{"id":"8fb6c28d-03f6-4b2b-8136-4dae2842561a","arxiv_id":"2504.19620","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":8,"one_line_summary":"The proximity effect in graphene switches from local to collective superconductivity depending on the superconductor-normal interface conductance, which is set by substrate doping.","lead":"Scanning tunneling microscopy shows that lead islands on graphene induce superconductivity that is either localized near the islands or spread uniformly across the whole sheet, depending on the graphene's doping. The difference is traced to how transparent the lead-graphene interface is, which controls the strength and reach of the induced pairing.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The Si-side minigap may be a single-island long-coherence-length effect; the island-removal test leaves other islands within ~1ξ, so 'collective' is not uniquely established.","rationale":"The paper's central claim has two components: (i) gamma controls the strength and range of the proximity effect, and (ii) on Si-side graphene the observed homogeneous gap is a collective phenomenon stabilized by many islands. Component (i) is well supported by the C-side SNS fits and the qualitative crossover in the array model. Component (ii) is the weaker link. The experimental robustness test is not a true single-island control: the remaining islands sit ~500 nm away, less than the quoted ξ(Δp)≈600 nm, so their pair field can still reach the measurement region. The quoted long coherence length is itself the reason a single low-transparency island would produce a slowly varying LDoS, making uniformity over 250 nm unsurprising. The array-model removal calculation in SM Fig. 5 removes one electrode from a dense periodic array, a different geometry than the large island-free region in the experiment. The claim that the 1D model cannot explain the d-independence of the Si-side minigap is asserted without showing the 1D result at low gamma; if the 1D model at gamma~1 also gives a nearly d-independent gap for d<xi, the central motivation for the array model is weakened. This does not invalidate the role of gamma, but it does mean the 'collective' label and the fitted gamma values are less secure than the paper suggests. A single numerical control—an isolated island in the same Usadel framework—would settle whether the collective mechanism is necessary. For these reasons I retain the conditional verdict but flag this specific unexcluded alternative.","tokens_in":16295,"tokens_out":7481,"duration_ms":83959,"concrete_test":"Use the same array Usadel code to simulate a truly isolated superconducting island (one island, no periodic images) on an infinite N sheet with Si-side parameters (l=53 nm, γ≈1, ξ=150 nm), and compute the LDoS at distances up to 250 nm. If a ~0.2 meV minigap persists uniformly, a collective state is not required to explain the data; if the gap closes or becomes strongly position-dependent, the collective claim is supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central evidence for the collective state is the persistence of the ~0.2 meV minigap after removing nearby Pb islands (Fig. 3a-c, SM Fig. 5). The paper interprets this as cooperative coupling of many islands, enabled by ξ(Δp)≈600 nm. But the same low-gamma parameters imply that a single island already induces a nearly uniform LDoS over the 250 nm field of view, because the decay length at E≈Δp is ≈600 nm. In SM Fig. 5 the islands are pushed only 'more than 500 nm away'—i.e., within one coherence length—so the residual gap can be supplied by those remaining islands without requiring a many-island collective state. The array-model check in SM Fig. 5h-i removes one island from an otherwise periodic dense array, not the experimental configuration of a large island-free region with only distant islands at ~500 nm. The paper also states that the 1D S/N/S model 'predicts gap opening for any γ' and therefore cannot explain the d-independence of the minigap, but no 1D calculation at the relevant low γ is shown; a low-transparency S/N/S junction with d≲ξ(Δp) may show a similar weak dependence on d. If so, the need for the array/collective model is not demonstrated. The attribution of the uniform minigap to collective proximity is therefore underdetermined by the presented data.