{"id":"1a3ee1cc-f26e-4a23-8b94-338b9268400a","arxiv_id":"2505.23490","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"A comment showing that the interpretation of nonlocal conductance in a topological insulator nanowire experiment is not justified, because conductance alone cannot separate crossed Andreev reflection from elastic cotunneling.","lead":"This comment re-examines a recent Nature Physics claim of long-range crossed Andreev reflection in a topological insulator nanowire. It argues that conductance measurements alone cannot distinguish between crossed Andreev reflection and elastic cotunneling, and that the reported bias dependence can be explained by a self-gating effect.","discovery_kind":"replication","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The degeneracy transformation preserves T_he - T_ee, so the conductance matrix does determine which nonlocal process dominates; the impossibility claim overreaches.","rationale":"The reader's verdict accepted the degeneracy argument as a rigorous proof that conductance cannot determine the relative strength of CAR and ECT, especially which one dominates. On close inspection, the proof only establishes that adding a common constant to both nonlocal probabilities (and subtracting it from both local probabilities) leaves G unchanged. This transformation preserves T_he12 - T_ee12 exactly. Since G12 = G0 (T_he12 - T_ee12) within the model used by the comment, the sign of G12 is a direct measurement of which process has the larger transmission probability. Dominance is therefore identifiable from conductance alone, in the absence of self-gating. The paper's own Eq. (2c) and Appendix A contradict the abstract's claim. The self-gating discussion in Appendix B is a legitimate separate concern: extra bias-derivative terms in Eq. (5) can make the sign of G12 ambiguous. But the paper presents the impossibility of determining dominance as an even more important, fundamental point independent of self-gating ('Even more importantly...'), and that point is mathematically false within the adopted framework. This flaw is load-bearing because the title, abstract, and summary all assert that conductance measurements cannot distinguish CAR from ECT. A comment that merely shows absolute probability values are unobservable, while the sign of the nonlocal conductance does reveal the dominant process, would be a much weaker statement and would not support the same conclusion. The reader's weakest_assumption concerned the validity of the scattering formalism beyond linear response; that is an external caveat, not the internal logical error identified here. Therefore I disagree with the reader's framing. The correct verdict is to reject the comment in its current form, or require major revision that narrows the claim to non-identifiability of absolute values and to the specific self-gating ambiguity, removing the assertion that dominance is fundamentally inaccessible from conductance data.","tokens_in":5645,"tokens_out":7674,"duration_ms":75513,"concrete_test":"Analytical test: use Eq. (2c) to solve for T_he12 - T_ee12 = G12/G0. Because G12 is measured, this difference is fixed, and its sign determines which nonlocal probability is larger. Apply the paper's proposed transformation, T_he12 → T_he12 + δT and T_ee12 → T_ee12 + δT, and recompute the difference: it is unchanged, so the transformed configuration has the same dominance ordering as the original. Explicitly, for a measured G12 = 0.2G0, any allowed pair must satisfy T_he12 - T_ee12 = 0.2, forcing T_he12 > T_ee12 in every realization; no δT can produce ECT dominance (T_ee12 > T_he12) while preserving the same G12. This directly contradicts the assertion that the same conductance matrix is compatible with either CAR or ECT dominating.","verdict_should_be":"REJECT","load_bearing_attack":"The central impossibility claim—that the full conductance matrix cannot reveal which of CAR and ECT dominates—is not established by the proof given. Within the authors' own scattering formalism, Eq. (2c) gives G12 = G0 (T_he12 - T_ee12), and Appendix A confirms this relation remains valid for energy-dependent transmissions when self-gating is absent. Therefore the sign of the measured G12 is exactly the sign of T_he12 - T_ee12: it does tell which nonlocal transmission probability is larger. The proposed degeneracy transformation decreases T_ee11 and T_he11 by δT and increases T_ee12 and T_he12 by the same δT. Substitution into Eq. (2c) leaves G12 unchanged, but it also