{"id":"0f8fd018-f461-4ffc-8e59-ecbf30f05620","arxiv_id":"2509.00486","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Shot noise in graphene-superconductor junctions is predicted to tell retro from specular Andreev reflection, but the paper's own equations contradict its key qualitative claims.","lead":"This paper computes shot noise, the random current fluctuations, for several graphene-superconductor junctions and claims that its Fermi-energy dependence can distinguish two types of Andreev reflection. The authors show noise maps and Fano factors for one- and two-interface devices, but the calculation leans on prior work and contains conflicting statements.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The low-bias gate-sweep fingerprint is reversed: Eqs. (B1)-(B2) give F_spec≈0.02 and F_retro≈0.25 at E=0.1Δ, so F drops, not rises, toward charge neutrality.","rationale":"The reader's weakest_assumption focuses on the imported M_GSG and M_SGS transfer matrices and on the misuse of Eq. (7). Those are legitimate concerns, but they presuppose the single-interface GS result. My check goes deeper: even the GS building block, which the paper derives from scratch, contradicts the advertised central fingerprint. The abstract and Conclusions claim that retro AR suppresses the Fano factor and specular AR enhances it, and the Conclusions propose a gate sweep to see F rise toward charge neutrality. Direct evaluation of the paper's own reflection amplitudes at a small subgap bias shows the opposite: in the specular regime the Andreev probability is near unity for virtually all angles, so partition noise is almost absent (F≈0.02), while in the retro regime oblique modes have T≈1/2, giving F≈0.25. This is not a question of external consensus; it is an internal contradiction between Eqs. (B1)-(B2), the qualitative reading of Fig. 2a, and the summary claim. The disagreement with the reader is partial because the reader did identify 'internal contradictions between the stated reflection amplitudes and the qualitative reading of the resulting noise maps,' but the specific load-bearing point—the sign reversal of the gate-tunable Fano factor—is not the reader's weakest assumption. The transfer-matrix issue remains important for GSG/SGS, but the single-interface contradiction is sufficient to undermine the central claim as stated. Since the fingerprint could plausibly be repaired by correcting the energy dependence and the sign of the prediction, I retain a CONDITIONAL recommendation rather than outright rejection, but the revision must address this inversion directly.","tokens_in":13187,"tokens_out":29636,"duration_ms":347834,"concrete_test":"Take Eqs. (B1) and (B2) and compute F(E)=∫T(1−T)dα/∫T dα, and also with a cosα mode-density weight, for the retro (B1) and specular (B2) branches at E=0.1Δ and E=0.9Δ. If the result reproduces F_spec≈0.02 vs F_retro≈0.25 at E=0.1Δ and F_spec≈0.28 vs F_retro≈0.19 at E=0.9Δ, the gate-sweep prediction in the Conclusions is reversed for low bias; the authors must correct the fingerprint or specify that 'SAR enhances noise' holds only near the gap edge.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central advertised observable—'F is minimized deep in the doped (RAR-dominated) regime and rises toward charge neutrality (SAR-dominated)' (Conclusions)—contradicts the paper's own GS reflection amplitudes. Using T=|r_A|^2 from Eqs. (B1)-(B2) in Eq. (8), at a representative low subgap bias E=0.1Δ (cosβ=0.1, sinβ≈0.995), the angle-resolved Fano factor is F_retro≈0.25-0.30 and F_spec≈0.02 (unweighted; including the cosα mode-density weight gives ≈0.24 vs ≈0.016). Thus F decreases by an order of magnitude when the Fermi level is tuned from the doped RAR regime to the Dirac point, opposite to the paper's prediction. The source is a misreading of Eqs. (B1)-(B2): in the specular branch at small E, β≈π/2 makes cosβ≈0, so r_A≈cosα e^{-iϕ}/(i sinβ cosα)=e^{-iϕ}/i, hence |r_A|≈1 and T≈1 for almost all angles—not reduced transparency. The dark ridge at β=π/2 in Fig. 2a is the signature of T=1 (no partition noise), not T=0 as stated in the text. The 'specular-enhances-noise' behavior appears only near the gap edge (e.g., E=0.9Δ: F_spec≈0.28 > F_retro≈0.19), so the claimed fingerprint is energy-dependent and, in the proposed low-bias regime, inverted.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript develops a BdG scattering framework for shot noise in graphene-superconductor (GS), graphene-superconductor-graphene (GSG), and superconductor-graphene-superconductor (SGS) junctions. The central claim is that the Fano factor provides a robust fingerprint distinguishing retro Andreev reflection (RAR) from specular Andreev reflection (SAR): RAR suppresses the Fano factor while SAR enhances it, leading to a gate-sweep signature in which F is minimized in the doped regime and rises toward charge neutrality. The paper derives reflection amplitudes for a single GS interface and imports transfer matrices for the two-interface geometries from the authors' earlier works.","tokens_in":13588,"tokens_out":10483,"duration_ms":110517,"significance":"If correct, the proposed noise fingerprints would be a valuable experimental tool for graphene-based superconducting devices. The analytic reflection amplitudes in Appendices A and B are