{"id":"45bbdb6e-2f0c-4032-b94e-3e978c82b30e","arxiv_id":"2506.08763","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Micro-ARPES on (Hg,Re)1223 shows the superconducting gap of the outer CuO2 plane is about 57 meV, much larger than Bi2223's roughly 43 meV, while the inner-plane gap is similar, implicating outer-plane pairing in the record Tc.","lead":"Using a tightly focused X-ray beam, researchers measured how the superconducting gap differs between the two types of copper-oxide layers in the mercury-based three-layer cuprate with the highest known transition temperature at normal pressure. They found the outer layers carry a much larger pairing energy than in the bismuth-based cousin, suggesting outer-plane pairing, not inner-plane pairing, is what pushes Tc the highest.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Near-nodal gap calibration, not IP/OP assignment, is the load-bearing uncertainty for the claimed OP enhancement.","rationale":"The reader identifies the IP/OP branch assignment as the weakest assumption. I disagree that this is the most load-bearing step for the central claim. If the two branches were swapped, the measured gap set {57, 63} would simply exchange labels: the OP would carry the 63 meV gap and the IP the 57 meV gap. Against Bi2223's ~43 meV OP and ~60 meV IP, the qualitative hierarchy—OP substantially larger than Bi2223's OP, IP comparable to Bi2223's IP—would survive. The branch assignment mainly affects doping estimates and the small-pocket interpretation, not the gap-enhancement conclusion. The genuinely load-bearing step is the conversion of near-nodal small-gap spectra into absolute gap values. The paper uses the empirical Δ ≈ 2.2 Δ_LEM for all points with d-wave order parameter < 0.2; these points set the slope of the linear extrapolation to Δ0. No internal validation of this factor is presented, and the quoted errors exclude its uncertainty. A 20% change in the factor would move Δ0(OP) by roughly 10 meV, eroding most of the 14 meV difference from Bi2223. This is a settleable systematic: re-extract the near-nodal gaps with a model fit or higher resolution and compare Δ0 values to Bi2223 under identical analysis. The rest of the paper—careful micro-spot ARPES, separate IP/OP dispersions, and the Δ0–Tc scaling—is a plausible and valuable first result; the conditional verdict should stand pending such a check.","tokens_in":14690,"tokens_out":10575,"duration_ms":131798,"concrete_test":"Re-analyze the raw symmetrized EDCs for the near-nodal OP and IP cuts (Supplemental Fig. S2) by fitting a model superconducting spectral function (e.g., a Dynes-type gap with a d-wave order parameter and an appropriate self-energy) to extract Δ directly, without invoking Δ ≈ 2.2 Δ_LEM. If the re-derived near-nodal points yield a linear slope giving Δ0(OP) below ~50 meV—or if the same re-analysis applied to the Bi2223 reference data removes the 14 meV difference—the claimed significant OP enhancement is not robust. Alternatively, repeat the ARPES measurement with an energy resolution ΔE ≤ 5 meV so that coherence peaks can be resolved at |cos(kx)−cos(ky)|/2 < 0.2, and check whether the extrapolated Δ0 values reproduce the reported 57±1 and 63±3 meV.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The quantitative claim that Δ0(OP)=57±1 meV is significantly larger than Bi2223's ~43 meV depends on the near-nodal gap calibration, not on the IP/OP branch assignment. Swapping the two branch labels would exchange the two measured gap values (57 and 63 meV); the OP would still have a gap well above Bi2223's OP (~43 meV) and the IP would still be comparable to Bi2223's IP (~60 meV). Thus the branch-assignment ambiguity does not by itself undermine the central qualitative conclusion. In contrast, Supplemental Sec. II shows that all gap points with d-wave order parameter |cos(kx)−cos(ky)|/2 < 0.2—precisely the points that set the slope of the linear d-wave extrapolation in Fig. 3(l)—are obtained from leading-edge midpoints via the imported empirical relation Δ ≈ 2.2 Δ_LEM. The reported ±1 meV error bar only includes smoothing extrapolation and photon-energy drift; it does not include uncertainty in this conversion factor or in the 12 meV energy resolution. If the true conversion factor differs by ~20%, as can happen when self-energy or background conditions change, the extrapolated Δ0(OP) shifts by ~10 meV, shrinking the 14 meV 'enhancement' over Bi2223 to within systematic noise. The causal statement that enhanced OP pairing is essential for the highest Tc would then lose its quantitative basis.