leaves T_he12 - T_ee12 unchanged, because adding the same constant to both terms preserves their difference. Thus any configuration with G12 > 0 has T_he12 > T_ee12, and no choice of δT can flip that ordering. The transformation merely shifts the common baseline of the two nonlocal probabilities; it does not obscure their relative ranking. The paper's 'fundamental shortcoming' therefore shows at most that absolute values of CAR and ECT probabilities cannot be extracted from conductance, not that their dominance is unidentifiable. The self-gating corrections in Appendix B can add extra terms to G12, so the sign of G12 may no longer equal the sign of T_he12 - T_ee12 at a single energy; but that is a separate, model-dependent caveat, whereas the paper presents the dominance-unidentifiability claim as a general consequence of Eqs. (1a-1b). Since the title and abstract rest on this overstrong claim, the central argument fails as stated.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This Comment criticizes the interpretation of the non-local conductance measurements in the NSN nanowire experiment of Feng et al. (Nature Physics 2025). It advances two main claims: first, that the observed bias-voltage dependence of the non-local differential conductance, and in particular the diagonal symmetry in Fig. 3f of the commented paper, is not evidence for systematic control of crossed Andreev reflection (CAR) versus elastic co-tunneling (ECT), but is instead a fine-tuned self-gating effect; and second, that the full conductance matrix is fundamentally insufficient to determine the relative values of the CAR and ECT probabilities, so interpreting the sign of G12 as indicating dominance of one process is speculative. The authors support these claims with a scattering-matrix derivation, an explicit degeneracy transformation, and a second-order expansion of self-gating corrections in Appendices A and B.","tokens_in":5909,"tokens_out":4824,"duration_ms":52509,"significance":"If the impossibility claim were correct, it would invalidate a central interpretive step in a high-profile experiment and have implications for a broad class of non-local conductance studies. The paper is useful in drawing attention to self-gating as an alternative explanation and to the complementary role of shot-noise/thermal-conductance measurements. The algebraic derivation of G12 in the constant-landscape limit is transparent and the self-gating expansion in Appendix B is a constructive contribution. However, the central 'fundamental shortcoming' claim is not supported by the paper's own equations: within the authors' formalism the sign of G12 does determine the relative ordering of CAR and ECT probabilities. The paper therefore overreaches in its main conclusion, even though the narrower self-gating caveat may be valid.","major_comments":[{"comment":"The degeneracy transformation does not establish the claimed impossibility. Decreasing T^ee_11 and T^he_11 by δT and increasing T^ee_12 and T^he_12 by the same δT leaves every Gij unchanged, but it also leaves T^he_12 - T^ee_12 unchanged because the same constant is added to both terms. Since Eq. (2c) gives G12 = G0 (T^he_12 - T^ee_12), the sign of G12 is exactly the sign of T^he_12 - T^ee_12. Thus the conductance matrix does determine which of the two non-local processes dominates; what remains indeterminate is the absolute scale or the sum T^he_12 + T^ee_12, not the relative ordering. The paper's statement that the dominance cannot be determined is therefore false within the very formalism it uses.","section":"Section 'Even more importantly' / Eqs. (1b) and (2c)"},{"comment":"The paper presents the insufficiency of the conductance matrix as a general, fundamental limitation, but Appendix A itself shows that in the constant-landscape limit G12 = G0 [T^he_12(E=eV2) - T^ee_12(E=eV2)]. Consequently, measuring G12 as a function of V2 determines the energy-resolved difference of the two probabilities, and hence their relative ordering. The self-gating corrections in Appendix B introduce additional bias-derivative terms into G12, but that is a model-dependent correction whose quantitative relevance to the commented experiment is not established, not a fundamental obstruction. The claim of a fundamental shortcoming is not supported by the derivation.","section":"Appendix A and the paragraph containing Eq. (2c)"},{"comment":"The claim that the bias dependence of the non-local conductance in the commented experiment is 'random' rather than systematic is not quantitatively substantiated. The authors do not provide a statistical measure, a comparison with a null model, or a quantitative estimate of the fine-tuning required for the self-gating explanation. Without such analysis, the assertion that the data are 'mostly inconsistent' with the original experiment's interpretation remains a qualitative impression rather than a demonstrated result.","section":"Paragraph discussing Figs. 4 and 5 ('The above analysis does not support...')"