{"id":"12a35c44-f597-4db5-9bf1-20f820d88a8d","arxiv_id":"1908.05549","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"End-to-end correlated subgap bound states are strong in a 300-nm hybrid nanowire and reduced by a factor of about four in a 900-nm device, quantified by a peak-based correlator and mutual information.","lead":"Researchers measured electrical conductance from both ends of superconducting nanowires and counted how often subgap bound states appeared at matching energies on both ends. Correlations were strong in a 300-nanometer device and about four times weaker in a 900-nanometer device, giving a tool for identifying nonlocal states.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Finite impedance of the etched-Al ground could produce exactly the observed length-dependent end-to-end correlations; the paper does not report a direct crosstalk check.","rationale":"The reader's weakest_assumption identifies the non-invasive Al ground, and I agree it is the most load-bearing premise. The central claim is a comparison of end-to-end correlations across two device lengths; if the etched-Al terminal is not a true virtual ground, every correlation metric (both the binary-mask correlator C in Eq. (1) and the mutual-information analysis) is contaminated by common-mode voltage fluctuations on the wire bulk. The concern is sharpened by the fact that the independent variable is the Al-segment length itself: contact resistance and interface quality are plausibly length-dependent, so the observed factor-3.7 drop could track ground impedance rather than bound-state extent. The authors' own supplement validates the alternate biasing configuration only on the short device and does not report off-diagonal conductances, which are the direct probe of this leakage path. I do not think this requires rejection: the proposed crosstalk measurement is straightforward and, if clean, would support the claim. I also weighed the lack of normalization of C by peak density and the n=1-per-length device count; these weaken the quantitative factor but not the qualitative protocol, and the crosstalk check is more decisive. Since the reader's verdict is already CONDITIONAL and this concern is exactly the condition that should be verified, I leave the verdict unchanged.","tokens_in":11085,"tokens_out":7539,"duration_ms":78845,"concrete_test":"On both the 300 nm and 900 nm devices, at the same plunger/bias points used for Figs. 2 and 3, measure the off-diagonal lock-in conductances dIL/dVR (right bias, left current) and dIR/dVL (left bias, right current) with VAl held at 0 V. If these crosstalk terms are below, say, 10% of the diagonal subgap conductances dIL/dVL and dIR/dVR, a finite-Al-ground common-mode path cannot account for C=0.97; if they are comparable, or scale with Al length, the interpretation is confounded. A stronger control is to insert a known series resistor (around 10 kΩ) in the VAl line and recompute C: a non-invasive ground should leave C unchanged, whereas a crosstalk-limited measurement should show C rising as the ground impedance increases.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central inference—that coincident subgap peaks at both ends arise from a shared bound state—requires the etched-Al third terminal to be a virtual ground at the Al-InAs interface. The paper states this terminal is fabricated from a subtractive process after growth precisely in order not to disrupt the interface, but no electrical test of the ground quality is reported. If the Al terminal has finite series resistance or interface impedance, current injected from one normal lead develops a common-mode voltage on the wire bulk, which biases the opposite junction; left and right conductances then share fluctuations even for purely local states. Crucially, the Al segment length is itself the independent variable (300 nm vs 900 nm), so ground quality and wire length are not independently varied: a shorter Al contact with higher effective resistance would inflate the correlator C in Eq. (1) in exactly the short device where C=0.97 is claimed, and a longer contact with lower resistance would deflate C in the long device. The supplement's comparison of bias configurations (Fig. S1) was performed only on the short device and does not quantify the off-diagonal conductances dIL/dVR and dIR/dVL at subgap biases. Without that crosstalk bound, the factor-3.7 drop in C could be a ground-impedance artifact rather than evidence for the spatial extent of subgap states.