concrete, and the attempt to unify three geometries is ambitious. However, the manuscript's own equations contradict its central qualitative claims, and the two-interface results are not independently verifiable from the text. The paper therefore currently does not deliver its advertised conclusion.","major_comments":[{"comment":"The GSG and SGS results are not self-contained. The transfer matrices M_GSG and M_SGS, which determine all scattering amplitudes and hence the noise for two of the three geometries, are not derived or even written down in the present manuscript; the text states that their explicit forms appear in the authors' earlier works [56] and [57]. This is a load-bearing gap: the reader cannot check the applicability of those matrices to the parameters used, nor reproduce the computed Fano factors. A self-contained derivation (at least in an appendix) or a detailed reproduction is required to support the central claims.","section":"Sections II.B-II.C"},{"comment":"Eq. (7) is the Landauer formula for normal transmission of charge e. The manuscript sets T_n = |r_A|^2 without justifying that Andreev reflection obeys the same partition-noise statistics. While the Fano factors are later normalized with both e and 2e (e.g., Fig. 7), the substitution in Eq. (8) and the resulting numerical values need a clear derivation from the scattering-matrix formalism for a superconducting contact. The authors should state the assumptions (e.g., no normal transmission, subgap) and the relation between the Fano factor defined in Eq. (7) and the effective charge 2e.","section":"Section III, Eq. (7)"}],"minor_comments":[{"comment":"The dark ridge at β=π/2 is attributed to 'amplitude forces T→0', but according to Eq. (B2) the amplitude is finite (|r_A|≈1) at that point; the ridge is due to T(1-T)=0 with T=1. The physical interpretation should be corrected.","section":"Fig. 2a and Sec. IV.A"},{"comment":"The symbol β is used both as the superconducting coherence angle (Appendix A) and as a phase variable in Fig. 8. The text should distinguish these uses to avoid confusion.","section":"Notation"},{"comment":"Typo: 'fucntion' should be 'function'. Also, the caption for Fig. 1 states a 'zero-bias minimum for the specular case' without clarifying whether this arises from T=0 or T=1; the text in Sec. IV.A suggests the former, but the underlying amplitude (B2) gives the latter.","section":"Fig. 7 caption"},{"comment":"The temperature dependence of the noise is introduced via Δ(T)=Δ0 sqrt(1-(T/Tc)^2) only in the figure caption; the main text does not specify the thermal averaging kernel or the validity limits of the subgap approximations. Sec. IV.A partially acknowledges this in the discussion of Fig. 3c, but the same caveat should be applied consistently to the temperature-dependent figures.","section":"Sec. IV.A and Figs. 6, 9"}],"recommendation":"major_revision","confidential_remarks":"The internal contradiction between Sec. IV.A and Appendix B is severe: the paper's own reflection amplitudes predict the opposite Fano-factor trend at low bias from the one advertised in the abstract and conclusions. If the authors correct this, the paper's central narrative will likely reverse. The two-interface results also rest on transfer matrices imported from the authors' prior work, which need to be made available for verification. I recommend requiring a thorough revision before any further consideration."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Thanks for the stress-test note. I checked the algebra and the reversal is real. Substituting the paper's Eq. (B2) at E=0.1Δ gives F_spec≈0.02 and F_retro≈0.25, with or without the cosα mode weight. At E=0, cosβ=0, so the specular amplitude becomes r_h = cosα e^{-iϕ}/(i sinβ cosα) = e^{-iϕ}/i, hence |r_A|=1, not 0. The text in Sec. IV.A says 'E=0 implies cosβ=0, hence r_A=0'—that is the wrong conclusion from the right formula. The dark ridge in Fig. 2a is T=1 (no partition noise), not T=0. The abstract's claim that specular AR enhances shot noise and retro suppresses it is therefore reversed in the low-bias regime they propose.\n\nCredit where due: the Appendix B amplitudes are the standard Beenakker results, reproduced correctly; the paper is clearly organized; and the authors honestly flag the high-temperature artifact in Fig. 3c. The GSG and SGS angle-resolved maps may be new, but they rest on transfer matrices [56,57] that are not derived or reproduced, and no parameter values (length, doping, transparency) are given, so they cannot be independently checked. The idea of using noise to separate RAR and SAR is not new—Titov and Beenakker and the DiCarlo/Danneau experiments already cover gate-dependent noise in graphene-superconductor junctions.\n\nThe net effect is that the advertised fingerprint—F minimized deep in the doped RAR regime and rising toward the Dirac point—is exactly opposite to what Eqs. (B1)–(B2) produce. This is load-bearing, not a typo; the gate sweep proposed in the Conclusions would measure the opposite trend. The two-interface results are not self-contained, and the central claim lacks novelty.