemission (tr-ARPES). The analysis rides on momentum-distribution-curve fitting, where the Lorentzian width $\\Gamma(\\omega) = Z\\, \\Sigma''(\\omega)$ gives the product of quasiparticle residue and imaginary self-energy while the Lorentzian area $A_L \\propto Z$ isolates the residue, so pump-induced changes in $\\Gamma$ and $A_L$ track layer-specific coherence in real time. The charge-order assignment is carried by the angular location of the spectral-weight crossover ($\\pm 6^\\circ$ around the node, matching backfolding by $Q \\simeq \\pm 0.33$ r.l.u.) and by RXS peaks at that wavevector with correlation length $\\xi_{\\mathrm{CO}} \\sim 20$–$30$ Å. On the theory side, a three-layer single-band Hubbard model with different on-site energies per layer, solved by the cluster rotationally-invariant slave-boson method, supplies the layer-resolved quasiparticle weights and d-wave gaps that the mechanism requires.","core_discovery":"On its own terms, the paper establishes that the inner and outer CuO$_2$ planes of Bi2223 do not behave like independent copies of the cuprate phase diagram. The inner plane carries a small Fermi surface ($p = 0.08 \\pm 0.02$), a superconducting gap of $\\Delta^{\\mathrm{IP}}_0 \\approx 67$ meV, and — as shown by a sign change in the pump-induced spectral-weight response at Fermi-surface angles beyond $\\pm 6^\\circ$ from the node — short-range charge order at $Q \\simeq 0.33$ r.l.u. that is confirmed by resonant X-ray scattering. Despite being underdoped, this plane has a quasiparticle residue and scattering rate comparable to the overdoped outer planes, and suppressing the charge-order fluctuations with the pump raises its coherence further toward the outer-plane value. The paper interprets these observations as evidence for an interlayer mechanism: the overdoped outer planes ($p=0.25 \\pm 0.02$, $\\Delta^{\\mathrm{OP}}_0 \\approx 36$ meV) gain pairing strength from the strongly paired inner plane, while the inner plane gains coherence from its proximity to the metallic, overdoped layers. Three-layer Hubbard calculations with layer-resolved dopings reproduce the qualitative pattern — inner-plane gap larger, outer-plane gap slightly enhanced over a single layer at the same doping — and the paper concludes that this proximity effect underlies the record $T_c$ of Bi2223.","pith_inferences":["Editorial inference: the mechanism is directly testable by a temperature-dependent RXS sweep over the same electronic temperatures used in the tr-ARPES; if the $Q \\simeq 0.33$ r.l.u. signal does not melt as inner-plane coherence rises, the charge-order attribution would need revision.","Editorial inference: reading the paper as a design rule suggests that alternating strongly and weakly correlated layers in other oxide heterostructures should raise $T_c$, with the testable prediction that adding more underdoped inner layers increases the gain.","Editorial inference: because the paper treats charge-order fluctuations as a competitor to the proximity-enhanced coherence, weakening the order — by strain, disorder, or magnetic field — should further increase the inner-plane quasiparticle weight at low temperature, a control not included in the current dataset."],"forward_implications":["The underdoped inner plane should not be modeled as an incoherent bad metal: its sharp quasiparticle peak is presented as a genuine, proximity-induced property rather than a violation of underdoped physics.","The outer-plane gap of about 36 meV, larger than in comparably doped Bi2212, is taken as evidence that strong pairing leaks from the inner plane outward, so a microscopic theory of Bi2223 must reproduce this overshoot.","The pump-induced increase of nodal spectral weight, opposite to the ubiquitous suppression in single- and bilayer cuprates, marks short-range charge order as a coherence-suppressing fluctuation whose melting can be followed in real time.","Optimizing $T_c$ in cuprates may require engineering an intralayer-unit-cell doping imbalance rather than tuning one uniform doping, consistent with the empirical record of multilayers."],"supporting_citations":[{"why":"Establishes the loss of nodal quasiparticle integrity in underdoped cuprates and supplies the spectral-weight integration procedure used to extract the quasiparticle residue.","marker":"[4]"},{"why":"Provides the time-resolved ARPES methodology that produces the layer-selective pump-probe spectral-weight dynamics.","marker":"[12]"},{"why":"Earlier ARPES determination of enhanced superconducting gaps in trilayer Bi2223 that this study refines and resolves by layer.","marker":"[18]"},{"why":"Demonstrates hybridization of the inner- and outer-plane Bogoliubov