{"id":"5a938db7-ad6c-489d-b719-5edd4364f79c","arxiv_id":"2412.06612","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"In 2M-WS2, superconductivity crosses from conventional to unconventional behavior below about 20 nm thickness, evidenced by an in-plane upper critical field exceeding the Pauli limit and correlating with reduced carrier density.","lead":"Thin flakes of the superconductor 2M-WS2 can withstand in-plane magnetic fields far above the usual Pauli limit once they are thinner than about 20 nanometers, while thicker flakes behave like conventional superconductors. This thickness-dependent crossover is presented as transport evidence for spin-orbit-parity coupled, potentially topological, superconductivity in this material.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The apparent sub-20 nm crossover depends on extrapolating in-plane Bc2(T) with a linearized-GL form inconsistent with the 2D Tinkham angular dependence; the claimed Pauli-limit violation may be a fitting artifact.","rationale":"The reader's weakest assumption focuses on unmeasured band-structure/disorder changes with thickness. I agree that is a live issue, but the more immediate vulnerability is one step earlier: the quantitative evidence for Pauli-limit violation is produced by a functional fit that conflicts with the 2D Tinkham analysis in the same paper. If the extrapolated Bc2^||(0) is inflated by the linear fit, there is no unconventional state to explain, so the carrier-density correlation no longer discriminates SOPC. The paper's explicit concession about the orbital effect reinforces this. Thus I partially agree with the reader: same region of fragility, but I would locate the primary load-bearing concern in the Bc2^||(0) extraction rather than the band-structure premise. The proposed refit is a concrete, data-only check; it does not require new measurements and would settle whether the crossover survives. Since the issue is addressable and the paper has substantial supporting transport data, the correct action is to keep the conditional verdict and add this refit as a required condition. In the allowed terms, the verdict is unchanged.","tokens_in":10301,"tokens_out":9121,"duration_ms":99753,"concrete_test":"Refit the raw Bc2^||(T) data for every sample in Fig. 4b with (i) the standard 2D GL expression Bc2^||(T)=Bc2^||(0)(1 - T/Tc)^α with α=1/2 and with α free, and (ii) a WHH model including orbital and Pauli pair breaking. Report extrapolated Bc2^||(0), confidence intervals, and fit residuals for each model. If the sub-20 nm samples no longer show Bc2^||(0)/B_P > 1 under the sqrt-law or WHH fits, or if α=1/2 fits the data as well as the linear form, the crossover claim is an artifact of linear extrapolation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Most load-bearing is the extraction of Bc2^||(0) in Fig. 4b. Seeing linear Bc2^||/B_P vs T, the authors reject the standard 2D GL IP form Bc2^|| = sqrt(12) Φ0/(2π ξ(0)d) (1 - T/Tc)^(1/2) and fit the IP data instead with the perpendicular linearized-GL form Bc2^⊥ = Φ0/(2π ξ(0)^2)(1 - T/Tc). This substitution is also in tension with the 2D Tinkham angular dependence used earlier for the same samples. The extrapolation is not harmless: for a thin-film superconductor the parallel critical field grows as (1 - T/Tc)^(1/2) near Tc, and a straight-line fit over a finite interval below Tc overestimates the zero-temperature intercept (for a pure sqrt law the intercept is H0( sqrt(1-t0) + 1/sqrt(1-t0) ) > H0). Because the 'unconventional crossover' is defined by Bc2^||(0)/B_P exceeding 1, the central claim hinges on this extrapolation. The paper itself states that 'determining whether the orbital effect plays a role requires further experimental studies,' yet orbital pair breaking is the conventional source of large parallel critical fields in thin films. No error bars are provided for the slopes or extrapolated values, so the sub-20 nm enhancement cannot currently be distinguished from an extrapolation artifact.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports a systematic transport study of exfoliated 2M-WS2 flakes with thicknesses from 3 to 50 nm. The authors observe thickness-dependent superconducting properties, including Tc decreasing from 8.76 K to 6.98 K, a reduction in 2D carrier density by over an order of magnitude, BKT behavior, and a strongly anisotropic upper critical field that follows the 2D Tinkham angular dependence. The central claim is a crossover from conventional s-wave superconductivity in thick samples to unconventional, spin-orbit-parity-coupled superconductivity in samples thinner than 20 nm, based on an extrapolated in-plane upper critical field Bc2^||(0) that exceeds the Pauli paramagnetic limit and whose slope correlates with reduced carrier density.","tokens_in":10648,"tokens_out":4538,"duration_ms":45432,"significance":"If the central claim is correct, the paper provides