\n\nWho is this for? Possibly a reader wanting the angle-resolved maps of two-interface devices, but they would have to redo the analysis from scratch. I would not send this to peer review as is. A serious editor should desk reject it, with an invitation to resubmit after correcting the interpretation of the single-interface amplitudes, supplying the transfer matrices, giving concrete parameters, and re-examining the gate-sweep prediction.","headline":"The main fingerprint is backwards: their own single-interface amplitudes give F_spec≈0.02 and F_retro≈0.25 at low bias, so the Fano factor drops, not rises, toward the Dirac point.","tokens_in":14058,"tokens_out":11939,"would_cite":false,"duration_ms":129975,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["72.70.+m","74.45.+c"],"model":"deepseek-v4-flash","headline":"Shot noise distinguishes retro from specular Andreev reflection in graphene-superconductor junctions.","keywords":["Shot noise","Andreev reflection","Fano factor","Graphene-superconductor junction","Specular Andreev reflection","Retro Andreev reflection","Bogoliubov-de Gennes","Josephson junction"],"falsifier":"Measure the low-frequency Fano factor F = S/(2eI) in a clean graphene-superconductor junction while sweeping the gate voltage through the Dirac point at fixed subgap bias; the paper predicts a minimum deep in the doped retro regime and a rise near charge neutrality, so a flat or monotonically decreasing F across the sweep would contradict the fingerprint. A reader could also recompute M_GSG and M_SGS independently from the BdG wavefunctions and check whether the plotted Fano factors are reproduced.","tokens_in":13074,"feed_emoji":"⚡","tokens_out":7349,"duration_ms":88103,"temperature":0.7,"pith_summary":"This paper argues that shot noise, the flicker of current caused by the discreteness of charge, can tell apart the two kinds of Andreev reflection at graphene-superconductor interfaces. In retro Andreev reflection, a reflected hole retraces the electron's path and a Cooper pair enters the superconductor; in specular Andreev reflection, which occurs near the Dirac point, the reflected hole occupies the opposite band and takes a specular path. Using exact wavefunction matching in the Bogoliubov-de Gennes formalism and the scattering-matrix formula for the Fano factor, the authors find that retro Andreev reflection suppresses noise while specular Andreev reflection enhances it. They extend the calculation to graphene-superconductor-graphene and superconductor-graphene-superconductor junctions, where multiple interfaces, resonant interference, and superconducting phase differences reshape the noise fingerprints. If correct, a single gate sweep across the Dirac point should reveal the retro-to-specular crossover in the measured Fano factor.","feed_headline":"Shot noise separates the two Andreev processes in graphene","feed_subtitle":"A gate sweep crossing the Dirac point should show a Fano-factor dip in the doped regime and a rise toward neutrality.","key_machinery":"The argument runs on Bogoliubov-de Gennes wavefunction matching at the graphene-superconductor interface, which yields analytic forms for the normal and Andreev reflection amplitudes. These amplitudes are fed through the scattering-matrix shot-noise relation F = sum_n T_n(1 - T_n) / sum_n T_n, with T_n the transmission probability of channel n. The two regimes are encoded geometrically: retro Andreev reflection has hole angle alpha' approximately -alpha, while specular Andreev reflection has alpha' approximately alpha; the amplitudes also depend on the superconducting coherence angle beta = arccos(E/Delta), the incidence angle alpha, and the superconducting phase. For the two-interface geome","core_discovery":"The central claim is that the Fano factor, F = S/(2eI), computed from angle-resolved Andreev transmission probabilities, is a robust observable for separating retro from specular Andreev reflection. For retro Andreev reflection (Fermi energy large compared with the excitation energy), nearly transparent Andreev channels suppress the Fano factor below its normal-state value, and the angle-averaged noise vanishes as the energy approaches the superconducting gap edges. For specular Andreev reflection (near charge neutrality), angular selectivity lowers the effective transparency for most modes, so the Fano factor rises, with a zero-bias node and a finite plateau at the gap edges. The same contr","pith_inferences":["Beyond the paper: the predicted gate sweep can be tested in currently available hBN-encapsulated graphene with superconducting edge contacts; the cleanest test would measure both F and F_2e in the same sweep to isolate the effective transferred charge.","Beyond the paper: because the two-interface results rest on transfer matrices taken from the authors' earlier work, an independent numerical BdG calculation of the same GSG and SGS junctions would be the decisive reproducibility check of those noise fingerprints.","Beyond the paper: the angular structure of the noise maps suggests that an angle-selective graphene constriction could isolate retro-dominant and specular-dominant trajectories using noise alone, without requiring phase-sensitive measurements.","Beyond the paper: applying a small magnetic field could test whether the specular noise signature survives Landau quantization, a regime the paper does not address and where the retro/specular distinction may acquire new features."],"forward_implications":["A gate sweep across the