},{"comment":"The self-gating analysis relies on the assumption that local transmission probabilities in terminal 1 are unaffected by V2, stated as 'for the case of the experiment of Ref. [1] this procedure is simplified'. No experimental evidence is given for this assumption. If V2 also modifies the potential landscape near terminal 1, additional terms involving derivatives of T^αβ_11 with respect to V2 contribute to G12 and would alter the expansion in Eq. (5) and the fine-tuning argument. The assumption is load-bearing for the specific form of Eq. (6) and should be justified or relaxed.","section":"Appendix B, assumption T^αβ_11 = T^αβ_11(E,V1)"}],"minor_comments":[{"comment":"The second-order expansion in Eq. (4) is introduced without stating the small parameter or the range of validity; the authors should specify the energy and bias scales over which truncation is controlled.","section":"Eq. (4)"},{"comment":"The sign convention for currents is defined in footnote [4], but it is easy to misread Eq. (1b) because the authors use a different sign convention from the commented paper; a sentence in the main text restating the convention would improve clarity.","section":"Footnote [4] and Eq. (1b)"},{"comment":"The symbol µS for the superconductor chemical potential is used in the caption but not defined in the main text; please define it where the figure is first referenced.","section":"Fig. 1 caption"},{"comment":"The text refers to terms 'highlighted in blue' and 'highlighted in red', but in a monochrome production these highlights may be lost; the terms should also be identified by equation numbers or labels.","section":"Appendix B, sentence about highlighted terms"},{"comment":"There are several minor grammatical errors, such as 'the G ij is insensitive' and 'an ECT and CAR probabilities', which should be corrected in a revised version.","section":"Throughout"}],"recommendation":"reject","confidential_remarks":"The Comment contains one valuable and defensible point—the self-gating caveat and the need for supplementary measurements—but the central 'fundamental shortcoming' claim is demonstrably wrong on the authors' own equations. Because that claim is the paper's headline conclusion and is used to dismiss the sign-based interpretation in the commented experiment, the error is not a local fix but undermines the main message. I would not encourage resubmission unless the authors are willing to substantially rewrite the paper around the narrower self-gating argument and explicitly retract the dominance-impossibility claim."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Tikhonov and Khrapai make one genuinely sharp point: in the standard scattering formalism the nonlocal differential conductance G12 does not know about the bias combination. Eq. (2c) holds for any V1, V2 in linear response, and Appendix A extends it to finite bias as long as the potential landscape is fixed. The claim from the original Nature Physics paper that the CAR/ECT competition can be tuned by choosing V1 = V2 or V1 = -V2, transplanted from quantum-dot total-current experiments, has no support for differential conductance. That objection is correct and worth publishing on its own. The second-order self-gating expansion in Appendix B is also new and useful: it spells out how bias-dependent landscape terms can produce the diagonal V1V2 symmetry and, in principle, corrupt a naive sign interpretation.\n\nThe soft spot is the 'fundamental shortcoming' claim, and it is not minor. The degeneracy transformation decreases the local probabilities and increases the nonlocal ones by the same δT. That leaves the conductance matrix invariant, but it also adds the same δT to both T_he12 and T_ee12, so their difference is untouched. When Eq. (2c) holds, the sign of G12 is exactly the sign of T_he12 - T_ee12, and the measurement does tell you which nonlocal process dominates. The transformation proves that absolute values of CAR and ECT probabilities cannot be disentangled from conductance alone; it does not prove that dominance is unknowable. The title and abstract claim the stronger thing, and the proof does not reach it. The self-gating corrections can add terms that break the sign relation, but that is a separate, model-dependent caveat about the actual device, not a general impossibility.