{"id":"dfa11146-cc22-4046-ab04-e537fab6c443","arxiv_id":"2411.14903","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Half-integer conductance quantization in superconductor-QAHI devices comes from edge-state voltage equilibration at the superconducting contact, not from chiral Majorana modes.","lead":"This experiment shows that a half-unit conductance plateau in a superconductor/quantum anomalous Hall device is caused by the superconductor acting like an ordinary metal contact, not by Majorana particles. The result removes a commonly cited smoking gun for Majorana modes and tells researchers to use much smaller superconducting contacts.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (16) models the floating SC as a voltage node with a free supercurrent; the derivation of Eq. (8) and hence the k≈0 extraction depends on this boundary condition, which is not the physical no-current condition for a floating island.","rationale":"The reader's weakest assumption identifies the same point: the floating SC electrode is treated as an ideal voltage node with an unconstrained supercurrent, and Eq. (8) is not guaranteed under a more physical floating-island constraint. This is load-bearing because the paper's quantitative claim that k≈0, and therefore that the half-integer conductance arises from trivial equilibration, is derived from this equation. If the boundary condition is corrected, the mapping between measured resistances and the transmission coefficients changes; the experiment alone does not settle which boundary condition applies to a micron-scale Nb island proximitizing the QAHI edge. I do not recommend changing the verdict because the paper has independent supportive evidence: the trench device still shows the same edge potentials even when no longitudinal transmission across the SC is possible, the resistance pattern is unchanged above Hc2, and no negative nonlocal resistance is observed. These controls make the qualitative conclusion plausible even if the quantitative k extraction is conditional. The appropriate action is to request the authors to clarify and justify the floating-SC boundary condition and to show that the central conclusion survives the physically correct condition; this is consistent with the existing CONDITIONAL verdict rather than a rejection or full acceptance.","tokens_in":16132,"tokens_out":20869,"duration_ms":206835,"concrete_test":"Re-solve the Appendix B transport equations for the floating configuration with the physical boundary condition I11=0 (or I11+I_SC_11=0 with I_SC_11 determined by the island's phase dynamics rather than free), using the same a-matrix. Then recompute R3-4, R9-8 and R8-11 and compare with Eqs. (8)-(9) and (13)-(14). A decisive version: set T_ee_L=T_eh_L=T_ee_T=T_eh_T=0, T_D=1 (purely normal-metal-like SC contact) and verify whether the corrected model reproduces V11=(V1+V6)/2 and R3-4=h/e2; if not, the paper's k=0 deduction from Fig. 2 is model-dependent. The data are on Zenodo (10.5281/zenodo.14176676), so the re-fit can be run directly.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central inference that the measured h/e2 resistances imply k≈0 and edge-state equilibration rests on Eq. (8), V11=(V1+V6)/2, obtained in Appendix B by solving the LB equations with Eq. (16), I1+I6+I11+I_SC_11=0, where I_SC_11 is an unconstrained supercurrent 'flowing into the device from contact 11.' For an electrode that is truly floating, there is no external current path; the time-averaged total current through the NS interface must vanish, i.e. I11=0 (or, if a condensate current is defined, I11+I_SC_11=0 with the supercurrent fixed by phase dynamics, not free). Allowing I_SC_11 to be a free parameter effectively grounds the SC through a zero-impedance supercurrent path, imposing an ideal voltage-node condition. Re-solving Eqs. (1) with the printed a-matrix of Appendix A under the floating-island constraint I11=0 does not generally yield Eq. (8): V11 is then determined by the contact equations and depends on T_D, T_L and T_T. Consequently Eqs. (9), (13), and the inference V3≈V8≈V1/2 from Fig. 2 are conditional on this boundary-condition choice. If the correct floating-SC condition changes these formulas, the extracted k≈0 and the 'equilibration' explanation of the half-integer quantization are not uniquely established. The qualitative trench-device control (no CMEM possible) remains suggestive, but it does not by itself validate the quantitative k extraction.