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports scanning tunneling microscopy measurements of Pb islands on graphene grown on the two faces of SiC. On the C-terminated side the proximitized state is locally strong but decays with distance, and S/N/S junctions show a gap that grows as the junction is shortened. On the Si-terminated side the measured minigap is smaller (~0.2 meV), spatially homogeneous over ~250 nm, and insensitive to the spacing between islands. The authors attribute this difference to the interface conductance γ between Pb and graphene, with high γ giving local proximity and low γ giving a long-range collective state stabilized by many islands. They support this interpretation with quasiclassical Usadel calculations, including a new 'array model' in which the graphene sheet is a thin normal slab with periodic superconducting islands coupled through a boundary conductance.","tokens_in":16627,"tokens_out":5455,"duration_ms":56891,"significance":"If the central claim held, the paper would identify the S/N interface conductance as a tunable control parameter for the spatial extent and collective character of proximity-induced superconductivity in graphene, with implications for gate-controlled hybrid superconducting devices. The experimental work has real strengths: the C-side data are internally consistent, the tip-manipulation demonstration of tunable S/N/S junctions is convincing, and the spectra are carefully deconvoluted. The use of an explicit quasiclassical model with a clearly described boundary-condition framework is a step beyond purely qualitative interpretation. However, as presented, the central claim is not quantitatively established: γ is a free parameter fitted to each measured spectrum, the Si-side simulations use ξS from the literature rather than a value measured in the same sample, and the key island-removal experiment does not cleanly separate collective from single-island long-range proximity because the remaining islands are within one inferred coherence length. The manuscript currently reads as a plausible qualitative scenario rather than a demonstrated mechanism.","major_comments":[{"comment":"The γ values quoted for the Si-side array model are mutually inconsistent. The text states that a nearly homogeneous minigap forms at γ = 0.75 (Fig. 4c,d), but the claimed reproduction of the experimental Si-side LDoS in Fig. 4e uses γ = 4.4 with a different geometry (L = 375 nm, l = 187.5 nm), and the S/N/S-stability calculation in Fig. 4f,g uses γ = 1. Since γ is the central control parameter of the paper, the reader cannot determine which transparency regime is actually claimed for the Si side. The manuscript should either reconcile these values through the definition of γ in Eq. (6) of the SM, or present a single geometry with a single fitted γ.","section":"§4, 'Modeling the collective proximity effect', Fig. 4"},{"comment":"The island-removal experiment in Fig. 3a-c and SM Fig. 5 is not a clean test of collective proximity. The SM states that the other islands are pushed 'more than 500 nm away', while the Discussion infers ξ(Δp) ≈ 600 nm for the Si-side state. A single low-transparency island is therefore expected to produce a nearly uniform LDoS over the entire 250 nm field of view, so the observed persistence of the 0.2 meV minigap is consistent with a single-island, long-coherence-length proximity effect and does not by itself require many-island cooperation. In addition, SM Fig. 5h-i removes one electrode from a dense periodic array, which is not the experimental configuration of an extended island-free region with only distant islands. The authors should show that a single island at ~500 nm cannot produce the measured uniform gap, or provide an array calculation with the actual sparse geometry.","section":"§3, 'Proximity effect of graphene on Si-side SiC' and SM Fig. 5"},{"comment":"The claim that the 1D S/N/S model 'predicts gap opening for any γ' and therefore cannot explain the d-independence of the minigap is not supported by any shown calculation. In a low-transparency junction with d ≲ ξ(Δp), the minigap may already depend only weakly on d; no 1D spectra at γ ≈ 1 for d = 115–52 nm are presented. The necessity of the array model for the d-independence would be established by a direct 1D versus array comparison at the same low γ and the same geometry. Without this comparison, the statement that the 1D model fails is an assertion, not a demonstrated result.","section":"§4, 'Modeling the collective proximity effect' and SM 'Motivation for Array Model'"},{"comment":"The quantitative support for γ as the controlling parameter is circular in the present form: γ is a free parameter fitted separately to each measured LDoS (C-side: γ = 8.3 and 20 in Fig. 2i,k; Si-side: γ = 4.4 and 1 in Fig. 4e,f), and no independent measurement of the interface conductance is provided. The Discussion's statement that the S/N interface conductance 'is a key parameter controlling the proximity effect' is therefore an interpretation of the fits rather than a parameter-free prediction. To make this claim load-bearing, the paper should either constrain γ independently (e.g., from transport or work-function data) or present at least one falsifiable prediction, such as a gate-controlled crossover at a specific γ or doping level.","section":"§4 and Discussion"}],"minor_comments":[{"comment":"The sentence 'from the value ∆p ∼ 600 nm, rescaled to ∆p from [34]' is logically and typographically confused: ∆p is an energy (~0.2 meV), not a length; the intended quantity appears to be ξ(Δp) ≈ 600 nm.","section":"Discussion"},{"comment":"The symbol γ is used both for the dimensionless interface conductance ratio in the main text and for γB in the SM equations; the relation between