\n\nTwo smaller worries. The 'randomly rather than systematically' characterization of the original data is asserted by inspection and never quantified, so it should be tempered or supported. And the comment leans on the authors' own shot-noise papers [6,7] for the claim that CAR and ECT are nearly equal to a few percent; that is a fair reliance, but the evidence lives there, not here.\n\nBottom line: this is a serious comment with a correct core and an overstated headline. It deserves refereeing, with the expectation that the authors restrict the impossibility claim to absolute probability extraction and soften the empirical assertions.","headline":"A correct and sharp bias-combination criticism saddled with an impossibility claim its own degeneracy algebra does not support.","tokens_in":6479,"tokens_out":9398,"would_cite":true,"duration_ms":85774,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Full conductance data still cannot reveal which nonlocal process dominates.","keywords":["crossed Andreev reflection","elastic co-tunneling","nonlocal conductance","conductance matrix","self-gating","scattering matrix formalism","NSN junction"],"falsifier":"Measure, in the same device, both the full conductance matrix and the shot noise or nonlocal heat conductance that gives $T^{he}_{12} + T^{ee}_{12}$; if the sign of $G_{12}$ singles out crossed Andreev reflection while the noise shows the two probabilities are equal within error bars, the conductance-only interpretation is refuted.","tokens_in":5386,"feed_emoji":"⚡","tokens_out":5295,"duration_ms":56776,"temperature":0.7,"pith_summary":"This comment argues that the interpretation of a recent three-terminal nanowire experiment is misleading: bias voltages do not systematically tune the competing crossed Andreev reflection and elastic co-tunneling processes, and the observed diagonal bias symmetry of the nonlocal conductance can be produced by a fine-tuned self-gating effect. More fundamentally, it shows that the full conductance matrix is invariant when local transmission probabilities are decreased by some amount and nonlocal ones are increased by the same amount, so the relative strength of the two processes cannot be extracted from conductance alone. If the paper is right, claims of dominant long-range crossed Andreev reflection based on the sign of nonlocal conductance are not supported by transport data.","feed_headline":"Conductance data cannot reveal which nonlocal process dominates","feed_subtitle":"Even a full conductance matrix hides whether crossed Andreev reflection or elastic co-tunneling wins.","key_machinery":"The load-bearing object is the scattering-matrix relation $G_{ij} = G_0\\left(\\delta_{ij} - T^{ee}_{ij} + T^{he}_{ij}\\right)$, taken from the Anantram–Datta scattering formalism and extended to finite bias. Its key property is the invariance under the $\\delta T$ compensation described above; the self-gating analysis is a second-order Taylor expansion of the transmission probabilities in $E$, $V_1$, and $V_2$ that isolates the $V_1 V_2$ terms with the diagonal bias symmetry of the experiment.","core_discovery":"Within the scattering-matrix description, the nonlocal differential conductance obeys $G_{12} = G_0\\left(-T^{ee}_{12} + T^{he}_{12}\\right)$ for any bias combination, so measuring $G_{12}$ as a function of $V_1$ and $V_2$ does not separate elastic co-tunneling from crossed Andreev reflection; the bias only changes the energy at which the probabilities are evaluated. In addition, the transformation that lowers all local probabilities $T^{\\alpha\\beta}_{ii}$ by $\\delta T$ and raises all nonlocal probabilities $T^{\\alpha\\beta}_{ij}$ by the same $\\delta T$ leaves every element of the conductance matrix unchanged. Beyond linear response, $\\delta T$ can be an arbitrary function of energy and bias, making the relative CAR and ECT probabilities undetermined by conductance data. When self-gating is included, extra bias-derivative terms enter $G_{12}$, so even the sign of $G_{12}$ cannot be read as a statement about which process dominates.","pith_inferences":["The same $\\delta T$ degeneracy should apply to any multiterminal conductance-only measurement, so shot noise or nonlocal heat conductance