a tunable platform for studying bulk-surface interplay in a topological superconductor candidate and establishes thickness as a control parameter for accessing unconventional superconducting states. The strengths of the paper include clean-limit transport (mean free path 300–2000 times the coherence length), a systematic thickness series, high sample quality (RRR up to 103), and a careful BKT analysis. However, the primary conclusion rests on the extrapolation of Bc2^||(0) using a perpendicular linearized GL formula rather than the expected 2D parallel-field form, and the exclusion of alternative mechanisms is asserted rather than demonstrated. These issues make the headline claim currently unsupported despite the interesting data.","major_comments":[{"comment":"The in-plane upper critical field is fitted with the linearized GL formula Bc2 = Φ0/(2πξ^2(0))(1 - T/Tc), which is the standard perpendicular-field expression, rather than the 2D parallel-field form Bc2^|| = (√12 Φ0)/(2πξ(0)d)(1 - T/Tc)^{1/2} that follows from the Tinkham angular dependence used in Fig. 4a. A linear fit over a finite temperature interval to a sqrt temperature dependence overestimates the zero-temperature intercept, and since the crossover claim is defined by Bc2^||(0)/BP exceeding 1, the reported effect may be an extrapolation artifact. Please provide fits with the correct 2D form, include error bars on the extrapolated values, and justify any genuinely linear regime with a specific microscopic model.","section":"Fig. 4b and the paragraph beginning 'Given the linearity of the BC2/BP versus TC curves...'"},{"comment":"The exclusion of multiband superconductivity, disorder-induced quantum fluctuations, and finite-momentum Cooper pairs relies on the assertion that no obvious changes in band structure or sample quality occur when the sample is thinner than 20 nm. However, the paper itself reports that Tc, carrier density, mobility, and RRR all vary with thickness over this same range, so this premise is not established. Direct evidence—such as thickness-dependent ARPES, quantum oscillations, or a disorder characterization—is needed before attributing the enhanced Bc2^|| uniquely to spin-orbit-parity coupling.","section":"Paragraph beginning 'We also rule out multi-band superconductivity...'"},{"comment":"This caveat is load-bearing because in thin films the orbital pair-breaking limit for parallel fields, B_orb^|| ≈ Φ0/(2πξ(0)d), increases as thickness decreases, providing a conventional route to Bc2^||(0) values above the Pauli limit. The manuscript should estimate B_orb^|| for the measured thicknesses and show that it exceeds the observed Bc2^||(0) before drawing the unconventionality conclusion. Without such an estimate, the data are also consistent with a conventional orbital mechanism enhanced by reduced dimensionality.","section":"Same paragraph, sentence 'We note that determining whether the orbital effect plays a role requires further…"}],"minor_comments":[{"comment":"The dotted curves for the 43 nm and 6 nm samples are not labeled with their thicknesses; please add labels and specify the temperature range used for each fit.","section":"Fig. 4b"},{"comment":"The text contains the typo 'upper crucial field'; it should read 'upper critical field'.","section":"Summary paragraph"},{"comment":"The same 'linearized GL formula' is used for OOP and IP fields without explicitly noting that the functional form is the perpendicular-field expression; given the different expected temperature dependences for the two geometries, this should be stated and discussed.","section":"Section on Fig. 4b fitting"},{"comment":"The mean free path formula l = h k_F/(2ρ0 N e^2) is presented without derivation; please provide a reference or clarify the definitions of N and ρ0.","section":"Methods/Figure S3b"},{"comment":"The comparison with the prior report on atomically thin 2M-WS2 (ref. 26) is brief; a direct comparison of Bc2^||(0) values, thickness ranges, and fitting procedures would clarify what is genuinely new beyond that work.","section":"Discussion of ref. 26"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within the scope of the journal, but the novelty relative to ref. 26 should be sharpened: ref. 26 already reported spin-orbit-parity coupled superconductivity in atomically thin 2M-WS2, so the present contribution is the systematic thickness series and the crossover claim. The extrapolation issue is the main technical risk; if the authors can demonstrate the enhanced Bc2^|| with the correct 2D GL form and error bars, the paper would be much stronger. The exclusion of orbital effects also needs quantitative treatment."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a careful transport study with a useful thickness series, but the central claim—a crossover to SOPC-based unconventional superconductivity—rests on a fitting move that is not defensible as presented. It deserves a serious referee but needs major revision before I would trust the unconventional part.