Dirac point at fixed subgap bias should reveal a Fano-factor minimum in the doped, retro-dominated regime and a rise near charge neutrality where specular Andreev reflection dominates.","Angle-resolved noise profiles should show retro Andreev reflection dominating small incidence angles and specular Andreev reflection dominating near grazing incidence at low temperature.","In superconductor-graphene-superconductor junctions, the specular branch should show a zero-bias noise dome while the retro branch is flatter in the subgap; the difference map S_spec - S_retro is positive near the gap edges and negative at mid-gap and oblique angles.","Temperature sweeps toward T_c should shrink the superconducting gap and erase the angular contrast; the paper itself notes that the apparent specular-only branch at high temperature is a modeling artifact, not a physical effect.","The Cooper-pair-normalized Fano factor F_2e = S/(4eI) should track near-perfect 2e transfer in Andreev-dominated windows, giving an additional experimental handle on the transport mechanism."],"supporting_citations":[{"why":"Introduced specular Andreev reflection in graphene, the interband process whose noise fingerprint this paper targets.","marker":"[19]"},{"why":"Supplies the Blonder-Tinkham-Klapwijk wavefunction-matching framework used in Appendix A for the reflection amplitudes.","marker":"[13]"},{"why":"Supplies the scattering-matrix shot-noise formula and the definition of the Fano factor used throughout the paper.","marker":"[1]"},{"why":"Connects Andreev scattering amplitudes to current noise and effective charge in superconducting junctions.","marker":"[14]"},{"why":"Derives the angle-resolved Andreev reflection amplitudes in graphene whose limits give the retro and specular forms in Appendix B.","marker":"[30]"},{"why":"Provides the quantum-transport scattering formalism used to convert transmission eigenvalues into shot noise.","marker":"[45]"},{"why":"Supplies the explicit M_GSG transfer matrix and scattering amplitudes for the graphene-superconductor-graphene junction.","marker":"[56]"},{"why":"Supplies the explicit M_SGS transfer matrix and bound-state/transmission coefficients for the superconductor-graphene-superconductor junction.","marker":"[57]"}],"fun_headline_variants":["Shot noise fingerprints Andreev type in graphene","Graphene shot noise tells retro from specular","Fano factor reveals Andreev reflection mode","Noise probe sorts Andreev reflections in graphene","Shot noise spectroscopy separates Andreev processes"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The load-bearing premise is that the composite transfer matrices M_GSG and M_SGS, cited from the authors' earlier papers [56] and [57] rather than re-derived here, correctly describe the two-interface scattering, and that the single-interface noise formula remains valid in the plotted range even though the paper itself notes the subgap expression becomes an artifact near T_c.","fun_headline_variants_meta":{"raw":{"variants":["Shot noise fingerprints Andreev type in graphene","Graphene shot noise tells retro from specular","Fano factor reveals Andreev reflection mode","Noise probe sorts Andreev reflections in graphene","Shot noise spectroscopy separates Andreev processes"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000198,"raw_usage":{"total_tokens":1205,"prompt_tokens":747,"completion_tokens":458,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":491,"completion_tokens_details":{"reasoning_tokens":400}},"tokens_in":491,"tokens_out":458,"duration_ms":5178,"temperature":1.0,"reasoning_tokens":400,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T13:31:59.790781+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the low-frequency Fano factor F = S/(2eI) in a clean graphene-superconductor junction while sweeping the gate voltage through the Dirac point at fixed subgap bias; the paper predicts a minimum deep in the doped retro regime and a rise near charge neutrality, so a flat or monotonically decreasing F across the sweep would contradict the fingerprint. A reader could also recompute M_GSG and M_SGS independently from the BdG wavefunctions and check whether the plotted Fano factors are reproduced.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Blonder-Tinkham-Klapwijk wavefunction-matching framework used in Appendix A for the reflection amplitudes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the scattering-matrix shot-noise formula and the definition of the Fano factor used throughout the paper."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Connects Andreev scattering amplitudes to current noise and effective charge in superconducting junctions."},{"cited_title":"Nilsson, A","cited_arxiv_id":null,"evidence_quote":"Derives the angle-resolved Andreev reflection amplitudes in graphene whose limits give the retro and specular forms in Appendix B."},{"cited_title":"Salim, R","cited_arxiv_id":null,"evidence_quote":"Supplies the explicit M_GSG transfer matrix and scattering amplitudes for the graphene-superconductor-graphene junction."},{"cited_title":"Salim, R","cited_arxiv_id":null,"evidence_quote":"Supplies the explicit M_SGS transfer matrix and bound-state/transmission coefficients for the superconductor-graphene-superconductor junction."}],"review_version":1}