Conductance measurements cannot distinguish crossed Andreev reflection from elastic co-tunneling in normal--superconductor--normal junctions

E.S. Tikhonov; V.S. Khrapai

REVIEW 4 major objections 5 minor 1 cited by

Conductance measurements cannot distinguish crossed Andreev reflection from elastic co-tunneling in normal--superconductor--normal junctions

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Full conductance data still cannot reveal which nonlocal process dominates.

desk verdict A correct and sharp bias-combination criticism saddled with an impossibility claim its own degeneracy algebra does not support. read the letter →

arxiv 2505.23490 v2 pith:J323DLNX submitted 2025-05-29 cond-mat.mes-hall cond-mat.supr-con

E.S. Tikhonov , V.S. Khrapai This is my paper

classification cond-mat.mes-hallcond-mat.supr-con

keywords crossedAndreevreflectionelasticco-tunnelingnonlocalconductancematrixself-gatingscatteringformalismNSNjunction

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

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

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

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.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the 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.

The 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.

Two 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.

Bottom 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.

Referee Report

4 major / 5 minor

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.

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 (4)

[Section 'Even more importantly' / Eqs. (1b) and (2c)] 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.
[Appendix A and the paragraph containing Eq. (2c)] 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.
[Paragraph discussing Figs. 4 and 5 ('The above analysis does not support...')] 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.
[Appendix B, assumption T^αβ_11 = T^αβ_11(E,V1)] 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.

minor comments (5)

[Eq. (4)] 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.
[Footnote [4] and Eq. (1b)] 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.
[Fig. 1 caption] 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.
[Appendix B, sentence about highlighted terms] 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.
[Throughout] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the degeneracy argument is a direct algebraic consequence of the externally sourced scattering-matrix formula; the paper's overreach about non-identifiability of dominance is a correctness issue, not a circular derivation.

full rationale

The paper's central derivation starts from the scattering-matrix conductance formula of Ref. [3] (Eq. 1b) and the finite-bias extension of Ref. [5], both external inputs with stated assumptions. The claimed degeneracy—that G_ij is unchanged when local transmission probabilities are decreased by δT and nonlocal probabilities increased by the same δT—is a direct algebraic identity of Eq. (1b), not a fitted result or a renamed conclusion. No parameter is fit to data to produce the impossibility claim, and no load-bearing premise is justified solely by the authors' own prior work: Appendix B expands the transmission probabilities using the framework of Ref. [5], while Refs. [6,7] serve only as illustrative experimental comparison. The logical gap in the paper—that adding the same δT to both nonlocal probabilities preserves T_he12 - T_ee12 and hence preserves the sign of G12 in the absence of self-gating—concerns the validity of the conclusion about dominance, not circularity of the derivation. The derivation chain is therefore self-contained and exhibits no circular step.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

The comment introduces no free parameters and no new entities. It relies on a standard scattering formalism plus two modeling assumptions, one of which the authors explicitly hedge. The algebraic degeneracy result is a rigorous consequence of the formalism and does not depend on fitting.

assumptions (3)

domain assumption Scattering matrix formalism of Ref. [3] describes transport in the NSN device beyond linear response when supplemented by finite-bias energy dependence
The comment uses this to derive G12; the authors note it 'may have shortcomings beyond the linear response regime' (main text, paragraph 2).
standard math Electron-hole symmetry relations T^ee_12(E)=T^hh_12(-E) and T^he_12(E)=T^eh_12(-E) hold
Used in Appendix A to simplify the conductance expression.
ad hoc to paper Local transmission probabilities in terminal 1 are unaffected by bias V2 (T^alpha_beta_11 = T^alpha_beta_11(E,V1))
Assumed in Appendix B to drop certain terms in G12; it is a modeling choice specific to the experiment's geometry.

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Cite this review

Pith. "Pith review of Conductance measurements cannot distinguish crossed Andreev reflection from elastic co-tunneling in normal--superconductor--normal junctions." pith.science (2026). https://pith.science/paper/J323DLNX

@misc{pith2026250523490,
  author       = {Pith},
  title        = {Pith review of: Conductance measurements cannot distinguish crossed Andreev reflection from elastic co-tunneling in normal--superconductor--normal junctions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/J323DLNX}},
  note         = {Machine review of arXiv:2505.23490}
}

read the original abstract

We argue that the interpretation of the experiment [Nature Physics 21, 708-715 (2025)] is misleading in two respects. First, the bias voltages impact the non-local differential conductance randomly, rather than systematically, and the bias symmetry of the non-local conductance in Fig. 3 can be explained by a fine tuned self-gating effect. Second, the full knowledge of the conductance matrix is insufficient to conclude on the relative values of the crossed-Andreev and elastic cotunneling probabilities, in particular on the dominance of one of them.