\n\nWhat is actually new and done well: the authors prepared 2M-WS2 flakes from 3 to 50 nm, avoided lithography-induced phase change by transferring onto pre-made electrodes, and measured Tc, critical current, Hall carrier density, and upper critical fields in both field directions. The BKT analysis, the 2D Tinkham angular fit, and the clean-limit estimate with mean free path much longer than coherence length are handled carefully. The observation that sub-20 nm flakes survive 12 T in-plane is striking, and the correlation between the in-plane Bc2 slope and the thickness-dependent 2D carrier density is a plausible lead. For people working on 2M-WS2 or other topological superconductor candidates, this is a useful dataset.\n\nThe soft spot is load-bearing. In Fig. 4b, the authors extract Bc2^||(0) by fitting in-plane data with the linearized GL perpendicular formula, after noting that the standard 2D GL in-plane form, which goes as sqrt(1 - T/Tc), does not fit. That is not a harmless substitution; for the parallel critical field of a thin film, the expected form near Tc is the sqrt law, and a linear fit over a finite temperature interval systematically overestimates the zero-temperature intercept. Since the crossover from conventional to unconventional is defined by Bc2^||(0)/B_P exceeding 1, the headline result could be an artifact of that extrapolation. The paper gives no error bars on the slopes or the zero-temperature values, so the sub-20 nm enhancement cannot be distinguished from systematic bias.\n\nThe authors also dismiss multiband, disorder, and finite-momentum Cooper-pair mechanisms with the assertion that band structure and sample quality do not change below 20 nm, but they do not measure either directly. They concede that orbital pair-breaking, the conventional source of large parallel critical fields in thin films, remains untested. That concession, together with the fit issue, makes the SOPC attribution premature.\n\nThe carrier-density correlation is suggestive but not diagnostic; thinning the flake moves the Fermi level, which changes both the orbital and paramagnetic limits. Prior work (Zhang et al., Nat. Phys. 2023) already reported SOPC behavior in atomically thin 2M-WS2, so the new contribution here is the systematic crossover threshold around 20 nm and the density correlation, not the SOPC concept itself.\n\nWho this is for: experimentalists in 2D superconductivity and proximity-induced topology. If the authors replace the in-plane Bc2 extraction with a defensible form, add proper uncertainty propagation, and address the orbital channel, the paper could become solid. As it stands, I would not cite it for the SOPC claim, though I would consider citing the thickness series data. My recommendation: send to peer review, with the extrapolation and missing uncertainty analysis flagged as the primary issues.","headline":"A worthwhile thickness series whose headline SOPC crossover is likely propped up by a wrong in-plane Bc2 extrapolation.","tokens_in":11192,"tokens_out":5035,"would_cite":false,"duration_ms":52933,"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":"In 2M-WS2, dropping below 20 nm switches superconductivity from conventional bulk s-wave to an unconventional surface-dominated state, with an in-plane upper critical field far above the Pauli limit that tracks the 2D carrier density.","keywords":["2M-WS2","topological superconductor","unconventional superconductivity","spin-orbit-parity coupling","upper critical field","Pauli limit","2D superconductivity","topological surface states"],"falsifier":"Electrostatically gate a single sub-20 nm flake at fixed thickness and measure $B_{C2}^{\\parallel}$ as a function of carrier density: the SOPC picture predicts the enhancement to track the Fermi level toward the band crossing, whereas a thickness-dependent disorder or band-structure explanation predicts little or no gate response. Alternatively, surface-sensitive probes such as tunneling spectroscopy or angle-resolved photoemission of flakes above and below 20 nm would directly show whether the topological surface band and its crossing move as thickness decreases.","tokens_in":10085,"feed_emoji":"🧲","tokens_out":7009,"duration_ms":67903,"temperature":0.7,"pith_summary":"The paper reports transport evidence that sample thickness controls which kind of superconductivity 2M-WS2 displays. Thick flakes above 20 nm behave as conventional s-wave superconductors whose in-plane upper critical field is capped by the Pauli paramagnetic limit. Flakes below 20 nm show an in-plane critical field well above that limit, surviving magnetic fields up to 12 T, and the enhancement grows as the 2D carrier density falls. The authors attribute this crossover to spin-orbit-parity coupling near the topological band crossing, where the bulk superconducting state