{"id":"d49f326f-c30c-4be4-9619-0b820babe440","arxiv_id":"1909.02433","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"In thin multilayer WTe2 Josephson junctions, supercurrent concentrates at the edges over about 1.3 to 1.4 microns, while in 60 nm thick flakes it flows uniformly through the bulk.","lead":"This paper reports measurements of electric current flow in superconducting junctions made from thin flakes of the material WTe2. In thin samples, current concentrates at the edges over micron-wide channels, while thick samples carry current uniformly through the bulk.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The SQI inversion cannot distinguish edge-localized supercurrent from an inhomogeneous interface or trivial edge states—an ambiguity the authors explicitly concede—so the reported edge width and edge/bulk ratio rest on the assumed edge-step model rather than on the data alone.","rationale":"The paper makes a deliberately narrow claim, and that framing should be credited: the Discussion says the observed edge superconductivity is not equivalent to superconductivity in edge modes and is not evidence of a topological superconducting phase. There is also real independent support for a thickness-driven crossover—Fraunhofer behavior in 40/60 nm devices, mixed Fraunhofer/SQUID patterns in thin devices, a bulk-only short junction (#9) that stays uniform, and the R1/R2 contrast. Those pieces make the qualitative claim plausible and keep the verdict from being REJECT or UNVERDICTED.\n\nHowever, all quantitative edge statements and, to a significant extent, the identification of 'edge' current flow are derived from fitting one assumed model to a Fourier-magnitude signal. The governing equation destroys phase information, and the paper's own Discussion concedes that trivial edge states and inhomogeneous interfaces can produce the same kind of nonuniform supercurrent; ref 26 is a concrete published example. This is not an external disagreement but an admitted gap inside the manuscript, so it must be counted. The R1/R2 geometry helps but is partly confounded by different junction lengths. The absence of raw data and of model-comparison/uncertainty analysis prevents the reader from distinguishing edge-step localization from equally plausible non-edge profiles.\n\nThe central claim is therefore conditionally supported, and the condition is exactly the one the authors state: exclude trivial/interface mechanisms. Since the reader's CONDITIONAL verdict already captures that, I leave the verdict unchanged. I agree with the reader that the Fourier-extraction/model assumption is the weakest point, but I would phrase it more as non-uniqueness of the inversion than as an error in L_eff, hence 'partial' agreement.","tokens_in":10181,"tokens_out":8372,"duration_ms":99383,"concrete_test":"Reanalyze the raw I_c(B) envelopes for devices #1, #2, #3-R1, and #8 with a non-parametric inversion that retrieves a nonnegative J_c(x) from the measured |FT| without imposing edge localization, and compare, with identical L_eff and flux-focusing corrections, the published edge-step model against (i) a uniform bulk with a Gaussian bump at arbitrary position, width, and amplitude, (ii) two arbitrary humps, and (iii) a smooth interface transmissivity modulation that is not edge-peaked. Use Monte Carlo noise resampling to report reduced chi-square and model-selection weights. If a non-edge model fits within the same noise band, the edge-localization claim and its quantitative widths are not established; if the edge-step model is statistically preferred and the recovered peaks sit at the physical mesa edges, the concern is settled.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that in ~10 nm WTe2 the supercurrent is confined to the edge—depends on the assumption that the measured SQI pattern uniquely identifies an edge-stepped current profile. The governing equation, I_c^max(B) = |∫ J_c(x) cos(2π L_eff B x/Φ0) dx|, records only the modulus of a Fourier transform, so many spatial profiles J_c(x) produce the same I_c(B) envelope. The paper's edge widths (1.3–1.4 μm) and edge/bulk ratio (2.76 in Fig. 4) are obtained by fitting a particular 'edge-stepped nonuniform supercurrent model' (SI Section VI) to device #2, and the fitted profile is then plotted in Fig. 2g as though it were the measured distribution. No error bars, raw data, or comparison with alternative J_c(x) profiles are given.\n\nThe Discussion explicitly concedes that trivial edge states and an inhomogeneous interface can also produce a similar non-uniform supercurrent, citing step-shaped current distributions in Nb-InGaAs/InP junctions (ref 26). Those alternatives would preserve the SQI lineshape while invalidating the inference that the current is intrinsic to the WTe2 edge. Since the central claim is precisely edge confinement, this admitted model non-uniqueness is the weakest point in the argument. The R1/R2 comparison (Fig. 3) is suggestive but not fully decisive, because the edge-crossing channel is also the shorter junction (L_b~0.4 μm vs L_s~4 μm), so its stronger coupling is expected even without edge-specific conduction.