γ, γB, L, and l (SM Eq. (5)) should be stated once in the main text, since Figs. 4 and 5 quote different γ values with different geometries.","section":"Eq. (6), SM and Figs. 2–4"},{"comment":"The phrase 'localized or collective superconducting states' in the abstract overstates the distinction: the experimental observable is a spatially local versus spatially uniform LDoS, not a thermodynamic state. Consider 'localized or collective proximity effect'.","section":"Abstract and §1"},{"comment":"There are several typos and inconsistencies that should be corrected: 'In constrast', 'workfuncion', 'Based on this results', 'SFig.' vs 'Fig.', and 'Fig.c and .d' in SM Fig. 4.","section":"Throughout"},{"comment":"The caption for the decay fit in Fig. 2c reports ξS and Γ but not the γ value used for the infinite-N S/N model; since γ is the paper's central parameter, the fitted value should be reported here as well.","section":"Fig. 2c caption"}],"recommendation":"major_revision","confidential_remarks":"The experimental data are of good quality and the tip-manipulation work is a clear strength. My main concerns are the internal inconsistency in the Si-side γ values (Fig. 4) and the underdetermined interpretation of the island-removal experiment; both are fixable with additional calculations and a more cautious framing. I would encourage the editor to ask for the single-island and 1D low-γ checks described in the major comments before acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The two things you should know: the experiment is genuinely new and well executed, but the paper's central 'collective' claim is underdetermined by the data as presented.\n\nWhat's new: the simultaneous comparison of C-side and Si-side graphene with Pb islands shows a clear doping-dependent contrast—strong, local proximity on the C-side versus a weak, spatially uniform minigap on the Si-side. The tip-manipulated S/N/S junctions on the C-side give a clean length-dependent gap, and the 1D Usadel fits with gamma=8.3/20 are convincing. The array Usadel model that includes an explicit interface boundary resistance and a thin-film limit is a real step beyond the 1D SNS treatments, and it qualitatively reproduces the uniform gap at low gamma. The idea that interface transparency, not just graphene doping, controls the range of proximity is interesting and relevant for device design.\n\nWhere it's soft: the gamma values are fitted to the very spectra they are used to explain—there's no independent determination of gamma. On the Si-side, xi_S is taken from Ref. [34] rather than measured in this system, and the quoted xi(Delta_p) ~600 nm is an extrapolation. The array model idealizes the islands as periodic, which is a reasonable first step but not a faithful representation of the disordered island distribution. The most load-bearing test, island removal, is weaker than it looks: the remaining islands are pushed ~500 nm away, which is within even the estimated xi(Delta_p) ~600 nm. So the uniform gap over 250 nm could be due to a single island with a long coherence length at low energy, not necessarily to collective coupling of many islands. The SM check that removes one island from a periodic array is not the experimental geometry (large island-free region with distant islands). And the claim that the 1D model cannot explain the d-independence of the Si-side minigap is not backed by a low-gamma 1D calculation; a low-transparency S/N/S with d < xi may show very weak d dependence. These are specific, fixable issues, not fatal ones.\n\nWho this is for: anyone working on proximity effects in graphene or van der Waals hybrids, and people interested in gate-tunable superconducting arrays. I'd bring it to our reading group—it's a good discussion paper.\n\nRecommendation: yes, send it to peer review. A good referee should ask for the low-gamma 1D calculation, a single-island simulation in the island-removal geometry, and ideally an in-situ measurement of xi or at least a statement of its uncertainty. The experimental observation will stand, but the collective interpretation needs more support before it's accepted.","headline":"Strong new STM data show two distinct proximity regimes on SiC graphene, but the collective-state interpretation on the Si-side is not uniquely established by the island-removal test.","tokens_in":17226,"tokens_out":3629,"would_cite":true,"duration_ms":36780,"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":"The transparency of the interface between a superconductor and graphene controls whether the induced pairing is a local phenomenon or a collective one.","keywords":["proximity effect","graphene superconductivity","interface conductance","Usadel equations","scanning tunneling microscopy","collective superconductivity","SiC graphene","Andreev reflection"],"falsifier":"Remove every Pb island from a large Si-face region except one, and map the $0.2$ meV minigap as a function of distance from that island over several coherence lengths; in the collective picture the gap should stay uniform