quasiparticle bands, showing interlayer coupling is already active in the superconducting state.","marker":"[21]"},{"why":"Documents the ubiquitous suppression of nodal coherent spectral weight in single- and bilayer Bi-based cuprates that the inner-plane behavior contradicts.","marker":"[28]"},{"why":"Provides the single-layer Bi2201 charge-order reference whose RXS lineshape and wavevector anchor the identification of charge order in Bi2223.","marker":"[32]"},{"why":"Introduces the cluster rotationally-invariant slave-boson method used to compute the normal-state layer-resolved quasiparticle weights.","marker":"[35]"},{"why":"Extends the slave-boson method to the superconducting state, yielding the layer-resolved d-wave gaps used in the theoretical comparison.","marker":"[36]"}],"fun_headline_variants":["Differently doped layers team up to boost cuprate superconducting temperature","Trilayer cuprate: underdoped inner plane gains coherence from overdoped neighbors","Why trilayers win: disparate dopings optimize pairing and coherence","Cuprate record explained: interlayer synergy between underdoped and overdoped planes","Trilayer cuprate's record Tc arises from interlayer doping mismatch"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire layer-selective story depends on the premise that the momentum-dependent spectral-weight change seen by time-resolved photoemission is caused by short-range charge order living specifically on the inner plane, because the X-ray scattering data that confirm the charge-order wavevector are not layer-resolved and no temperature-dependent charge-order measurement is shown.","fun_headline_variants_meta":{"raw":{"variants":["Differently doped layers team up to boost cuprate superconducting temperature","Trilayer cuprate: underdoped inner plane gains coherence from overdoped neighbors","Why trilayers win: disparate dopings optimize pairing and coherence","Cuprate record explained: interlayer synergy between underdoped and overdoped planes","Trilayer cuprate's record Tc arises from interlayer doping mismatch"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000928,"raw_usage":{"total_tokens":4048,"prompt_tokens":1090,"completion_tokens":2958,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":706,"completion_tokens_details":{"reasoning_tokens":2856}},"tokens_in":706,"tokens_out":2958,"duration_ms":18797,"temperature":1.0,"reasoning_tokens":2856,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T11:43:28.936443+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the charge-order reflection with layer sensitivity — for example by resonant scattering tuned to the inner-plane environment — while repeating the pump-probe coherence measurement; if the $Q \\simeq 0.33$ r.l.u. signal survives at electronic temperatures where the inner-plane coherence has already risen, or vanishes while the coherence gain remains, the proposed mechanism fails. A simpler first check is a temperature sweep of the RXS intensity through the same electronic temperatures used in the time-resolved experiment, which would show whether charge-order melting actually tracks the coherence enhancement.","supporting_citations":[{"cited_title":"Fournier, G","cited_arxiv_id":null,"evidence_quote":"Establishes the loss of nodal quasiparticle integrity in underdoped cuprates and supplies the spectral-weight integration procedure used to extract the quasiparticle residue."},{"cited_title":"Boschini, M","cited_arxiv_id":null,"evidence_quote":"Provides the time-resolved ARPES methodology that produces the layer-selective pump-probe spectral-weight dynamics."},{"cited_title":"Ideta, K","cited_arxiv_id":null,"evidence_quote":"Earlier ARPES determination of enhanced superconducting gaps in trilayer Bi2223 that this study refines and resolves by layer."},{"cited_title":"Kunisada, S","cited_arxiv_id":null,"evidence_quote":"Demonstrates hybridization of the inner- and outer-plane Bogoliubov quasiparticle bands, showing interlayer coupling is already active in the superconducting state."},{"cited_title":"Zonno, F","cited_arxiv_id":null,"evidence_quote":"Documents the ubiquitous suppression of nodal coherent spectral weight in single- and bilayer Bi-based cuprates that the inner-plane behavior contradicts."},{"cited_title":"Comin, A","cited_arxiv_id":null,"evidence_quote":"Provides the single-layer Bi2201 charge-order reference whose RXS lineshape and wavevector anchor the identification of charge order in Bi2223."},{"cited_title":"Lechermann, A","cited_arxiv_id":null,"evidence_quote":"Introduces the cluster rotationally-invariant slave-boson method used to compute the normal-state layer-resolved quasiparticle weights."}],"review_version":1}