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports superconducting quantum interference (SQI) measurements on Nb/WTe2/Nb Josephson junctions made from multilayer WTe2 flakes of different thicknesses. In thick flakes (~60 nm), the critical-current modulation is a Fraunhofer-like pattern and the inferred supercurrent density is approximately uniform across the junction. In thin flakes (10–16 nm), the pattern becomes a mixture of Fraunhofer and SQUID-like oscillations with a narrower central lobe, which the authors interpret as supercurrent confined to edge channels of width 1.3–1.4 μm, with an edge/bulk supercurrent density ratio up to 2.76. The authors also report an asymmetry |Ic+(B)| ≠ |Ic−(B)| in thin devices, and an R1/R2 comparison where an edge-crossing junction is superconducting while an edge-untouched junction is not. The paper is careful to state that the observed edge superconductivity is not evidence of topological edge modes or a topological superconducting phase.","tokens_in":10515,"tokens_out":2485,"duration_ms":29363,"significance":"If the central claim holds, the paper provides a clear thickness-controlled crossover from bulk-dominated to edge-dominated supercurrent in a type-II Weyl semimetal, which is of genuine interest for proposals to realize topological superconductivity in WTe2. The study benefits from several strengths: SQI data are shown for multiple devices of different thicknesses; the Fraunhofer-to-SQUID-like crossover is read directly from the interference patterns and does not depend on the fitted model; devices #1, #2, and #3 reproduce the edge-dominated pattern; the R1/R2 control junction in Fig. 3 is a useful additional comparison; and the authors explicitly disclaim any inference about topological edge modes. The quantitative edge width and edge/bulk amplitude ratio, however, depend on an assumed current-density profile and are not supported by uncertainty estimates or model comparison, which limits the strength of the quantitative claims.","major_comments":[{"comment":"Equation (1) records only the modulus of a Fourier transform of J_c(x), so many different spatial profiles produce the same I_c(B) envelope. The extracted edge widths of 1.3–1.4 μm and the edge/bulk ratio of 2.76 in Fig. 4 are obtained by fitting the edge-stepped model of SI Section VI to device #2, and no error bars, raw data residuals, or comparison with alternative J_c(x) profiles are provided. The Discussion itself concedes that trivial edge states and inhomogeneous interfaces can also produce a similar non-uniform supercurrent. Since the quantitative edge-confinement claims rest on this model, the authors should either provide model comparison and uncertainties or explicitly relegate the quantitative widths and ratios to illustrative status.","section":"The superconducting quantum interference measurements; SI Section VI"},{"comment":"The R1/R2 comparison confounds edge-crossing geometry with junction length: the edge-crossing channel R1 has L_b~0.4 μm, while the edge-untouched channel R2 has L_s~4 μm on the edge side. The stronger coupling of R1 is therefore expected from its shorter electrode separation even without any edge-specific conduction. To support the edge-specific claim, the authors need a control with comparable junction lengths or quantitative modeling that accounts for the geometric difference.","section":"Figure 3 and accompanying text"},{"comment":"The claim that the non-symmetric critical current is an intrinsic property of inversion-symmetry-broken edges, expressed through Eq. (2) with I1 ≠ I2, is presented as the likely explanation, but the authors list vortex trapping and vortex motion as alternative possibilities. The observation of symmetric behavior in the thick sample reduces but does not eliminate these alternatives for the thin junctions, because flux trapping and vortex configurations depend on junction dimensions and edge properties. This point should be framed as a conjecture rather than a conclusion, or supported by additional measurements such as repeated field sweeps or a systematic comparison of symmetric and asymmetric devices.","section":"Discussion, paragraph on |Ic+(B)| ≠ |Ic−(B)|"}],"minor_comments":[{"comment":"The sentence 'we need to point out that the edge superconductivity we observed is not equivalent to the superconductivity in the edge modes nor any evidence of toplogical super conducting phase' contains a typo ('toplogical') and should be rephrased for clarity.","section":"Discussion"},{"comment":"The phrase 'the affection by the SiO2 substrate and the capping layer' should be changed to 'the effect of the SiO2 substrate and the capping layer'.","section":"Discussion, paragraph on trivial effects"},{"comment":"In subpanel (e), the text says the supercurrent is carried by the helical edge states, but the Discussion later states that the observed edge superconductivity is not evidence of topological edge modes. The caption should use language consistent with that caveat, e.g., 'putative edge