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports zero-field tunneling spectroscopy of both ends of three-terminal selective-area-grown Al-InAs hybrid nanowires, with an etched Al third terminal serving as the voltage reference. Subgap conductance peaks are identified independently on the left and right sides, and a cross-correlator C of binary peak masks (Eq. 1) is computed as a function of bias offset. For a 300-nm device the correlator peaks at C = 0.97 at zero offset, whereas for a 900-nm device it peaks at C = 0.27, a factor of 3.7 lower. The paper also computes normalized mutual information between the left and right subgap conductance distributions, finding a sharp peak at zero shift for the short device and a relatively flat profile for the long device. The authors interpret the strong short-device correlation as evidence that subgap bound states extend across the entire 300-nm hybrid segment, and the length dependence as evidence for a characteristic length scale of subgap states.","tokens_in":11314,"tokens_out":7171,"duration_ms":73578,"significance":"If the interpretation is correct, the work offers a reusable experimental protocol for statistically quantifying end-to-end correlations in Majorana candidate devices, using parameter-free statistical measures (a correlator and mutual information) rather than fits. The use of selective-area growth to create a non-invasively formed Al ground terminal is a promising platform advance, and the paper is careful in its error-band estimates from plunger-shifted data and in its explicit acknowledgment that the measurements are at zero field where topological effects are not expected. However, the central claim rests on a single short/long device pair and on the assumption that the Al third terminal is an ideal ground; the absence of a direct crosstalk check leaves the interpretation open to a common-mode artifact.","major_comments":[{"comment":"","section":"Device description (three-terminal setup) and Eq. (1)"},{"comment":"","section":"Results (Fig. 3) and Supplement Fig. S2"}],"minor_comments":[{"comment":"The normalized mutual information maps in Fig. 4(c,d) and the pointwise maps in Fig. 4(e,f) are shown without uncertainty estimates; because the adaptive binning minimum-samples cutoff (80 points) is a free parameter, a sensitivity analysis or error bars would strengthen the claimed distinction between the short and long devices.","section":"Fig. 4 and Supplement 'Quantifying conductance correlations'"},{"comment":"The caption of Fig. 2(c) refers to 'horizontal lines in Fig. 1(a,b)', which appears to be a cross-referencing error; the lines are shown in Fig. 2(a,b) of the same figure.","section":"Fig. 2 caption"},{"comment":"The sentence 'In the short device, C is peaked around δV = 0. Including only the subset of data from Fig. 3(a) results in a correlator that is significantly less than unity' would be easier to interpret with the numerical peak values for the dashed traces in both panels.","section":"Main text, Fig. 3 discussion"},{"comment":"The comparison between the adaptive-binning and non-parametric mutual-information estimates is reassuring, but the red non-parametric value is shown as a single horizontal line without an uncertainty band; reporting a spread over bootstrap resamples would better quantify the binning dependence.","section":"Supplement Fig. S4"}],"recommendation":"major_revision","confidential_remarks":"The paper is likely to be a strong contribution if the grounding/crosstalk premise can be verified. The most important missing element is a direct electrical test of the Al third terminal or a quantitative bound on the off-diagonal conductances. Without such a control, the central length-dependence claim rests on an untested assumption. A second concern is the weak statistical significance of the long-device peak; a permutation or bootstrap analysis would help. These are fixable within the manuscript's scope, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Clear take: this is a useful experimental paper, worth refereeing, and it mostly delivers what it promises. What is actually new is the protocol itself: independently measuring both ends of a SAG Al-InAs nanowire through a non-invasively formed third terminal, then quantifying end-to-end correlations with a peak-mask correlator over thousands of peaks, plus mutual information on the conductance distributions. That is a genuinely reusable tool for a field that has been arguing about local versus nonlocal subgap states on single-end data. The short-versus-long device comparison, C = 0.97 versus C = 0.27, is an honest attempt to extract a length scale for trivial subgap states, and the error bands derived from plunger-shifted data are a reasonable way to estimate statistical uncertainty. The supplement is candid about the two different biasing configurations and shows a direct comparison on the short device. No fitted parameters go into the main claim, so circularity is not a concern.\n\nSoft spots, in proportion. The biggest one is exactly what the stress-test flags: the central inference assumes the etched-Al terminal is a clean virtual ground at the Al-InAs interface, so that left and right conductances are independent probes of each wire end. The paper does not report any electrical check of that ground quality, no measured off-diagonal conductance dIL/dVR or dIR/dVL at subgap biases, and no estimate of the Al contact resistance. Since wire length is the independent variable, a length-dependent ground impedance cannot be fully separated from length-dependent bound-state extent. That does not kill the paper, but it deserves a direct crosstalk bound or a control measurement.