and island-independent, whereas in a local picture it should decay and disappear far from the island. A complementary check is to measure $\\gamma$ independently, for instance from the excess resistance of controlled Pb–graphene contacts: the explanation fails if the Si-face interface turns out to be highly transparent.","tokens_in":16087,"feed_emoji":"⚡","tokens_out":9691,"duration_ms":93124,"temperature":0.7,"pith_summary":"The paper sets out to show that one experimentally accessible quantity, the dimensionless conductance $\\gamma$ of the interface between a Pb island and graphene, determines the character of the proximity-induced superconducting state. On the C-face of SiC, where the interface is transparent ($\\gamma \\sim 8$–$20$), the pairing is local: strong coherence peaks appear near the islands, the induced gap shrinks as the normal region between two islands grows, and the state is fragile to island removal. On the Si-face, where the interface is more opaque ($\\gamma \\sim 1$), the induced minigap is smaller ($\\Delta_p \\sim 0.2$ meV) but uniform over hundreds of nanometers and insensitive to removing most islands. Because the lower transparency lengthens the effective coherence length to roughly 600 nm, many islands cooperate to stabilize a collective superconducting state. If this is right, doping, which shifts the interface conductance, becomes a practical knob for switching a graphene device between two qualitatively different superconducting regimes.","feed_headline":"One interface parameter decides local vs collective superconductivity","feed_subtitle":"Low-transparency Pb contacts spread pairing across many islands; transparent contacts pin it locally.","key_machinery":"The central object is the dimensionless interface-conductance ratio $\\gamma = G_I/G_N$ that enters the boundary condition of the diffusive Usadel equations; it measures how easily Andreev reflection crosses the Pb–graphene contact. The paper's array model treats graphene as a thin diffusive normal slab with superconducting islands acting as distributed source terms, so pair amplitudes from all islands add up in the uncovered graphene. The carrier of the argument is the relation $\\xi(E)=\\sqrt{\\hbar D/E}$: lowering $\\gamma$ narrows the induced gap, which in turn lengthens the coherence length until it exceeds the inter-island spacing, turning many weakly coupled islands into one collective superconductor.","core_discovery":"The paper's central claim is that the proximity effect in graphene is governed by the conductance $\\gamma$ of the Pb–graphene interface, and that this single parameter separates two regimes. In the transparent regime the coherence length at the gap edge is short, so each island proximitizes only its immediate neighborhood: spectra show pronounced coherence peaks at $\\Delta_S=1.35$ meV, the proximity gap in an S/N/S junction varies with spacing, and removing an island removes the local signal. In the opaque regime the same equations give a much longer coherence length, so the pair correlations from many islands add up over the whole graphene sheet; the result is a minigap $\\Delta_p\\approx 0.2$ meV that stays uniform over 250 nm, survives confinement in S/N/S junctions down to 52 nm, and barely changes when almost all islands in an area are pushed away. A two-dimensional array model based on the diffusive Usadel equations with $\\gamma\\approx 1$ reproduces these observations, while the same model with $\\gamma\\approx 6$ reproduces the local behavior of the C-face.","pith_inferences":["If $\\gamma$ is the true control parameter, patterning islands with different interface transparencies, whether through different metals, inserted tunnel barriers, or local dopants, could map local and collective superconducting regions onto one graphene chip; the paper does not test this directly.","The same collective mechanism should appear in other two-dimensional conductors covered by conventional-superconductor islands, so the C-face/Si-face comparison gives a template for searching for the crossover elsewhere.","Because $\\gamma$ depends partly on the work-function mismatch between graphene and the metal, replacing Pb with a superconductor of different work function should shift a system along the local–collective axis; this is a testable prediction the paper leaves implicit."],"forward_implications":["Doping shifts the Pb–graphene interface conductance, so gating the graphene should be able to move a device between the local and collective proximity regimes.","A collective regime makes the induced superconducting gap insensitive to island removal and to disorder in island positions, relaxing constraints on fabricating large proximitized graphene areas.","In the low-$\\gamma$ regime the effective coherence length reaches roughly 600 nm, so superconducting correlations can extend across many island spacings rather than dying out at the edge of one island.","The array model shows the collective minigap is controlled by the weakest inter-island link, so island spacing relative