states' or 'edge channels'.","section":"Figure 2 caption"},{"comment":"The phrase 'It is then necessary to make them distinct from the coexisting bulk ones' is awkward; consider 'It is therefore necessary to distinguish them from the coexisting bulk states'.","section":"Introduction, paragraph 2"}],"recommendation":"major_revision","confidential_remarks":"The qualitative finding is credible and well aligned with similar observations in the literature, but the quantitative claims need substantial reinforcement. The paper's own Discussion already concedes the model non-uniqueness, so the main issue is not a hidden flaw but an unsupported quantitative overreach. If the authors can present uncertainties, alternative-profile comparisons, or explicitly soften the quantitative claims, the paper would be suitable for publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know about arXiv:1909.02433. First, the central qualitative claim survives: across several devices, thin (~10 nm) multilayer WTe2 junctions show a Fraunhofer/SQUID mixture consistent with supercurrent concentrated near the edges, while thick (~60 nm) junctions show uniform Fraunhofer patterns. The authors are careful to say this is edge-region superconductivity, not evidence of topological modes. Second, the quantitative numbers—edge width 1.3–1.4 μm and edge/bulk ratio 2.76—come from fitting an assumed edge-step model to the same data that motivated the model, with no error bars and no raw data deposited. I would not build anything on those specific values.\n\nThe new element is the systematic thickness dependence from 16 to 60 nm, with the edge-to-bulk crossover around 16–20 nm, and the non-symmetric critical current in thin devices. The R1/R2 comparison on a 16 nm flake is a nice control: the edge-untouched channel stays resistive while the edge-crossing channel goes superconducting. It is suggestive rather than conclusive—the edge-crossing channel is also the shorter junction—but together with the bulk-only device #9 showing a plain Fraunhofer pattern, it supports the qualitative edge picture.\n\nThe biggest soft spot is the SQI inversion. The measured Ic(B) is only the magnitude of a Fourier transform of Jc(x), so many spatial profiles give the same envelope. The authors themselves concede in the Discussion that trivial edge states or an inhomogeneous interface could produce a similar step-shaped current distribution, citing ref 26. That admission is honest but it means the quantitative edge width is not uniquely determined by the data. The same issue applies to the edge/bulk ratio: it comes from fitting the same edge-step model to device #2, not from independent measurement. Notably, the introduction says SQI has not been applied to topological semimetals, which is wrong—ref 11 (Shvetsov et al.) did exactly that on WTe2. That's a minor but definite error in the literature framing. Data availability is also limited to 'upon reasonable request'; no raw SQI traces are deposited.\n\nWho is this for? Anyone working on proximity-induced superconductivity in topological semimetals, and to a lesser extent on distinguishing edge from bulk supercurrent by interference. The qualitative result is useful; the quantitative extraction needs to be treated with caution. I would send it to a serious referee, with the expectation that the referee asks for raw SQI data, error analysis, and fits to at least one alternative Jc(x) profile. I'd cite the qualitative result, not the numbers.","headline":"A believable qualitative edge-vs-bulk supercurrent result in multilayer WTe2, whose quantitative extraction is model-dependent and should be read with caution.","tokens_in":11082,"tokens_out":2974,"would_cite":true,"duration_ms":27945,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["74.50.+r","73.20.-r"],"model":"deepseek-v4-flash","headline":"This paper reports that in thin multilayer WTe2 Josephson junctions the supercurrent is confined to edge channels up to 1.4 μm wide, while thick flakes carry it uniformly through the bulk.","keywords":["WTe2","type-II Weyl semimetal","Josephson junction","edge superconductivity","superconducting quantum interference","Fraunhofer pattern","SQUID pattern","asymmetric Josephson effect"],"falsifier":"A scanning SQUID microscope image of the magnetic field above a thin (≈10 nm) device biased near its critical current would show two localized current filaments near the physical edges if edge superconductivity is real; a uniform or central distribution would falsify the claim. Alternatively, chemically etching away the mesa edges of a thin device should remove the SQUID-like side lobes from $I_c(B)$ if edge channels carry the supercurrent.","tokens_in":9957,"feed_emoji":"🧲","tokens_out":7478,"duration_ms":69913,"temperature":0.7,"pith_summary":"Using critical-current interference in Nb/WTe2/Nb Josephson junctions, the paper shows that the supercurrent distribution changes with WTe2 thickness. In thick flakes (~60 nm) the supercurrent is uniform across the junction and the interference pattern is a standard Fraunhofer single-slit