{"id":"755a4617-45a7-4424-a9ff-72037ccaa346","arxiv_id":"2506.03563","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"Pb-InSb hybrid devices exhibit a large, gate-tunable hard superconducting gap up to about 1.4 meV and effective g-factors up to 76, attributed to strong spin-orbit coupling from lead.","lead":"Pb-InSb hybrid nanowire devices show a proximity-induced superconducting gap up to about 1.4 meV, roughly seven times larger than in aluminum devices, and this gap stays hard while being tunable from maximum down to near zero with a gate voltage. Magnetic-field measurements reveal effective g-factors up to 76, which the authors trace to strong spin-orbit coupling from lead, a combination that could benefit Majorana zero-mode experiments.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The g-factor and strong-SOC claims hinge on unvalidated line-slope extraction; a global 2D peak-tracking check on Fig. 2 should decide whether the reported g up to 76 reflects real Zeeman states or the stitching of unrelated conductance peaks.","rationale":"The paper contains two separable claims: (i) a large, hard, gate-tunable induced superconducting gap, and (ii) large effective g-factors and strong SOC persisting into the strong-coupling limit. Claim (i) is supported by direct conductance linecuts, two devices, and a reasonable exclusion of Coulomb blockade; I do not object to it. Claim (ii) carries the title and the claimed resolution of the Al trade-off, but its only evidence is the slope of conductance lines in field-dependent maps plus anti-crossings, with a peak-extraction pipeline that ends in visual fitting. The multimode Hamiltonian has enough free parameters (three alpha_i, three g_i, gamma, barrier height, mu, Delta) to fit nearly any slope pattern, so it cannot independently authenticate the extraction. The deepest risk is not noise alone: as B evolves, a conductance peak can be transferred between subgap states or between subgap and continuum features, so a straight line through such points is not a Zeeman dispersion. Because Figure 3(e) and the quoted g up to 76 are the quantitative payload of the second claim, the paper should be conditional on a more robust state-tracking analysis. This is the same weakest assumption identified by the reader; my pass sharpens the proposed check by specifying a global 2D peak-tracking validation with amplitude and width continuity, rather than relying on smoothed per-slice peaks and visual slope selection. The recommended verdict therefore remains unchanged: the paper is promising and conditionally acceptable, but the g-factor/SOC headline should not be accepted until the line-identity test is passed.","tokens_in":12557,"tokens_out":15133,"duration_ms":199855,"concrete_test":"Use the raw data behind Fig. 2 without per-slice smoothing: run a global 2D peak-tracking algorithm on each (V_bias, B) conductance map that follows local conductance maxima and records amplitude, width, and curvature along each trajectory. Re-extract g-factors only from trajectory segments where amplitude and width vary smoothly, indicating a plausibly single state, and validate the same tracking on a Kwant simulation of Eq. (1) with known g and alpha to confirm it recovers the input g. If the g>50 slopes arise only from stitching together different peaks, the enhanced-g-factor claim fails; if the slopes persist under continuous single-state tracking, the conditional concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing element of the central claim is the mapping from the slopes of the finite-bias conductance lines in Fig. 2 to effective g-factors up to 76, and from the anti-crossings to strong spin-orbit coupling. The extraction described in the Supplemental Material smooths each bias trace with a Savitzky-Golay filter, finds peaks, symmetrizes positive and negative bias, and then \"visually evaluate[s]\" the slopes and error bars. Nothing in this pipeline proves that a fitted straight segment follows one physical eigenstate across the whole magnetic-field range; in a multimode nanowire the conductance maximum can shift from one mode to another as B and the induced gap evolve, and the resulting slope is then a mix of unrelated states rather than a clean Zeeman slope. The supporting multimode model (Eq. S3) uses three modes with independent alpha_i and g_i, plus mode-mixing gamma and barrier parameters, so it has enough freedom to reproduce almost any set of linear slopes; it also keeps Delta constant and omits both the B-dependence of the parent Pb gap and the orbital response of the light-mass InSb wire. If the line identity or the linear-Zeeman interpretation fails, the claims of Pb-induced SOC preservation and enlarged g-factors lose support; what survives is the large, hard, tunable induced gap.