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports the first momentum-resolved ARPES study of the trilayer cuprate (Hg,Re)Ba2Ca2Cu3O8+δ, a material with Tc = 130 K that holds the ambient-pressure record. Using a 10 µm micro-focused beam, the authors separate quasiparticle dispersions from the inner and outer CuO2 planes and extract the superconducting gap along the Fermi surface. From a near-nodal d-wave extrapolation they obtain Δ0(IP) = 63 ± 3 meV and Δ0(OP) = 57 ± 1 meV, which they compare with the corresponding values in Bi2223 (about 60 and 43 meV). The central claim is that the outer-plane pairing energy is substantially enhanced relative to Bi2223, and that this enhancement, rather than the inner-plane gap, is essential for the highest Tc at ambient pressure.","tokens_in":14911,"tokens_out":4978,"duration_ms":65615,"significance":"If the result holds, it is a significant step: it is the first momentum-resolved superconducting gap in a Hg-based trilayer cuprate, a system long inaccessible to ARPES, and it offers a direct test of the prevailing view that the inner plane dominates pairing in trilayer cuprates. The paper also provides a useful comparison of Δ0 versus Tc across several cuprate families and proposes a plausible mechanism based on reduced Cu-3d/(apical-O) hybridization at the outer plane. The experimental methodology—micro-spot ARPES with spatial selection of clean regions, symmetrized-EDC analysis, and explicit accounting of statistical smoothing/photon-drift errors—is careful and reproducible in spirit, although no code or raw data are deposited.","major_comments":[{"comment":"The near-nodal gap points that determine the slope of the linear d-wave extrapolation in Fig. 3(l) are obtained from leading-edge midpoints via the imported empirical relation Δ ≈ 2.2 Δ_LEM. The quoted uncertainties (Δ0(IP)=63±3 meV, Δ0(OP)=57±1 meV) propagate only the smoothing extrapolation and photon-energy drift, not the uncertainty in the 2.2 conversion factor nor the effect of the 12 meV instrumental resolution. Since the claimed OP enhancement over Bi2223 (~43 meV) is only about 14 meV, a plausible ±20% variation in the conversion factor would shift Δ0(OP) by roughly 10 meV, reducing the comparison to within systematic noise. The authors should provide a quantitative propagation of this systematic uncertainty into Δ0, or explicitly restrict the conclusion to a qualitative statement of enhanced OP pairing.","section":"Supplemental Sec. II; main-text Fig. 3(l)"},{"comment":"The assignment of the two Fermi-surface branches to the IP and OP relies on the NMR-based doping ordering and is made before the gap analysis. The text does not discuss the robustness of the central conclusion to a swap of the branch labels. Although a swap would exchange the two measured Δ0 values (57 and 63 meV) and would not change the qualitative claim that the OP branch has a larger gap than Bi2223's OP (~43 meV), the authors should state this explicitly; as written, the reader could infer that the IP/OP identification is a necessary premise of the result. This clarification would strengthen the paper without new data.","section":"Fig. 2(e); main text after the tight-binding fit"}],"minor_comments":[{"comment":"Typographical errors: 'charaterization' should be 'characterization', and 'psuedogap' should be 'pseudogap' (appears twice).","section":"Introduction"},{"comment":"The phrase 'electron-photon coupling' should be 'electron-phonon coupling'.","section":"Last paragraph of main text"},{"comment":"The small-pocket Fermi-surface area estimate is based on averaging two extreme cases, and the text does not propagate the resulting uncertainty in pFS into the comparison with Bi2223. A brief statement of the range (e.g., pFS(OP)=0.12–0.17) in the main-text discussion would be appropriate.","section":"Supplemental Sec. I"},{"comment":"The gray line in Fig. 4 is described as a guide to the eye; given that the scaling claim is central to the paper's interpretive framework, the authors should indicate whether a linear correlation is statistically significant and how the trilayer points (which are averages over two planes) were treated in the comparison.","section":"Fig. 4"},{"comment":"The symbol σ is used both for the total error and for the standard deviation in the formula σ = sqrt(σ_gap^2 + σ_hν^2); renaming the total error, for example to δΔ, would avoid ambiguity.","section":"Supplemental Sec. II"}],"recommendation":"major_revision","confidential_remarks":"The paper is technically interesting and likely correct in its qualitative conclusion, but the quantitative claim of a 14 meV OP enhancement over Bi2223 needs a more honest treatment of systematic uncertainties, particularly the 2.2 leading-edge conversion factor. The single-crystal/single-doping limitation is also worth flagging to the editor, though it is not disqualifying for a first ARPES study of this material. I would not recommend reject; the issue is fixable by adding a systematic-error estimate or softening the quantitative claim."