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper addresses the debated origin of the half-integer two-terminal conductance plateau observed in superconductor/quantum-anomalous-Hall-insulator (SC/QAHI) heterostructures. Using a Landauer-Büttiker description of a multi-terminal device with a micrometre-scale Nb strip, the authors show that the two-terminal conductance depends only on a combination k of the electron and hole transmission coefficients across and along the SC electrode. They report measurements on V-doped (Bi,Sb)2Te3 Hall bars with floating and grounded Nb electrodes, and infer k ≈ 0 from the observed resistances. Together with a trench-device control in which no chiral Majorana mode can propagate, they conclude that the half-integer plateau in their devices arises from equilibration of the incoming edge-state potentials at the SC electrode, not from chiral Majorana edge modes. The paper also argues that two-terminal measurements alone cannot distinguish Majorana physics from this trivial mechanism, and it critiques a recent claim of Majorana signatures in similar devices.","tokens_in":16438,"tokens_out":33008,"duration_ms":307225,"significance":"If the central claim holds, the paper provides a clear resolution to a long-standing controversy: the half-integer conductance plateau in SC/QAHI devices is not a smoking gun for chiral Majorana modes. The theoretical observation that the two-terminal conductance is determined by a single combination k of four transmission coefficients is simple and important, and the experimental control (the trench device, where no longitudinal Majorana transmission is possible) is a strong and appropriate test. The manuscript also ships its data on Zenodo, which is a concrete reproducibility strength. The main result is a useful contribution to the Majorana search literature, and it aligns with earlier work by Kayyalha et al. while extending the analysis to a multi-terminal framework.","major_comments":[{"comment":"The derivation of Eq. (8) is presented as following from Eq. (16), but as written Eq. (16) imposes no constraint on the voltages because I_SC_11 is an unconstrained variable that can absorb any value of I11. This makes the treatment of the floating SC electrode look like an ideal voltage-node assumption. In fact, Eq. (8) follows from the zero-current conditions at contacts 3 and 8 [Eq. (15)] together with the current boundary conditions at contacts 1 and 6, and it does not require Eq. (16) at all for k ≠ 1. The authors should rewrite the derivation to show this explicitly, and either remove Eq. (16) or state clearly that it merely defines the balancing supercurrent after the voltage solution is obtained. This is load-bearing because the experimental inference V3 ≈ V8 ≈ V1/2 and hence k ≈ 0 depends directly on Eq. (8).","section":"Appendix B, Eq. (16) and Section III-B, Eq. (8)"},{"comment":"The statement that Eq. (8) is independent of the choice of T_D, T_ee_L, T_eh_L, T_ee_T, and T_eh_T is not strictly correct. For k = 1 (for example, T_ee_L = 1 with all other transmission coefficients zero), the linear system for the voltages becomes singular and Eq. (8) is not enforced. The statement should be restricted to k ≠ 1, which is the experimentally relevant regime (k ≈ 0). The same caveat applies to the broad claim in the Conclusion that 'any experimental results on the two-terminal configuration can be explained by the SC electrode equilibrating all the chiral edge state potentials'; this should be qualified to avoid overstatement.","section":"Section III-B, paragraph after Eq. (8)"},{"comment":"The critique of Ref. [24] relies on an ad hoc parameter T_S representing an electric short across the SC strip, and the conclusion that the kinks observed by Huang et al. are 'most likely not related to the N=1 topological SC state' is speculative. The argument is not needed for the central claim of this manuscript, and the strength of the wording should be tempered, or the analysis should be supported by a more direct model or by data from the present devices. As written, this section may be read as overreach and could distract from the otherwise well-supported main result.","section":"Section VII-D, Eqs. (22)-(25)"}],"minor_comments":[{"comment":"The list of nonzero proportionality coefficients a_ij is incomplete; for example, coefficients connecting contacts along the chiral edge (such as a_{i,i-1}) are not listed. The authors should provide the full matrix or explicitly state the convention for how the chiral edge connects the contacts.","section":"Appendix A"},{"comment":"The phrase 'supercurrent flowing into the device from contact 11' is ambiguous about sign conventions. The authors should define the direction of I_SC_11 clearly, for instance by stating that a positive value corresponds to a current entering the SC electrode from the external circuit.","section":"Appendix B, Eq. (16)"},{"comment":"The vertical axis label 'R (h/e2)' in Fig. 2(c-f) is unconventional; the authors should define it in the caption or use 'Resistance (h/e²)' to avoid confusion.","section":"Section III-B, Fig. 2"},{"comment":"The word 'unambiguously' is used in the abstract and conclusion. Given the caveat about the k = 1 exceptional case and the model assumptions, a more cautious formulation such as 'consistently shows' would be more appropriate.","section":"Abstract and Conclusion"},{"comment":"The statement that R3-4 and R9-8 'cannot become negative, since -1 ≤ k ≤ 1' is correct within the model, but