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports tunneling spectroscopy measurements on Pb-InSb hybrid nanowire devices. The authors demonstrate a proximity-induced superconducting gap up to ~1.4 meV (matching bulk Pb), with hardness reaching two orders of magnitude, and show that the gap can be continuously tuned by the back gate from near zero up to its maximum while remaining hard. In out-of-plane magnetic fields, the conductance maps show multiple finite-bias radial lines with different slopes; these are interpreted as spin-split resonance lines, and their slopes are converted into effective g-factors up to 76. A single-mode and a multi-mode one-dimensional model are used to argue that spin-orbit coupling from Pb renormalizes the g-factor and produces the observed bending, anti-crossings, and mode-dependent slopes. The central claims are (i) a large, hard, tunable induced gap and (ii) preserved strong spin-orbit coupling and enhanced g-factors in the strong-coupling regime.","tokens_in":12775,"tokens_out":4086,"duration_ms":49544,"significance":"If both claims hold, this work would be an important step for Majorana-based quantum computing: Pb provides a ~7x larger induced gap than Al, tunable without loss of hardness, and the effective g-factors up to 76 exceed those of Al-based hybrids, potentially enlarging the topological parameter space. The large, hard, gate-tunable gap is directly supported by conductance data with strong subgap suppression and is the most robust contribution. The g-factor and strong-SOC conclusions are plausible but rest on a less rigorous extraction of slopes from noisy conductance maps and on an illustrative rather than quantitative model. The paper also ships a useful multimode simulation framework, but its parameters are not fitted to data.","major_comments":[{"comment":"The extraction pipeline (Savitzky-Golay smoothing, peak finding, symmetrization of positive and negative bias, and then visual evaluation of slopes) does not demonstrate that a fitted straight segment follows the same physical eigenstate over the entire magnetic-field range. In a multimode nanowire, the conductance maximum can shift from one mode to another as B and the induced gap evolve, and the resulting slope would then be an artifact of stitching unrelated states. This is load-bearing for the headline g-factor values up to 76 and for the conclusion that Pb preserves strong SOC in the strong-coupling regime. Please provide a global peak-tracking algorithm that enforces continuity of a line in the 2D map, report how many identified peaks are discarded, and show that the extracted slopes are stable with respect to smoothing parameters and peak-finding thresholds.","section":"Supplemental Material, \"Extraction of the g-factor\" and Fig. 2"},{"comment":"The multimode model, which uses independent α_i, g_i, γ, μ, Δ, and barrier parameters, is used only for qualitative illustration; no quantitative comparison with the experimental conductance maps is made. The claim that the observed slopes arise from g-factor renormalization by Pb's spin-orbit coupling is therefore not tested against alternatives. The model also keeps Δ constant and omits the B-dependence of the parent Pb gap, and although the authors argue that orbital effects are isotropic, the parent-gap suppression could influence the line slopes. Please fit at least representative experimental traces, or provide a sensitivity analysis showing how robust the extracted g-factors are to variations in the model parameters.","section":"Appendix C and Eq. (S3)"},{"comment":"The abstract states that the induced gap exceeds that of Al by \"an order of magnitude\", but the text (page 2, around the discussion of [24]) and later statements give a factor of approximately six to seven. The measured maximum of ~1.4 meV compared to Al's ~0.2 meV is roughly a factor of seven, not an order of magnitude. This overstatement should be corrected to avoid misleading readers about the quantitative improvement.","section":"Abstract and page 2"}],"minor_comments":[{"comment":"The colored dashed lines used to indicate the radial resonance lines are difficult to distinguish in black-and-white print; please use distinct line styles or add labels directly on the panels.","section":"Fig. 2"},{"comment":"The second exclusion argument (the maximum induced gap is nearly identical to the parent Pb gap) is not by itself decisive against a Coulomb gap, since a charging energy of order 1 meV is possible; however, when combined with the gate-voltage range and absence of excited states it is reasonable. Please state explicitly that the large gate range over which the gap persists is the primary discriminator.","section":"Appendix