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From local to collective superconductivity in proximitized graphene

T0 review · 4 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The transparency of the interface between a superconductor and graphene controls whether the induced pairing is a local phenomenon or a collective one.

desk verdict 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. read the letter →

arxiv 2504.19620 v1 pith:WLSFJEOK submitted 2025-04-28 cond-mat.mes-hall cond-mat.supr-con

Stefano Trivini , Tim Kokkeler , Jon Ortuzar , Eva Cortés-del Río , Beatriz Viña Bausá , Pierre Mallet , Jean-Yves Veuillen , Juan Carlos Cuevas
show 3 more authors
Ivan Brihuega F. Sebastian Bergeret Jose Ignacio Pascual
This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.supr-con
keywords proximityeffectgraphenesuperconductivityinterfaceconductanceUsadelequationsscanningtunnelingmicroscopycollectiveSiCAndreevreflection
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

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.

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 (4)
  1. [§4, 'Modeling the collective proximity effect', Fig. 4] 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.
  2. [§3, 'Proximity effect of graphene on Si-side SiC' and SM Fig. 5] 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.
  3. [§4, 'Modeling the collective proximity effect' and SM 'Motivation for Array Model'] 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.
  4. [§4 and Discussion] 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.
minor comments (5)
  1. [Discussion] 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.
  2. [Eq. (6), SM and Figs. 2–4] 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.
  3. [Abstract and §1] 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'.
  4. [Throughout] 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.
  5. [Fig. 2c caption] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the model's gamma is a fitted effective parameter, and the claimed additional checks (d-independence, island-removal robustness) are separate observables rather than the fitted input itself.

full rationale

The paper's derivation chain rests on the quasiclassical Usadel framework with standard Kupriyanov-Lukichev boundary conditions, not on a result defined by the target conclusion. The interface conductance ratio gamma is an effective parameter obtained by fitting the measured LDoS; the paper explicitly uses the language 'reproduce' and 'capture' rather than presenting these fits as independent predictions. On the C-side, the same gamma values (8.3 and 20) are carried over from the 107 nm junction to the 44 nm junction, providing a consistency check across distinct junction lengths. On the Si-side, the low-gamma regime inferred from the homogeneous minigap is then used to compute the d-independence of the gap and the robustness to island removal; these are distinct experimental observables, so the model has predictive content beyond the initial fit. No load-bearing step is justified solely by a self-citation: the supporting references for coherence lengths (Natterer et al.), collective proximity (Feigel'man et al.), and gate control (Han et al.) are external, and the self-citations are methodological or contextual. No uniqueness theorem from the authors' prior work is invoked. The observation that different figures use somewhat different gamma values (0.75, 1, 1.5, 4.4, 6) is a legitimate identifiability or overfitting concern, but it does not amount to the model's output being equivalent to its input by construction. Therefore, under the strict standard of requiring an explicit reduction of a claimed prediction to a fitted parameter or a self-citation chain, no significant circularity is found.

Assumptions & free parameters 8 free parameters · 8 assumptions · 0 invented entities

The central claim rests on a free parameter, the interface conductance gamma, which is fitted to each dataset rather than measured independently. The model also relies on standard quasiclassical and diffusive assumptions, plus the idealization of a periodic island array. No new physical entities are postulated.

free parameters (8)
  • interface conductance gamma (C-side, top island) = 8.3
    Fitted to reproduce the asymmetric LDoS in the 107 nm S/N/S junction (Fig. 2i).
  • interface conductance gamma (C-side, bottom island) = 20
    Fitted in the same 107 nm junction; the asymmetry is attributed to different island-graphene transparencies.
  • interface conductance gamma (C-side, short junction) = 20 and 8.3
    Same values used for the 44 nm junction to show the model captures the wider gap without refitting.
  • coherence length xi_S (C-side) = 200 +/- 10 nm
    Extracted from the spatial decay of coherence peaks in Fig. 2c; implies D about 820 cm2/s.
  • interface conductance gamma (Si-side, array fit) = 4.4
    Used in Fig. 4e to reproduce the measured Si-side LDoS; the paper states the model 'can be reproduced' with this value.
  • interface conductance gamma (Si-side, junction stability) = 1
    Used in Fig. 4f-g to reproduce the stability of the minigap under confinement.
  • interface conductance gamma (illustrative array values) = 6, 1.5, 0.75
    Used to show the crossover from local to collective proximity in the periodic array model (Fig. 4b-d).
  • coherence length xi_S (Si-side) = 150 nm
    Taken from Ref. [34] and 'rescaled to Delta_S', not measured in this work; used in all Si-side simulations.
assumptions (8)
  • domain assumption Usadel equation describes the diffusive graphene layer
    The paper assumes the elastic scattering length (about 50 nm) is much smaller than superconducting length scales (about 160 nm), justifying a diffusive description (SM Section III).
  • domain assumption Quasiclassical approximation is valid for graphene
    Fermi energy is assumed much larger than the superconducting gap, so quasiclassical theory applies (SM Section III).
  • domain assumption Pair correlations are approximately constant in the vertical direction
    The thin-layer limit d_g << xi is used to expand the Green's function in z and derive the array Usadel equation (SM Eq. 4).
  • standard math Kupriyanov-Lukichev boundary condition models the S/N interface
    The interface is described by a boundary conductance G_B and an indicator function theta_I; this is a standard boundary condition for diffusive S/N hybrids.
  • domain assumption Inverse proximity effect of graphene on the thick Pb islands is negligible
    Justified by the much larger number of modes in the superconducting islands compared to graphene (SM Section III).
  • domain assumption C-side multilayer graphene behaves as a single conducting sheet
    Moire-free domains are treated like free-standing graphene, following Refs. [48,49].
  • domain assumption A periodic array model represents the disordered experimental island distribution
    The array model uses periodic boundary conditions and a repeating unit cell; the paper argues results are robust across unit cell sizes of 3, 6, and 7 islands (SM Figures 8-12).
  • domain assumption The difference in doping between C-side and Si-side is the origin of the different interface conductance
    The paper cites work function and contact separation arguments (Refs. [59,60]) but does not directly measure gamma on either side.

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Pith. "Pith review of From local to collective superconductivity in proximitized graphene." pith.science (2026). https://pith.science/paper/WLSFJEOK

@misc{pith2026250419620,
  author       = {Pith},
  title        = {Pith review of: From local to collective superconductivity in proximitized graphene},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WLSFJEOK}},
  note         = {Machine review of arXiv:2504.19620}
}
read the original abstract

The superconducting proximity effect induces pairing correlations in metallic systems via Andreev scattering. This effect is particularly intriguing in graphene, as it enables two-dimensional superconductivity that is tunable through doping. Understanding how superconducting correlations propagate within the metal is crucial to unveiling the key factors behind this tunability. Here, we employ scanning tunneling microscopy to investigate the energy and length scales of the proximity effect induced by Pb islands on graphene. Using tip-induced manipulation, we assemble S/N/S junctions with tunable N-region spacing and explore the evolution of the proximitized state in the confined normal region. We find that different doping levels can lead to either localized or collective superconducting states. By combining our experimental results with quasiclassical theory, we demonstrate that interface conductance plays a key role in determining the strength and coherence length of pairing correlations and inter-island coupling. Our findings provide new insights into the design of novel superconducting states and the control of their properties.

Figures

Figures reproduced from arXiv: 2504.19620 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 2
Figure 2. Figure 2: Fig2. a) and b) of the main text. b) [PITH_FULL_IMAGE:figures/full_fig_p009_2.png]

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Forward citations

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.