to the coherence length is a second design parameter for the gap's stability."],"supporting_citations":[{"why":"It supplies the reference STM measurement of proximity superconductivity in multilayer graphene and the coherence-length value $\\xi_S\\approx150$ nm used for rescaling.","marker":"[34]"},{"why":"It introduces the boundary-condition parameter $\\gamma$ that the paper uses to quantify interface conductance.","marker":"[28]"},{"why":"It provides the diffusive Usadel equation on which the array model is based.","marker":"[17]"},{"why":"It provides the one-dimensional quasiclassical model whose spectral decay fits the C-face data.","marker":"[40]"},{"why":"It is the theoretical basis for a collective proximity state stabilized by many superconducting islands on graphene.","marker":"[55]"},{"why":"It gives the density-of-states calculation for diffusive SNS junctions with nonideal interfaces that motivates the $\\gamma$ dependence.","marker":"[30]"},{"why":"It establishes the STM tip-manipulation method used to assemble S/N/S junctions with tunable spacing.","marker":"[36]"}],"fun_headline_variants":["One interface knob flips graphene superconductivity from local to collective","Interface conductance decides if pairing stays put or goes global in graphene","Proximitized graphene: transparent pins pairing, opaque spreads it far","A single parameter rules how graphene couples superconducting islands","Graphene pairing regime hinges on the metal contact transparency"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the uniform $0.2$ meV minigap on the Si face is the cooperative sum of pair correlations from many weakly transparent Pb islands, not the local proximity of the nearest island, a substrate-doping effect on graphene's electronic structure, or a mathematical artifact of the STM spectral deconvolution.","fun_headline_variants_meta":{"raw":{"variants":["One interface knob flips graphene superconductivity from local to collective","Interface conductance decides if pairing stays put or goes global in graphene","Proximitized graphene: transparent pins pairing, opaque spreads it far","A single parameter rules how graphene couples superconducting islands","Graphene pairing regime hinges on the metal contact transparency"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000248,"raw_usage":{"total_tokens":1537,"prompt_tokens":924,"completion_tokens":613,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":540,"completion_tokens_details":{"reasoning_tokens":529}},"tokens_in":540,"tokens_out":613,"duration_ms":7569,"temperature":1.0,"reasoning_tokens":529,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T05:47:21.640984+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Remove every Pb island from a large Si-face region except one, and map the $0.2$ meV minigap as a function of distance from that island over several coherence lengths; in the collective picture the gap should stay uniform and island-independent, whereas in a local picture it should decay and disappear far from the island. A complementary check is to measure $\\gamma$ independently, for instance from the excess resistance of controlled Pb–graphene contacts: the explanation fails if the Si-face interface turns out to be highly transparent.","supporting_citations":[{"cited_title":"Scanning tunneling spectroscopy of proximity superconductivity in epitaxial multilayer graphene,","cited_arxiv_id":null,"evidence_quote":"It supplies the reference STM measurement of proximity superconductivity in multilayer graphene and the coherence-length value $\\xi_S\\approx150$ nm used for rescaling."},{"cited_title":"Influence of boundary transparency on the critical current of “dirty","cited_arxiv_id":null,"evidence_quote":"It introduces the boundary-condition parameter $\\gamma$ that the paper uses to quantify interface conductance."},{"cited_title":"Generalized Diffusion Equation for Superconducting Alloys,","cited_arxiv_id":null,"evidence_quote":"It provides the diffusive Usadel equation on which the array model is based."},{"cited_title":"Thermoelectric effects in superconducting proximity structures,","cited_arxiv_id":null,"evidence_quote":"It provides the one-dimensional quasiclassical model whose spectral decay fits the C-face data."},{"cited_title":"Proximity-induced superconductivity in graphene,","cited_arxiv_id":null,"evidence_quote":"It is the theoretical basis for a collective proximity state stabilized by many superconducting islands on graphene."},{"cited_title":"Density of states and supercurrent in diffusive SNS junctions: Roles of nonideal interfaces and spin-flip scattering,","cited_arxiv_id":null,"evidence_quote":"It gives the density-of-states calculation for diffusive SNS junctions with nonideal interfaces that motivates the $\\gamma$ dependence."},{"cited_title":"Shaping graphene superconductivity with nanometer precision,","cited_arxiv_id":null,"evidence_quote":"It establishes the STM tip-manipulation method used to assemble S/N/S junctions with tunable spacing."}],"review_version":1}