pattern. In thin flakes (~10–13 nm) the supercurrent is localized near the sample edges, with edge channels about 1.3–1.4 μm wide and an edge/bulk supercurrent density ratio up to 2.76. The authors are careful to state that this edge superconductivity is not claimed to be carried by topological edge modes and does not by itself evidence a topological superconducting phase. The result offers a thickness-controlled way to separate edge from bulk supercurrent in a type-II Weyl semimetal candidate and to probe inversion-symmetry-breaking effects through the asymmetric critical current.","feed_headline":"Thin WTe2 sends supercurrent along its edges","feed_subtitle":"Magnetic interference maps show edge-confined supercurrent in 10-nm flakes; 60-nm flakes stay uniform through the bulk.","key_machinery":"The central object is the superconducting-quantum-interference relation $I_c^{\\max}(B) = \\left|\\int J_c(x) \\cos(2\\pi L_{\\mathrm{eff}} B x / \\Phi_0)\\, dx\\right|$, which converts the magnetic-field dependence of the critical current into a real-space map of supercurrent density, given an effective junction length $L_{\\mathrm{eff}}$ that accounts for flux focusing and London penetration. The paper uses the uniform-density limit (Fraunhofer formula) for thick flakes and an edge-stepped current-density model for thin flakes; this transform-type machinery is what lets a transport measurement claim spatial localization.","core_discovery":"On the paper's own terms, the central discovery is that a lateral Nb/WTe2/Nb Josephson junction made from a thin (about 10 nm) WTe2 flake carries its supercurrent predominantly through regions near the two mesa edges, not through the interior, and that this edge domination disappears when the flake is thick (about 60 nm). The evidence comes from the magnetic-field dependence of the critical current: thick flakes show symmetric Fraunhofer oscillations consistent with uniform $J_c$, while thin flakes show a mixture of Fraunhofer and SQUID-like lobes, which the authors fit with an edge-stepped supercurrent model to extract edge channels 1.3–1.4 μm wide. The paper further shows that a 16 nm junction with two electrode pairs conducts only when the electrodes cross the edge, and that the critical current in thin devices is asymmetric in the swept current direction ($|I_c^+(B)| \\neq |I_c^-(B)|$), which they attribute to the two edges having different Fermi velocities under inversion-symmetry breaking. Finally, they explicitly state that the edge superconductivity is not equivalent to topological edge-mode superconductivity and is not evidence of a topological superconducting phase.","pith_inferences":["A natural extension is to use Shapiro-step measurements on edge-dominated junctions: a topological edge supercurrent should produce a 4π-periodic a.c. Josephson response, whereas a trivial edge channel would not; the paper mentions this as a future direction, so the test is concrete.","The extracted edge width of 1.3–1.4 μm is much larger than an atomic one-dimensional channel, suggesting the 'edge' is a mesoscopic region—possibly Fermi-arc surface states, a finite proximity coherence length, or bulk states weakly coupled to the edge. Experiments on narrower junctions or with gate-defined edges could disentangle these.","The asymmetry in $I_c(B)$ could be made a quantitative probe of inversion breaking: reversing the crystal orientation or applying an in-plane magnetic field should swap or modify the $I_1$ vs $I_2$ imbalance in the two-edge Josephson formula.","One could test the crossover thickness prediction (16–20 nm) by fabricating a thickness-gradient device and mapping the supercurrent distribution continuously with SQI, avoiding sample-to-sample variation."],"forward_implications":["Thickness is a control knob: the edge/bulk supercurrent ratio rises as WTe2 is thinned, with the estimated crossover from bulk- to edge-dominated superconductivity at 16–20 nm.","Edge-crossing electrode pairs show Josephson coupling while edge-untouched pairs on the same flake do not, so junction geometry can be used to couple selectively to edge channels.","The asymmetric critical-current response $|I_c^+(B)| \\neq |I_c^-(B)|$ in thin samples is an observable signature of inversion-symmetry breaking at the edges, and the bulk contribution to this asymmetry is excluded by the symmetric response of thick flakes.","The same SQI mapping method can be applied to other layered semimetals with surface or edge states to search for analogous edge superconductivity.","If the edge channels are eventually tied to topological boundary states, Josephson junctions on thin WTe2 become a candidate platform for topological superconductivity and Majorana bound states; the present work does not itself establish that."],"supporting_citations":[{"why":"Supplies the cosine-integral relation between critical current and magnetic field that is the basis for extracting the supercurrent distribution.","marker":"[21]"},{"why":"Used to justify the effective junction length $L_{\\mathrm{eff}}$ that accounts for magnetic flux