it would be helpful to note that this follows from the unitarity constraints on the transmission coefficients, which are not explicitly stated in the main text.","section":"Section III-B, Eq. (9)"}],"recommendation":"major_revision","confidential_remarks":"The central result is likely correct and important, and the experimental control (trench device) is convincing. However, the derivation of Eq. (8) in Appendix B is presented in a way that is open to the objection that the floating SC is effectively treated as an ideal voltage node; although the result survives a careful algebraic check for the relevant regime, the manuscript needs to be rewritten to make the role of the supercurrent term transparent. The critique of Ref. [24] is speculative and should be toned down to avoid distracting from the main message. If these issues are addressed, the paper would be a solid contribution to the field."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThis paper is a solid experimental contribution to the ongoing demolition of the e2/2h plateau as a Majorana smoking gun. The genuinely new pieces are the multi-terminal Landauer–Büttiker formulas, the direct edge-potential measurements, and the trench-device control that rules out chiral Majorana modes by construction. The above-Hc2 control, where nothing changes when Nb becomes normal, is convincing and sticks with you. The authors deserve credit for being upfront that their main conclusion echoes Kayyalha et al. and for pushing further with a more complete edge-potential picture.\n\nThe soft spots are real but not disqualifying. The treatment of the floating SC contact as an ideal voltage node with a free supercurrent in Eq. (16) is delicate. For a truly floating island the physical constraint is zero total current; the paper does not fully justify why I_SC_11 can be an unconstrained parameter, and this affects the derivation of Eq. (8) and the k≈0 extraction. However, the trench device—where no CMEM can exist and the same edge potentials still appear—carries the main argument without leaning on that boundary condition. The grounded configuration and the field-independent resistances above Hc2 also stand on their own. So the central claim survives.\n\nMinor issues: the appendix omits several nonzero a_ij coefficients, which makes the algebra needlessly hard to audit, and the quantitative dismissal of Huang et al. rests on a fitted T_S parameter that is somewhat ad hoc. The contact-resistance interpretation for the grounded configuration is plausible but inferred rather than directly measured.\n\nBottom line: this paper deserves serious peer review. The theory section should be tightened—the floating-SC condition needs a careful justification or a fix—but the experimental evidence for the non-Majorana origin of the half-integer plateau is strong and independently supported by the trench control. I would accept it after minor-to-moderate revision.","headline":"A careful experimental study showing the half-integer plateau is a trivial equilibration effect; the floating-SC boundary condition in the theory needs tightening, but the trench control carries the claim.","tokens_in":17041,"tokens_out":8750,"would_cite":true,"duration_ms":83395,"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":"The half-integer two-terminal conductance in a superconductor–quantum anomalous Hall insulator heterostructure is shown to arise from edge-state potential equilibration at the superconducting electrode, not from chiral Majorana edge modes.","keywords":["quantum anomalous Hall insulator","chiral Majorana edge modes","half-integer conductance quantization","Landauer-Büttiker formalism","superconducting proximity effect","edge-state equilibration","crossed Andreev reflection","V-doped (Bi,Sb)2Te3"],"falsifier":"Replace the superconducting strip by an identical normal-metal strip: the paper's mechanism predicts the same $e^2/(2h)$ plateau with $k\\approx 0$ and the same edge potentials, whereas any Majorana-based explanation predicts the plateau disappears when superconductivity is absent. A second test is to measure the same multi-terminal resistances in a device known to be in the $N=1$ topological phase; if $R_{3-4}$ and $R_{9-8}$ remain exactly $h/e^2$, the plateau carries no information about the phase.","tokens_in":15896,"feed_emoji":"⚛️","tokens_out":10366,"duration_ms":90707,"temperature":0.7,"pith_summary":"Superconductor–quantum anomalous Hall insulator (QAHI) heterostructures, in which a ferromagnetic topological insulator thin film carries a chiral one-dimensional edge state, have been proposed to host chiral Majorana edge modes, with a two-terminal conductance of $e^2/(2h)$ proposed as their smoking-gun signature. This paper argues that the plateau is not a Majorana signature: in a Landauer–Büttiker description of the multi-terminal device, the conductance is $\\sigma_{2T}=(e^2/(2h))(1+k)$, and $k=0$—the value giving the plateau—occurs whenever the superconducting electrode