\n\nSmaller issues: the NMI maps carry no error bars, the long-device correlated region is identified post hoc, and no code or raw data are provided, which limits reproducibility. The long-device correlator peak being 3-sigma is statistically real but modest, so the interpretation of a factor-of-3.7 reduction should be stated with appropriate weight, which the paper more or less does.\n\nCitation pattern looks fine; the prior Majorana and trivial-state literature is well covered, and the self-citations are to directly relevant companion work. Overall this is a serious piece of experimental work, and the authors seem aware of its limits. I would put it in front of a good referee, asking specifically for the ground-impedance/crosstalk check, error bars on NMI, and a commitment to release data and code. I would not demand the crosstalk test be performed in exactly the form I suggested; any direct bound on common-mode coupling would substantially strengthen the central inference.","headline":"Solid experimental protocol paper; central correlation claim is plausible but the missing crosstalk test against the etched-Al ground is a real soft spot that should be addressed before publication.","tokens_in":11904,"tokens_out":1267,"would_cite":true,"duration_ms":11284,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Subgap bound states seen from both ends of a 300-nm hybrid nanowire coincide in nearly every trace (C=0.97), whereas in a 900-nm wire the coincidence drops to C=0.27, indicating that zero-field subgap states can span the short device and…","keywords":["Majorana bound states","hybrid nanowires","superconductor-semiconductor","subgap states","end-to-end correlations","tunneling spectroscopy","mutual information","selective area growth"],"falsifier":"Build a control device with the same geometry but no superconducting segment (a normal metal middle lead) and compute C between left and right traces; if C remains near unity at zero bias shift, the coincident peaks reflect common-mode coupling through the middle terminal rather than a shared subgap state, and a complementary 600-nm hybrid device would test the predicted monotonic decay of C with length.","tokens_in":10901,"feed_emoji":"🔬","tokens_out":7094,"duration_ms":63311,"temperature":0.7,"pith_summary":"This paper establishes a statistical protocol for asking whether the same subgap bound state is visible from both ends of a superconductor-semiconductor nanowire. Using a selective-area-grown aluminum terminal to ground the wire bulk without disturbing the fragile Al-InAs interface, the authors independently measure left and right tunneling conductances at zero magnetic field and count coincidences between thousands of identified conductance peaks. In a 300-nm device the end-to-end peak correlator reaches C=0.97, while in a 900-nm device it drops to C=0.27. The authors interpret this length dependence as evidence that zero-field subgap states can extend several hundred nanometers, essentially spanning the short device, and that conductance fluctuations on the two ends carry extra mutual information. If correct, this turns the question 'is this state shared by both ends?' into a quantifiable statistical test that can be rerun in the topological regime.","feed_headline":"End-to-end subgap correlations fall from 0.97 to 0.27 with wire length","feed_subtitle":"A statistical peak-matching protocol shows short hybrid nanowires share subgap states end to end, while long wires do not.","key_machinery":"The central object is the binary peak-mask correlator, C(δV) = <B_L(V,V_P) B_R(V+δV,V_P)> − <B_L(V,V_P)><B_R(V,V_P)>, which counts, for each plunger-gate setting, whether a conductance peak appears at the same bias voltage on the left and right when one trace is shifted by a bias offset δV. Averaging over thousands of subgap peaks, C at δV=0 measures the fraction of end-to-end coincidences beyond chance. A second instrument is normalized mutual information between the left and right conductance distributions, computed with adaptive binning, and its pointwise version mapped back onto gate and bias voltage. Together these separate 'the same bound state seen at both ends' (peak coincidence) from 'conductance values correlated across the two ends' (mutual information).","core_discovery":"The paper's central claim is that zero-field subgap states in short hybrid nanowires are end-to-end correlated, meaning the same bound state is observed from both ends, and that this correlation is length dependent. The authors report that in a 300-nm Al-InAs device, 2353 identified conductance peaks yield a cross-correlator C=0.97 at zero bias offset, while in a 900-nm device 2058 peaks yield C=0.27, a factor of 3.7 reduction. Corroborating evidence comes from the joint distribution of left and right conductances: normalized mutual information is sharply peaked at zero bias and plunger shift for the short device and flat for the long device, and pointwise mutual information is elevated on a stable low-lying bound state. On the paper's interpretation, subgap states can extend several hundred nanometers, essentially spanning the short device, while in the long device most subgap features belong to a single end.","pith_inferences":["If the residual C=0.27 in the 900-nm device comes from a localized region of gate voltage, as the supplemental analysis suggests, then devices