threading into the superconducting contacts.","marker":"[22]"},{"why":"Support the London-penetration and Meissner flux-focusing corrections that set $L_{\\mathrm{eff}}$ and the oscillation period.","marker":"[23, 24]"},{"why":"Provides the edge-stepped supercurrent model used to fit the mixed Fraunhofer/SQUID pattern in thin WTe2.","marker":"[16]"},{"why":"Comparison system where edge superconductivity was mapped by the same interference technique, giving a similar edge width scale.","marker":"[15]"},{"why":"Documents a step-shaped current density producing a similar mixed pattern, cited as a non-topological alternative explanation.","marker":"[26]"},{"why":"Theoretical basis for the asymmetric Josephson effect expected from inversion-symmetry breaking in topological materials.","marker":"[27]"},{"why":"Provides the two-edge Josephson current formula used to describe asymmetric critical current from edges with different Fermi velocities.","marker":"[28]"},{"why":"Establishes the long-junction limit that determines the $I_c R_N \\propto 1/L$ scaling used to characterize the junctions.","marker":"[18]"}],"fun_headline_variants":["Thin WTe2 funnels supercurrent to its edges","WTe2 thickness flips supercurrent from bulk to edges","Edge supercurrent seen in thin WTe2 Josephson junctions","Supercurrent hugs edges in thin WTe2, not thick"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The result rests on the assumption that the measured critical-current oscillations are accurately described by the cosine-transform integral with a reliably known effective junction length $L_{\\mathrm{eff}}$, so that the edge widths extracted from the fit reflect the true supercurrent distribution; incorrect $L_{\\mathrm{eff}}$, flux-focusing artifacts, or inhomogeneous interfaces would undermine the edge-localization conclusion.","fun_headline_variants_meta":{"raw":{"variants":["Thin WTe2 funnels supercurrent to its edges","WTe2 thickness flips supercurrent from bulk to edges","Edge supercurrent seen in thin WTe2 Josephson junctions","Supercurrent hugs edges in thin WTe2, not thick"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000257,"raw_usage":{"total_tokens":1618,"prompt_tokens":1023,"completion_tokens":595,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":639,"completion_tokens_details":{"reasoning_tokens":524}},"tokens_in":639,"tokens_out":595,"duration_ms":5866,"temperature":1.0,"reasoning_tokens":524,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T04:50:27.098684+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A scanning SQUID microscope image of the magnetic field above a thin (≈10 nm) device biased near its critical current would show two localized current filaments near the physical edges if edge superconductivity is real; a uniform or central distribution would falsify the claim. Alternatively, chemically etching away the mesa edges of a thin device should remove the SQUID-like side lobes from $I_c(B)$ if edge channels carry the supercurrent.","supporting_citations":[{"cited_title":"Introduction to superconductivity","cited_arxiv_id":null,"evidence_quote":"Supplies the cosine-integral relation between critical current and magnetic field that is the basis for extracting the supercurrent distribution."},{"cited_title":"Anomalous Fraunhofer interference in epitaxial superconductor-semiconductor Josephson junctions","cited_arxiv_id":null,"evidence_quote":"Used to justify the effective junction length $L_{\\mathrm{eff}}$ that accounts for magnetic flux threading into the superconducting contacts."},{"cited_title":"Local and Nonlocal Fraunhofer-like Pattern from an Edge-Stepped Topological Surface Josephson Current Distribution","cited_arxiv_id":null,"evidence_quote":"Provides the edge-stepped supercurrent model used to fit the mixed Fraunhofer/SQUID pattern in thin WTe2."},{"cited_title":"Induced superconductivity in the quantum spin Hall edge","cited_arxiv_id":null,"evidence_quote":"Comparison system where edge superconductivity was mapped by the same interference technique, giving a similar edge width scale."},{"cited_title":"Superconductor/Semiconductor Junctions","cited_arxiv_id":null,"evidence_quote":"Documents a step-shaped current density producing a similar mixed pattern, cited as a non-topological alternative explanation."},{"cited_title":"Asymmetric Josephson effect in inversion symmetry breaking topological materials","cited_arxiv_id":null,"evidence_quote":"Theoretical basis for the asymmetric Josephson effect expected from inversion-symmetry breaking in topological materials."},{"cited_title":"Josephson current in s -wave-superconductor Sr2RuO4 junctions","cited_arxiv_id":null,"evidence_quote":"Provides the two-edge Josephson current formula used to describe asymmetric critical current from edges with different Fermi velocities."},{"cited_title":"Josephson critical current in a long mesoscopic S -N-S junction","cited_arxiv_id":null,"evidence_quote":"Establishes the long-junction limit that determines the $I_c R_N \\propto 1/L$ scaling used to characterize the junctions."}],"review_version":1}