B"},{"comment":"The error bars on the extracted g-factors are described only as being obtained from visual evaluation in the Supplemental Material. Please specify whether these error bars include systematic uncertainty from the ambiguity of line identification, and how the error bars were calculated.","section":"Fig. 3(e)"},{"comment":"The sign convention for E± and the branch of the square root should be stated explicitly, along with the condition under which the gap closes; this would help readers connect the analytical formula to the numerical spectra in Fig. 4.","section":"Eq. (2)"},{"comment":"The statement that the gap remains hard while being tuned \"down to nearly zero\" is ambiguous, as the hardness ratio (above-gap vs subgap conductance) is ill-defined when the induced gap vanishes. Please clarify the gate-voltage range over which the hardness is quantified.","section":"Fig. 1 and main text"}],"recommendation":"major_revision","confidential_remarks":"The large, hard, tunable induced-gap result is convincing and valuable, and I expect it will be of interest to the hybrid-nanowire community. My main reservation concerns the g-factor and strong-SOC claims: the extraction method is not rigorous enough to exclude line-stitching artifacts, and the model is illustrative rather than fitted. With a more robust peak-tracking analysis and at least a partial quantitative model comparison, the paper could become suitable for publication. I also recommend correcting the \"order of magnitude\" overstatement in the abstract. The authors appear to have high-quality data and the ability to perform the additional analysis."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Peter,\n\nYou should know two things about arXiv:2506.03563. First, the central experimental result—a large, hard, gate-tunable induced gap in Pb-InSb hybrids—looks real and is a useful advance over Al-based devices. Second, the claimed enhancement of the effective g-factor up to 76 is plausible but not yet solid; it rests on visual slope-fitting of conductance lines whose identity is not uniquely established.\n\nWhat's genuinely new: quantitative tunneling spectroscopy on Pb-InSb, a material combination not covered by the earlier Pb-InAs (Kanne) or Pb-PbTe (Zhang) papers. The data in Fig. 1 show a hard gap reaching ~1.4 meV in the island device, with subgap conductance suppressed by two orders of magnitude. The gate tunability from ~0 to 1.4 meV while keeping the gap hard is impressive; Al devices typically get soft at small gaps. The Appendix B argument excluding Coulomb blockade is clean and convincing.\n\nThe soft spot is the g-factor extraction. The Supplemental describes Savitzky-Golay smoothing and peak-finding, but the slopes are then visually evaluated. Nothing proves that a fitted straight segment follows a single physical eigenstate across the whole field range. In a multimode wire, the conductance maximum can jump between modes, and the slope then mixes unrelated states. The authors note that lines bend at low field and fit only the high-field slopes, but they don't quantitatively model that bending beyond pointing to their model. The multimode model has enough free parameters (alpha_i, g_i, mixing gamma, barrier V, Delta, mu) that its agreement with the slopes is not a strong constraint. The abstract also overstates the gap as an \"order of magnitude\" larger than Al when the text says six-fold; that's an easy fix but should not be left as is.\n\nIf I had to bet, the large-gap result will survive scrutiny, and the g-factor observation is interesting enough to warrant a follow-up with better line-tracking. The paper deserves a serious referee; it should not be desk-rejected. A careful referee should ask for automated peak-tracking across the 2D maps, explicit criteria for line identity, and error bars that come from something other than visual inspection. The theory section should be repositioned as illustrative rather than as confirmation.\n\nOverall: a solid experimental contribution with a soft interpretive overlay. Worth citing for the gap, and worth a reading-group discussion on how much slope-based g-factor extraction can be trusted.","headline":"Solid Pb-InSb gap experiment with a tunable hard gap; g-factor claims are suggestive but rest on visual line-slope fitting, so the paper needs a cautious referee.","tokens_in":13483,"tokens_out":2792,"would_cite":true,"duration_ms":30264,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["74.45.+c","71.70.Ej","73.23.