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"What you need to know: this is the first momentum-resolved superconducting gap measurement on a Hg-based trilayer cuprate, and that alone is a real achievement. The authors used micro-focused ARPES on a notoriously difficult cleavage surface, resolved the IP and OP bands separately, and report Δ0(OP)=57±1 meV versus ~43 meV in Bi2223, with Δ0(IP)=63±3 meV comparable to Bi2223's ~60 meV. The paper is worth reading.\n\nWhat it does well: the spatial mapping to find a clean surface is careful, the bilayer-split Fermi surfaces are plausibly assigned using NMR hole counts, and the small-pocket doping reinterpretation is flagged honestly rather than buried. The analysis is standard for the field: symmetrized EDCs, d-wave extrapolation from near-nodal points. No circularity; the gap values are measured, not fitted to a conclusion.\n\nThe soft spot is exactly where the stress-test puts it. The near-nodal points with d-wave order parameter below 0.2—the ones pinning the linear extrapolation—come from leading-edge midpoints converted through the empirical Δ≈2.2Δ_LEM relation. The ±1 meV error bar includes smoothing and photon drift, not uncertainty in that conversion factor. If the factor is off by 20%, a plausible scenario when self-energy or background changes, Δ0(OP) shifts by ~10 meV and the 14 meV enhancement over Bi2223 shrinks to noise. That is the load-bearing uncertainty.\n\nBy contrast, the IP/OP branch assignment is not the problem. Swap the labels and you get OP=63 meV (still well above Bi2223's 43) and IP=57 meV (still comparable to 60). The qualitative story survives the swap, though the quantitative numbers swap. So the reader's weakest-assumption worry is secondary.\n\nAlso real but less critical: one crystal, one doping, one surface spot, no systematic uncertainty budget. The causal statement that OP pairing is essential for the record Tc goes beyond the data, but the authors phrase it as a suggestion, and the cross-material correlation with Tc is suggestive, not proof.\n\nBottom line: a solid first measurement that deserves referee time. The main revision should address the calibration uncertainty—either by showing robustness of Δ0 to conversion-factor variation or by measuring more doping/samples. If that uncertainty is resolved, the result is a meaningful step for cuprate ARPES.","headline":"First ARPES gap map of a Hg-based trilayer cuprate, but the claimed OP enhancement stands or falls on the imported near-nodal calibration, not on the IP/OP assignment.","tokens_in":15552,"tokens_out":1531,"would_cite":true,"duration_ms":22131,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"In the trilayer cuprate (Hg,Re)1223, the outer CuO2 plane carries a much larger superconducting gap than in Bi2223, and the paper argues this outer-plane pairing is what enables the highest ambient-pressure Tc.","keywords":["trilayer cuprate","Hg1223","angle-resolved photoemission spectroscopy","superconducting gap","CuO2 planes","high-temperature superconductivity","d-wave gap","optimal doping"],"falsifier":"A bulk-sensitive measurement of IP and OP hole concentrations on the same crystals (for example, NMR) that contradicted the assumed doping ordering, or an ARPES experiment resolving interlayer Bogoliubov hybridization to fix the branch labels, would settle whether the enhanced gap truly sits in the outer plane.","tokens_in":1976,"feed_emoji":"🧲","tokens_out":3119,"duration_ms":70398,"temperature":0.7,"pith_summary":"This paper reports the first momentum-resolved superconducting gap measurements on the Hg-based trilayer cuprate (Hg,Re)Ba2Ca2Cu3O8+δ, the material family that holds the highest superconducting transition temperature at ambient pressure (Tc = 130 K here). Using a micro-focused photoemission beam, the authors resolve the Fermi surfaces and superconducting gaps of the two inequivalent CuO2 planes separately. They