of intermediate length (say 450 and 600 nm) should show a monotonically decreasing C with that residual region moving in gate space; this is a direct length-scaling prediction one could test.","A sharper check of the non-invasive aluminum ground would be to drive the middle terminal with a small AC bias and watch for common-mode peaks in both end traces; if coincident peaks persist even under asymmetric modulations of the middle terminal relative to each end, the shared-state interpretation gains strength.","The same peak-mask correlator could be applied to time-resolved or RF measurements to ask whether the correlated bound state actually transports charge through both contacts, which would distinguish a genuinely shared state from two independent states that happen to sit at the same bias."],"forward_implications":["In these SAG hybrid nanowires, an end-to-end correlated zero-field subgap state can be identified only when the hybrid segment is short enough; the apparent correlation length is on the scale of several hundred nanometers.","The correlator C, applied after automated peak extraction, can be used as a background-removing statistical search for correlated Majorana pairs at nonzero magnetic field.","Mutual information between left and right subgap conductances provides a binning-based, analysis-light test of conductance correlations, and its pointwise version can locate rare correlated features in gate-bias maps.","The soft confinement of accidental zero-field states implied by a several-hundred-nanometer extent will influence their behavior at nonzero magnetic field, so length-dependent correlation measurements should help refine simulations of topologically trivial subgap states.","The two biasing configurations used for the short and long devices give equivalent conductance maps on the short device, validating the comparison between the two datasets."],"supporting_citations":[{"why":"Provides the theoretical suggestion that hybrid superconductor-semiconductor nanowires can possess a topological phase, setting the motivation for studying Majorana bound states.","marker":"[4, 5]"},{"why":"Establishes the experimental baseline of single-end tunneling spectroscopy results broadly consistent with Majorana modes, which the present two-ended protocol extends.","marker":"[6–10]"},{"why":"Shows that localized non-topological or quasi-Majorana states can mimic many Majorana signatures, motivating the need for end-to-end correlations as a distinguishing test.","marker":"[11, 12]"},{"why":"Proposes that probing both ends of a Majorana wire can reveal end-to-end correlations and bulk signatures of the topological transition, providing the conceptual premise for the experiment.","marker":"[19, 23–27]"},{"why":"Introduces selective-area growth as a platform that allows lithographic processing on epitaxial contacts without disrupting the fragile superconductor-semiconductor interface, enabling the non-invasive grounding used here.","marker":"[30, 31]"},{"why":"Supplies the growth details of the Al-InAs nanowire material platform used to fabricate the devices.","marker":"[42]"},{"why":"The partner paper that explores finite-field effects, defining the zero-field scope of the present study.","marker":"[43]"}],"fun_headline_variants":["Subgap correlation drops 4x from short to long nanowires","End-to-end subgap states: short wires lock, long wires don't","Short nanowires share subgap states from end to end","Length kills end-to-end subgap coupling in nanowires","Correlated subgap states only in short hybrid nanowires"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole analysis assumes that the aluminum terminal acts as a non-invasive, clean ground for the nanowire bulk, so that left and right conductances each independently probe one end of the wire; if that ground couples the two ends or injects common-mode bias, coincident peaks could appear without a shared bound state.","fun_headline_variants_meta":{"raw":{"variants":["Subgap correlation drops 4x from short to long nanowires","End-to-end subgap states: short wires lock, long wires don't","Short nanowires share subgap states from end to end","Length kills end-to-end subgap coupling in nanowires","Correlated subgap states only in short hybrid nanowires"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000954,"raw_usage":{"total_tokens":4014,"prompt_tokens":840,"completion_tokens":3174,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":456,"completion_tokens_details":{"reasoning_tokens":3087}},"tokens_in":456,"tokens_out":3174,"duration_ms":24105,"temperature":1.0,"reasoning_tokens":3087,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T13:09:39.126484+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Build a control device with the same geometry but no superconducting segment (a normal metal middle lead) and compute C between left and right traces; if C remains near unity at zero bias shift, the coincident peaks reflect common-mode coupling through the middle terminal rather than a shared subgap state, and a complementary 600-nm hybrid device would test the predicted monotonic decay of C with length.","supporting_citations":[],"review_version":1}