are likely necessary to settle CAR/ECT ratios in other platforms.","A direct check of the paper's logic would be to take a model with known transmission probabilities, apply a $\\delta T$ compensation, and verify that every simulated $G_{ij}$ stays identical while the inferred physics changes.","If self-gating is as influential as the paper suggests, finite-bias conductance maps in other proximitized nanowire experiments may need to be revisited before assigning features to specific transport processes."],"forward_implications":["Bias choices $V_1 = V_2$ and $V_1 = -V_2$ cannot by themselves separate CAR from ECT in a differential conductance measurement.","The sign of $G_{12}$ alone does not establish the dominance of CAR or ECT, especially when self-gating terms contribute.","Claims of long-range crossed Andreev reflection based on the sign of nonlocal conductance need additional evidence beyond the conductance matrix.","Conductance-matrix data alone cannot constrain the relative values of local and nonlocal transmission probabilities.","Self-gating must be included before finite-bias nonlocal conductance data are interpreted in terms of specific quasiparticle processes."],"supporting_citations":[{"why":"The experimental data and claims that the comment reinterprets and challenges.","marker":"[1]"},{"why":"The quantum-dot experiment whose bias-combination logic the paper argues does not transfer to differential conductance.","marker":"[2]"},{"why":"The scattering-matrix formalism from which the conductance formula and its signs are taken.","marker":"[3]"},{"why":"The finite-bias extension with self-gating used for the Appendix B expansion.","marker":"[5]"},{"why":"InAs nanowire experiment combining conductance with shot noise and nonlocal thermal conductance to determine relative CAR and ECT probabilities.","marker":"[6]"},{"why":"Companion InAs nanowire experiment supporting near-equal CAR and ECT probabilities on average.","marker":"[7]"}],"fun_headline_variants":["Conductance can't separate crossed Andreev from co-tunneling","Full conductance matrix hides nonlocal process identity","Bias sweeps can't reveal which nonlocal process dominates","Conductance data blind to CAR vs ECT probabilities","Nonlocal conductance cannot pin down dominant mechanism"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument assumes the scattering-matrix conductance formula, and its finite-bias extension, still describes the real device beyond the linear-response regime — a validity the authors themselves flag as possibly incomplete.","fun_headline_variants_meta":{"raw":{"variants":["Conductance can't separate crossed Andreev from co-tunneling","Full conductance matrix hides nonlocal process identity","Bias sweeps can't reveal which nonlocal process dominates","Conductance data blind to CAR vs ECT probabilities","Nonlocal conductance cannot pin down dominant mechanism"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000227,"raw_usage":{"total_tokens":1424,"prompt_tokens":851,"completion_tokens":573,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":467,"completion_tokens_details":{"reasoning_tokens":493}},"tokens_in":467,"tokens_out":573,"duration_ms":6274,"temperature":1.0,"reasoning_tokens":493,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T12:44:32.814751+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure, in the same device, both the full conductance matrix and the shot noise or nonlocal heat conductance that gives $T^{he}_{12} + T^{ee}_{12}$; if the sign of $G_{12}$ singles out crossed Andreev reflection while the noise shows the two probabilities are equal within error bars, the conductance-only interpretation is refuted.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The experimental data and claims that the comment reinterprets and challenges."},{"cited_title":"Bordin, G","cited_arxiv_id":null,"evidence_quote":"The quantum-dot experiment whose bias-combination logic the paper argues does not transfer to differential conductance."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The scattering-matrix formalism from which the conductance formula and its signs are taken."},{"cited_title":"Maiani, M","cited_arxiv_id":null,"evidence_quote":"The finite-bias extension with self-gating used for the Appendix B expansion."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"InAs nanowire experiment combining conductance with shot noise and nonlocal thermal conductance to determine relative CAR and ECT probabilities."}],"review_version":1}