find that the inner-plane gap is comparable to that of the lower-Tc trilayer Bi2223, while the outer-plane gap is substantially larger. They conclude that enhanced pairing in the outer plane, not the inner plane, is what pushes the Hg-based trilayer to the top of the Tc scale. If correct, this shifts the focus for designing higher-Tc cuprates from the inner to the outer CuO2 plane.","feed_headline":"Outer plane pairing lifts trilayer cuprate to 130 K","feed_subtitle":"In (Hg,Re)1223, the outer CuO2 plane's superconducting gap far exceeds Bi2223's, while the inner plane barely changes.","key_machinery":"The key instrument is a micro-focused angle-resolved photoemission beam (10 µm × 10 µm spot) used on cleaved (Hg,Re)1223 single crystals, which lets the authors find clean surface regions despite the lack of natural cleavage planes. The argument then rests on assigning the two observed Fermi-surface branches to the inner and outer CuO2 planes (smaller radius to IP, larger to OP, guided by NMR doping estimates) and on extracting $\\Delta_0$ by linearly extrapolating the near-nodal d-wave gap to the antinode. A small Fermi-pocket picture based on the doped resonating-valence-bond spin liquid is invoked to convert measured Fermi-surface areas into hole dopings and to avoid the unphysical electron doping that a large-surface tight-binding fit would give for the inner plane.","core_discovery":"The central discovery is a plane-resolved comparison of superconducting gap magnitudes: in (Hg,Re)1223, $\\Delta_0(\\mathrm{IP}) = 63 \\pm 3$ meV, nearly the same as optimally doped Bi2223, but $\\Delta_0(\\mathrm{OP}) = 57 \\pm 1$ meV, sharply larger than the ~43 meV of Bi2223's outer plane. The d-wave gap amplitude $\\Delta_0$ is obtained by extrapolating the near-nodal linear part of the gap to the antinode, a procedure argued to isolate the superconducting component from the pseudogap. Because Tc rises from 110 K in Bi2223 to 130 K in (Hg,Re)1223 while the inner-plane gap barely changes, the authors attribute the Tc gain to the amplified outer-plane pairing. They also note that averaging $\\Delta_0$ over the CuO2 planes restores a smooth scaling with optimal Tc across single-layer, bilayer, and trilayer cuprates.","pith_inferences":["Editorial extension: if the outer-plane pairing is the decisive ingredient, theoretical models of trilayer superconductivity should focus on the OP environment (apical oxygen distance, crystal-field splitting, out-of-plane disorder) rather than on the IP alone.","Editorial extension: a testable prediction is that other trilayer cuprates with flattened, clean outer planes and similarly large apical-oxygen distances should also show an enhanced OP gap, while those with buckled OP should not.","Editorial extension: the plane-averaged scaling suggests that raising Tc further may require optimizing both planes simultaneously, so that the average gap grows instead of being limited by the smaller of the two."],"forward_implications":["In (Hg,Re)1223 the outer-plane hole concentration ($p_{\\mathrm{FS}} = 0.12$–0.17) is lower than in optimally doped Bi2223 ($p_{\\mathrm{FS}} = 0.23$), so the OP is less overdoped than previously assumed.","The highest ambient-pressure Tc in the Hg-based trilayer is attributable to the enhanced outer-plane pairing, with the inner-plane pairing roughly unchanged from Bi2223.","The average of IP and OP gap amplitudes scales with optimal Tc across LSCO, Bi2201, Bi2212, Bi2223, Hg1201, and (Hg,Re)1223, suggesting that the plane-averaged pairing energy governs Tc.","The flat, clean outer plane environment in Hg1223 (small buckling, distant disorder) likely supports the enhanced OP pairing through reduced $d_{x^2-y^2}$/$d_{3z^2-r^2}$ hybridization and stronger electron-phonon coupling to buckling modes.","The feasibility of micro-ARPES on Hg-based trilayers opens the way to resolve interlayer hybridization and other fine spectral features."],"supporting_citations":[{"why":"Supplies the reference Bi2223 values $\\Delta_0(\\mathrm{IP}) \\sim 60$ meV and $\\Delta_0(\\mathrm{OP}) \\sim 43$ meV that the (Hg,Re)1223 gaps are compared against.","marker":"[4]"},{"why":"NMR report that the IP has a smaller hole concentration than the OP, used to label the two Fermi-surface branches.","marker":"[17]"},{"why":"Newer NMR estimate of the IP-OP doping difference ($\\Delta p \\sim 0.05$), used to assess the Fermi-surface-derived doping values.","marker":"[18]"},{"why":"Established the reproducible single-crystal growth of (Hg,Re)1223 with Tc above 130 K, making the ARPES measurements possible.","marker":"[19]"},{"why":"Provides the small Fermi-pocket/doped resonating-valence-bond picture used to convert Fermi-surface area into hole doping.","marker":"[29]"},{"why":"Prior observation supporting the small-pocket description in underdoped cuprates, invoked to justify applying that picture to the IP.","marker":"[27]"},{"why":"Supplies the Hg1201 $\\Delta_0$ value and the argument that the cleaved Hg-based surface avoids polar reconstruction, supporting the surface neutrality assumption.","marker":"[39]"},{"why":"Establishes the $\\Delta_0$ versus optimal-Tc scaling and the near-doping-independence of $\\Delta_0$ used to separate superconducting gap from pseudogap.","marker":"[44]"},{"why":"Provides additional $\\Delta_0$ values and the extrapolation procedure for defining $\\Delta_0$ from near-nodal data.","marker":"[46]"},{"why":"Overdoped Bi2223 result showing $\\Delta_0(\\mathrm{OP})$ decreases while $\\Delta_0(\\mathrm{IP})$ persists, highlighting the IP-dominant picture that the present OP result contrasts with.","marker":"[8]"}],"fun_headline_variants":["Outer CuO2 gap fuels record-high 130 K in trilayer","Outer-plane pairing is key to 130 K trilayer superconductor","Tri-layer's outer plane holds key to 130 K","Why Hg-based trilayer hits 130 K: outer plane gaps"],"cache_read_input_tokens":17536,"weakest_assumption_plain":"The result depends on the assignment of the two Fermi-surface branches to the inner and outer planes, and on the small-Fermi-pocket model used to recover reasonable hole doping for the inner plane.","fun_headline_variants_meta":{"raw":{"variants":["Outer CuO2 gap fuels record-high 130 K in trilayer","Outer-plane pairing is key to 130 K trilayer superconductor","Tri-layer's outer plane holds key to 130 K","Why Hg-based trilayer hits 130 K: outer plane gaps"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000763,"raw_usage":{"total_tokens":3395,"prompt_tokens":961,"completion_tokens":2434,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":577,"completion_tokens_details":{"reasoning_tokens":2357}},"tokens_in":577,"tokens_out":2434,"duration_ms":19742,"temperature":1.0,"reasoning_tokens":2357,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T05:02:29.394551+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A bulk-sensitive measurement of IP and OP hole concentrations on the same crystals (for example, NMR) that contradicted the assumed doping ordering, or an ARPES experiment resolving interlayer Bogoliubov hybridization to fix the branch labels, would settle whether the enhanced gap truly sits in the outer plane.","supporting_citations":[{"cited_title":"Ideta, K","cited_arxiv_id":null,"evidence_quote":"Supplies the reference Bi2223 values $\\Delta_0(\\mathrm{IP}) \\sim 60$ meV and $\\Delta_0(\\mathrm{OP}) \\sim 43$ meV that the (Hg,Re)1223 gaps are compared against."},{"cited_title":"Magishi, Y","cited_arxiv_id":null,"evidence_quote":"NMR report that the IP has a smaller hole concentration than the OP, used to label the two Fermi-surface branches."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Newer NMR estimate of the IP-OP doping difference ($\\Delta p \\sim 0.05$), used to assess the Fermi-surface-derived doping values."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Established the reproducible single-crystal growth of (Hg,Re)1223 with Tc above 130 K, making the ARPES measurements possible."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Prior observation supporting the small-pocket description in underdoped cuprates, invoked to justify applying that picture to the IP."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Hg1201 $\\Delta_0$ value and the argument that the cleaved Hg-based surface avoids polar reconstruction, supporting the surface neutrality assumption."},{"cited_title":"Yoshida, M","cited_arxiv_id":null,"evidence_quote":"Establishes the $\\Delta_0$ versus optimal-Tc scaling and the near-doping-independence of $\\Delta_0$ used to separate superconducting gap from pseudogap."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides additional $\\Delta_0$ values and the extrapolation procedure for defining $\\Delta_0$ from near-nodal data."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Overdoped Bi2223 result showing $\\Delta_0(\\mathrm{OP})$ decreases while $\\Delta_0(\\mathrm{IP})$ persists, highlighting the IP-dominant picture that the present OP result contrasts with."}],"review_version":1}