-b"],"model":"deepseek-v4-flash","headline":"The paper claims that Pb-InSb hybrid devices offer a hard proximity-induced superconducting gap up to ~1.4 meV and effective g-factors up to 76, resolving a trade-off in aluminum-based Majorana platforms.","keywords":["Pb-InSb hybrid nanowires","proximity-induced superconductivity","hard superconducting gap","gate-tunable gap","large effective g-factor","Rashba spin-orbit coupling","Majorana zero modes","tunneling spectroscopy"],"falsifier":"Follow one of the tracked conductance lines to the highest accessible magnetic field: the paper's own analytic dispersion predicts the slope, hence the extracted g-factor, should bend at low field and saturate by roughly 5 T. If the slopes instead remain linear from zero field or fail to show the predicted bending, the spin-orbit renormalization explanation would be falsified.","tokens_in":12297,"feed_emoji":"🧲","tokens_out":6566,"duration_ms":74887,"temperature":0.7,"pith_summary":"This paper tries to establish that lead (Pb), rather than aluminum (Al), is a superior parent superconductor for semiconductor-nanowire hybrid devices aimed at topological superconductivity. In Pb-InSb tunnel junctions the authors report a proximity-induced superconducting gap as large as ~1.4 meV, matching bulk Pb and roughly an order of magnitude above Al-based systems, and they find the gap can be tuned continuously from that maximum down to nearly zero by a back gate while staying hard. Magnetic-field spectroscopy exposes multiple conductance lines whose slopes yield effective g-factors up to 76, values that persist even in the strong-coupling limit where Al devices lose spin-orbit coupling and g-factor. If correct, this removes a known trade-off and widens the parameter space in which Majorana zero modes could be stabilized.","feed_headline":"Lead-based nanowire device shows a 1.4 meV hard superconducting gap","feed_subtitle":"Unlike aluminum, lead keeps a large effective g-factor (~76) even when strongly coupled to the nanowire.","key_machinery":"The load-bearing objects are the measured conductance resonances in the magnetic-field maps and the one-dimensional model used to interpret them. The Hamiltonian combines kinetic energy, chemical potential, an induced pairing term $\\Delta(x)$, Rashba spin-orbit coupling $\\alpha$, and Zeeman energy $E_Z = \\frac{1}{2} g \\mu_B B$; from it the authors derive an analytic positive-energy spectrum $E_\\pm$ whose bending and anti-crossings reproduce the gap evolution. In the multimode version each transverse mode has its own $\\alpha_i$ and $g_i$ with off-diagonal mixing $\\gamma$, which accounts for multiple radial lines with different slopes that do not all share a common high-field slope. These modes are what connect the raw conductance maps to the extracted effective g-factors.","core_discovery":"The central claim is that a Pb superconductor on an InSb nanowire simultaneously solves the two bottlenecks of Al-based hybrids: the induced superconducting gap is large and hard, and the effective spin-orbit coupling and Landé g-factor remain large in the same coupling regime. In the measured devices the zero-field gap reaches ~1.4 meV, the above-gap to subgap conductance ratio reaches two orders of magnitude, and the gap can be gate-tuned from roughly zero back to its maximum without becoming soft. Out-of-plane magnetic-field maps show radial resonance lines, anti-crossings, and gap reopening, and the authors interpret the slopes of these lines as effective g-factors of about 7 to 76. They attribute the persistence of strong spin-orbit coupling in the strong-coupling limit to Pb's Rashba spin-orbit coupling, and they reproduce the qualitative structure with a one-dimensional multimode model in which each transverse mode carries its own g-factor and spin-orbit strength.","pith_inferences":["A natural experiment beyond the present data is to measure the high-field slope of the same resonance lines past 5 T; the analytical model predicts the extracted g-factor saturates there, which would distinguish spin-orbit renormalization from other line-drawing artifacts.","If Pb's Rashba coupling is indeed the source of the preserved g-factor, varying the Pb film thickness or the Ti wetting-layer details should systematically change the extracted effective g-factor, a knob the paper does not sweep.","The results suggest Pb-InSb islands should also show robust 2e-periodic Coulomb-blockaded Cooper-pair transport; demonstrating that would connect these spectroscopy findings to qubit-oriented island experiments.","Because the extracted g-factors come from line slopes rather than direct spin measurements, a spin-resolved or weak-antilocalization measurement of the same nanowires would give an independent estimate of the spin-orbit strength."],"forward_implications":["A Pb-based induced gap near 1.4 meV raises the upper bound on any topological gap roughly sevenfold relative to Al, making Majorana experiments less sensitive to thermal