equilibrates the potentials of the incoming edge states, exactly as a normal metal would. The authors confirm this in V-doped $(\\mathrm{Bi,Sb})_2\\mathrm{Te}_3$ films with micrometer-scale Nb strips by measuring the individual edge potentials, finding $k\\approx 0$, and they show the plateau survives even when the film is trenched underneath the superconductor so no longitudinal Majorana transmission is possible. If the paper is right, the $e^2/(2h)$ plateau cannot serve as evidence for topological superconductivity in QAHI systems, and searches must shift to contacts comparable to the superconducting coherence length.","feed_headline":"Half-integer plateau is electrode equilibration, not Majorana","feed_subtitle":"A simple voltage-averaging effect, present even without superconductivity, explains the half-integer plateau.","key_machinery":"The load-bearing object is the Landauer–Büttiker transport description of an eleven-terminal QAHI Hall bar with a superconducting strip (contact 11), expressed through electron and hole transmission coefficients $T^{ee}_L$, $T^{eh}_L$, $T^{ee}_T$, $T^{eh}_T$ and single-particle tunneling $T_D$. Its key identity is Eq. (5), $\\sigma_{2T}=(e^2/(2h))(1+k)$ with $k\\equiv(T^{ee}_L-T^{eh}_L)-(T^{ee}_T-T^{eh}_T)$, which collapses all possible microscopic processes into one number; for the floating superconducting electrode, Eq. (8), $V_{11}=(V_1+V_6)/2$, shows that the electrode equilibrates the incoming edge-state potentials regardless of the transmission coefficients. These relations let the multi-terminal measurements determine which processes actually carry the current, and they show that $k=0$—and hence the half-integer plateau—is produced by equilibration rather than by a single chiral Majorana mode.","core_discovery":"On its own terms, the paper's central result is a degeneracy: the two-terminal conductance $\\sigma_{2T}$ of a superconducting-strip QAHI device is $\\sigma_{2T}=(e^2/(2h))(1+k)$ with $k=(T^{ee}_L-T^{eh}_L)-(T^{ee}_T-T^{eh}_T)$, so the Majorana prediction of $k=0$ is only one of many transmission combinations that produce the half-integer plateau. In the experimentally realized floating-superconductor configuration, the formalism gives $V_{11}=(V_1+V_6)/2$ independent of all transmission coefficients, meaning the superconducting strip pins its potential to the average of the two incoming edge states; the measured resistances across the strip then give $k\\approx 0$. The multi-terminal data also show $T^{ee}_T\\approx T^{eh}_T$ and $T^{ee}_L\\approx T^{eh}_L$, no negative nonlocal resistances at low bias, and an unchanged plateau in a trenched device where the QAHI film is interrupted beneath the superconductor. The paper concludes that the half-integer quantization is a trivial edge-state equilibration effect, not a signature of chiral Majorana edge modes, and that superconducting proximity signatures in these films require electrode dimensions of the order of the induced coherence length.","pith_inferences":["The same degeneracy likely applies to other proposed Majorana transport observables whenever a floating superconducting island can equilibrate the incoming edge potentials; a direct check would be to compare noise or thermal conductance on samples with normal-metal versus superconducting strips of identical geometry.","The voltage-node assumption behind Eq. (8) suggests the plateau may become sensitive to the microscopic state of the superconducting island (charging energy, phase fluctuations, quasiparticle population) at smaller scales; probing with a gate-tunable or Josephson-coupled island could reveal deviations from $k=0$.","If equilibration is caused by in-gap states at the superconductor–QAHI interface, then cleaner interfaces or different barrier materials should change the transmission coefficients while preserving the plateau; a systematic barrier-thickness study could separate interface effects from intrinsic topological superconductivity."],"forward_implications":["The two-terminal $e^2/(2h)$ plateau is a degenerate signature: many transmission combinations, including a normal-metal-like superconducting contact with $T_D\\approx 1$, produce it, so it cannot certify the $N=1$ topological superconducting state.","Micrometer-scale superconducting electrodes on V-doped (Bi,Sb)$_2$Te$_3$ equilibrate incoming chiral edge potentials and show no negative nonlocal resistances, implying crossed Andreev reflection is not active over length scales much larger than the coherence length.","The grounded-superconductor configurations $R_{3-4}$ and $R_{8-4}$ isolate the transverse and longitudinal transmission coefficients, giving future experiments a way to search for genuine Andreev processes rather than relying on the two-terminal plateau.","A device with the QAHI film trenched underneath the superconductor still shows the same edge potentials and $k\\approx 0$, showing the plateau does not require transmission of a chiral Majorana edge mode beneath the strip.","Observing