Figures

Figures reproduced from arXiv: 2505.23490 by the authors.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Reply to the Comment by Tikhonov and Khrapai on "Long-range crossed Andreev reflection in a topological insulator nanowire proximitized by a superconductor"
cond-mat.mes-hall 2025-09 conditional novelty 1.0 of 10

The reply claims the Tikhonov-Khrapai comment fails to find scientific errors and that its model, by requiring finite CAR, supports the original paper's conclusions.

Reference graph

Works this paper leans on

7 extracted references · 6 canonical work pages · cited by 1 Pith paper

[1]

J. Feng, H. F. Legg, M. Bagchi, D. Loss, J. Klinovaja, and Y. Ando, Long-range crossed Andreev reflection in a topological insulator nanowire proximitized by a super- conductor, Nature Physics (2025)

work page 2025
[2]

Bordin, G

A. Bordin, G. Wang, C.-X. Liu, S. L. D. ten Haaf, N. van Loo, G. P. Mazur, D. Xu, D. van Driel, F. Zatelli, S. Gaz- ibegovic, G. Badawy, E. P. A. M. Bakkers, M. Wim- mer, L. P. Kouwenhoven, and T. Dvir, Tunable Crossed Andreev Reflection and Elastic Cotunneling in Hybrid Nanowires, Physical Review X13(2023)

work page 2023
[3]

M. P. Anantram and S. Datta, Current fluctuations in mesoscopic systems with Andreev scattering, Physical Re- view B53, 16390 (1996)

work page 1996
[4]

Following [3], we define the sign of the currents inflowing the device via all terminals as positive, which gives the opposite sign of the non-local conductance as compared to [1]

work page
[5]

Maiani, M

A. Maiani, M. Geier, and K. Flensberg, Conduc- tance matrix symmetries of multiterminal semiconductor- superconductor devices, Phys. Rev. B106, 104516 (2022)

work page 2022
[6]

A. O. Denisov, A. V. Bubis, S. U. Piatrusha, N. A. Titova, A. G. Nasibulin, J. Becker, J. Treu, D. Ruhstor- fer, G. Koblm¨ uller, E. S. Tikhonov, and V. S. Khrapai, Charge-neutral nonlocal response in superconductor-InAs nanowire hybrid devices, Semiconductor Science and Tech- nology36, 09LT04 (2021)

work page 2021
[7]

Denisov, A

A. Denisov, A. Bubis, S. Piatrusha, N. Titova, A. Nasi- bulin, J. Becker, J. Treu, D. Ruhstorfer, G. Koblm¨ uller, E. Tikhonov, and V. Khrapai, Heat-Mode Excitation in a Proximity Superconductor, Nanomaterials12, 1461 (2022)

2022

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

J. Feng, H. F. Legg, M. Bagchi, D. Loss, J. Klinovaja, and Y. Ando, Long-range crossed Andreev reflection in a topological insulator nanowire proximitized by a super- conductor, Nature Physics (2025)

work page 2025

[2] [2]

Bordin, G

A. Bordin, G. Wang, C.-X. Liu, S. L. D. ten Haaf, N. van Loo, G. P. Mazur, D. Xu, D. van Driel, F. Zatelli, S. Gaz- ibegovic, G. Badawy, E. P. A. M. Bakkers, M. Wim- mer, L. P. Kouwenhoven, and T. Dvir, Tunable Crossed Andreev Reflection and Elastic Cotunneling in Hybrid Nanowires, Physical Review X13(2023)

work page 2023

[3] [3]

M. P. Anantram and S. Datta, Current fluctuations in mesoscopic systems with Andreev scattering, Physical Re- view B53, 16390 (1996)

work page 1996

[4] [4]

Following [3], we define the sign of the currents inflowing the device via all terminals as positive, which gives the opposite sign of the non-local conductance as compared to [1]

work page

[5] [5]

Maiani, M

A. Maiani, M. Geier, and K. Flensberg, Conduc- tance matrix symmetries of multiterminal semiconductor- superconductor devices, Phys. Rev. B106, 104516 (2022)

work page 2022

[6] [6]

A. O. Denisov, A. V. Bubis, S. U. Piatrusha, N. A. Titova, A. G. Nasibulin, J. Becker, J. Treu, D. Ruhstor- fer, G. Koblm¨ uller, E. S. Tikhonov, and V. S. Khrapai, Charge-neutral nonlocal response in superconductor-InAs nanowire hybrid devices, Semiconductor Science and Tech- nology36, 09LT04 (2021)

work page 2021

[7] [7]

Denisov, A

A. Denisov, A. Bubis, S. Piatrusha, N. Titova, A. Nasi- bulin, J. Becker, J. Treu, D. Ruhstorfer, G. Koblm¨ uller, E. Tikhonov, and V. Khrapai, Heat-Mode Excitation in a Proximity Superconductor, Nanomaterials12, 1461 (2022)

2022