occupation and disorder.","Continuous gate tuning of a hard gap from maximum to near zero gives a single device a wide range of hybridization strengths, which is useful for mapping the topological phase diagram.","Effective g-factors up to 76, sustained in the strong-coupling regime, lower the Zeeman field needed for a trivial-to-topological transition and enlarge the safe field window below the parent superconductor's critical field.","The same platform can be used for Coulomb-blockaded Cooper-pair transport and artificial Kitaev chain geometries, where a larger gap and g-factor improve coherence and operating temperature."],"supporting_citations":[{"why":"Supplies the bulk values (Pb gap ~1.4 meV, Al gap ~0.2 meV) that anchor the comparison.","marker":"[24]"},{"why":"Provides the Al-based gate-tunability and soft-gap behavior that this paper contrasts with Pb.","marker":"[26]"},{"why":"Demonstrates gate-tunable supercurrent in a Pb-based junction, supporting Pb hybrid feasibility.","marker":"[27]"},{"why":"Shows robust gaps and Cooper-pair transport in Pb-InAs hybrids, the direct predecessor platform.","marker":"[33]"},{"why":"Gives the theory that gate-induced wavefunction redistribution changes SC-SM coupling and gap.","marker":"[38]"},{"why":"Establishes the bulk InSb g-factor range (40-50) that the measured values up to 76 are compared against.","marker":"[43]"},{"why":"Documents the small effective g-factor in strongly coupled Al hybrids, the contrast that motivates Pb.","marker":"[44]"},{"why":"Shows Al nanowire gap evolution under magnetic field, the experimental baseline for the field-dependent maps.","marker":"[45]"}],"fun_headline_variants":["Pb-InSb hybrid nanowire: 1.4 meV hard gap, tunable to zero","Lead-based nanowire device: hard gap and g-factor up to 76","Gate-tunable superconducting gap in Pb-InSb nanowire hybrids","Pb hybrid nanowire outperforms Al in gap, spin-orbit, g-factor","Large hard induced gap and strong spin-orbit in Pb-InSb devices"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The claim that the effective g-factors reach 76 rests on identifying the tracked conductance lines as spin-split bound states of nanowire modes; if those lines instead come from disorder states or interference effects, the extracted g-factors and the strong-spin-orbit conclusion would not be supported.","fun_headline_variants_meta":{"raw":{"variants":["Pb-InSb hybrid nanowire: 1.4 meV hard gap, tunable to zero","Lead-based nanowire device: hard gap and g-factor up to 76","Gate-tunable superconducting gap in Pb-InSb nanowire hybrids","Pb hybrid nanowire outperforms Al in gap, spin-orbit, g-factor","Large hard induced gap and strong spin-orbit in Pb-InSb devices"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000254,"raw_usage":{"total_tokens":1579,"prompt_tokens":965,"completion_tokens":614,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":581,"completion_tokens_details":{"reasoning_tokens":510}},"tokens_in":581,"tokens_out":614,"duration_ms":7043,"temperature":1.0,"reasoning_tokens":510,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T11:00:43.699586+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Follow one of the tracked conductance lines to the highest accessible magnetic field: the paper's own analytic dispersion predicts the slope, hence the extracted g-factor, should bend at low field and saturate by roughly 5 T. If the slopes instead remain linear from zero field or fail to show the predicted bending, the spin-orbit renormalization explanation would be falsified.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the Al-based gate-tunability and soft-gap behavior that this paper contrasts with Pb."},{"cited_title":"Zhang et al., Physical Review Materials 7, 086201 (2023)","cited_arxiv_id":null,"evidence_quote":"Demonstrates gate-tunable supercurrent in a Pb-based junction, supporting Pb hybrid feasibility."},{"cited_title":"Kanne et al., Nature Nanotechnology 16, 776 (2021)","cited_arxiv_id":null,"evidence_quote":"Shows robust gaps and Cooper-pair transport in Pb-InAs hybrids, the direct predecessor platform."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the theory that gate-induced wavefunction redistribution changes SC-SM coupling and gap."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the bulk InSb g-factor range (40-50) that the measured values up to 76 are compared against."},{"cited_title":"Vaitiekėnas, M","cited_arxiv_id":null,"evidence_quote":"Documents the small effective g-factor in strongly coupled Al hybrids, the contrast that motivates Pb."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows Al nanowire gap evolution under magnetic field, the experimental baseline for the field-dependent maps."}],"review_version":1}