superconducting proximity signatures in QAHI films will require superconducting electrodes with dimensions comparable to the induced coherence length, as in the sub-micrometer devices that showed negative downstream potentials."],"supporting_citations":[{"why":"Supplies the original proposal that $N=1$ chiral Majorana edge modes give $\\sigma_{2T}=e^2/(2h)$, the claim the paper argues is degenerate.","marker":"[5]"},{"why":"Provides the original two-terminal transmission-coefficient model with equal longitudinal and transverse Majorana transmissions that the paper generalizes.","marker":"[23]"},{"why":"Earlier experiment attributing the half-integer plateau to edge-state equilibration, which the present multi-terminal data support and extend.","marker":"[13]"},{"why":"Provides the fabrication recipe and the sub-micrometer Nb electrode that showed negative downstream potentials, the length-scale benchmark for proximity effect.","marker":"[18]"},{"why":"Reports long-range negative downstream resistance in NbTiN-InAs quantum Hall systems, the contrast case for why QAHI devices show none at micrometer scale.","marker":"[22]"},{"why":"Recent claim of kinks at $0.57$–$0.59\\,e^2/h$ interpreted as the $N=1$ state, which the paper reinterprets as not compatible with the predicted values.","marker":"[24]"},{"why":"The now-retracted observation of the half-integer plateau that motivated the debate and is addressed by the present analysis.","marker":"[15]"},{"why":"Establishes that chiral Andreev edge states carry potentials equal to the superconductor chemical potential, the physical mechanism behind the equilibration interpretation.","marker":"[12]"}],"fun_headline_variants":["Half-integer plateau? Just voltage averaging, not Majorana","Majorana signature debunked: half-integer plateau is trivial","No Majorana: half-integer conductance is electrode equilibration","Half-integer quantization explained without Majorana physics","Multiterminal setup reveals half-integer plateau is not Majorana"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The conclusion rests on treating the floating superconductor as an ideal voltage node that perfectly averages the incoming edge potentials; if its internal charging dynamics or non-equilibrium electronic state instead matter, the measured potentials would not directly give the transmission coefficients, and the plateau could have a different cause.","fun_headline_variants_meta":{"raw":{"variants":["Half-integer plateau? Just voltage averaging, not Majorana","Majorana signature debunked: half-integer plateau is trivial","No Majorana: half-integer conductance is electrode equilibration","Half-integer quantization explained without Majorana physics","Multiterminal setup reveals half-integer plateau is not Majorana"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000257,"raw_usage":{"total_tokens":1639,"prompt_tokens":1065,"completion_tokens":574,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":681,"completion_tokens_details":{"reasoning_tokens":488}},"tokens_in":681,"tokens_out":574,"duration_ms":5155,"temperature":1.0,"reasoning_tokens":488,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T14:44:58.211201+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Replace the superconducting strip by an identical normal-metal strip: the paper's mechanism predicts the same $e^2/(2h)$ plateau with $k\\approx 0$ and the same edge potentials, whereas any Majorana-based explanation predicts the plateau disappears when superconductivity is absent. A second test is to measure the same multi-terminal resistances in a device known to be in the $N=1$ topological phase; if $R_{3-4}$ and $R_{9-8}$ remain exactly $h/e^2$, the plateau carries no information about the phase.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the original proposal that $N=1$ chiral Majorana edge modes give $\\sigma_{2T}=e^2/(2h)$, the claim the paper argues is degenerate."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the original two-terminal transmission-coefficient model with equal longitudinal and transverse Majorana transmissions that the paper generalizes."},{"cited_title":"Kayyalha, D","cited_arxiv_id":null,"evidence_quote":"Earlier experiment attributing the half-integer plateau to edge-state equilibration, which the present multi-terminal data support and extend."},{"cited_title":"Hatefipour, J","cited_arxiv_id":null,"evidence_quote":"Reports long-range negative downstream resistance in NbTiN-InAs quantum Hall systems, the contrast case for why QAHI devices show none at micrometer scale."},{"cited_title":"Huang, Y","cited_arxiv_id":null,"evidence_quote":"Recent claim of kinks at $0.57$–$0.59\\,e^2/h$ interpreted as the $N=1$ state, which the paper reinterprets as not compatible with the predicted values."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The now-retracted observation of the half-integer plateau that motivated the debate and is addressed by the present analysis."}],"review_version":1}