and topological surface states meet. If correct, thickness becomes a practical dial for accessing topological superconductivity in a simple layered material.","feed_headline":"Under 20 nm, 2M-WS2 breaks the Pauli limit","feed_subtitle":"Thin flakes show an in-plane critical field far above the Pauli limit, tied to carrier density and spin-orbit-parity coupling.","key_machinery":"The load-bearing object is spin-orbit-parity coupling (SOPC), the coupling of electron spin, momentum, and band parity near a topological band crossing that can protect Cooper pairs against in-plane magnetic fields even in a centrosymmetric superconductor. The diagnostic that carries the argument is the comparison of the in-plane upper critical field normalized to the Pauli limit, $B_{C2}^{\\parallel}/B_P$, plotted against $T_C$: in thick flakes these curves collapse onto the Pauli-limited band, while in sub-20 nm flakes their slopes grow monotonically with decreasing thickness. The second diagnostic is the inverse correlation between $dB_{C2}^{\\parallel}/dT_C$ and the 2D carrier density, which the paper reads as the Fermi level moving closer to the band crossing where SOPC is strongest. The 2D nature of the superconductivity is established by fits to Tinkham's angular formula and by Berezinskii-Kosterlitz-Thouless power-law I-V characteristics.","core_discovery":"The central discovery is a thickness-induced crossover from conventional to unconventional superconductivity in 2M-phase WS2. In samples thicker than 20 nm, the normalized in-plane upper critical field $B_{C2}^{\\parallel}/B_P$ versus $T_C$ curves fall into a narrow band and superconductivity is suppressed at the Pauli limit $B_P = 1.84\\,T_C$, the signature of conventional s-wave pairing. Below 20 nm, the same curves steepen and extrapolate to $B_{C2}^{\\parallel}(0)$ substantially above $B_P$, and the slope $dB_{C2}^{\\parallel}/dT_C$ rises roughly threefold as the 2D carrier density falls roughly fivefold. Because 2M-WS2 preserves inversion symmetry, ordinary Ising-type spin-orbit coupling cannot explain the protection; the paper argues the enhancement is a hallmark of spin-orbit-parity coupling, which becomes effective only near the band crossing where topological surface states dominate transport in thin flakes.","pith_inferences":["A natural next probe is electrostatic gating of a single sub-20 nm flake: if the inverse carrier-density correlation is causal, moving the Fermi level through the band crossing should tune $B_{C2}^{\\parallel}$ continuously, a test the paper does not run.","The same thickness logic should apply to other centrosymmetric topological superconductors with bulk-surface proximity, suggesting a general criterion: thin enough that surface states carry a measurable fraction of the supercurrent.","The clean-limit mean free paths (300-2000 times the coherence length) imply that impurity scattering is not what sets the critical field; a thickness-disorder explanation would need to show disorder changing faster than carrier density below 20 nm."],"forward_implications":["Sub-20 nm 2M-WS2 flakes are 2D superconductors whose in-plane upper critical field can exceed the Pauli limit by a large margin, surviving magnetic fields up to at least 12 T.","Sample thickness is a control parameter for the relative weight of bulk and topological surface states, because the 2D carrier density falls by more than an order of magnitude as thickness drops from 40 nm to 3 nm.","The inverse correlation between critical-field enhancement and carrier density implies that positioning the Fermi level near the band crossing boosts the unconventional superconducting contribution.","If the crossover is real, ultra-thin 2M-WS2 is a platform for studying proximity-induced topological superconductivity, including Majorana zero modes in vortex cores and their thickness-driven hybridization."],"supporting_citations":[{"why":"Establishes 2M-WS2 as a superconductor with possible topological surface states via the reciprocal-space proximity effect, the material platform of the paper.","marker":"[17]"},{"why":"Provides the theoretical prediction of spin-orbit-parity-coupled superconductivity in an inversion-symmetric topological monolayer, the mechanism invoked for the enhanced in-plane critical field.","marker":"[6]"},{"why":"Earlier observation of spin-orbit-parity-coupled superconductivity in atomically thin 2M-WS2, whose upper-critical-field behavior the present work extends and contrasts with its linear $B_{C2}$ versus $T_C$ analysis.","marker":"[26]"},{"why":"Evidence of anisotropic Majorana bound states in 2M-WS2, linking the thin-flake superconducting state to topological superconductivity.","marker":"[20]"},{"why":"Direct observation of the topological surface state in 2M-WS2, the surface ingredient that the proximity picture requires.","marker":"[25]"},{"why":"Observation of topological superconductivity in stoichiometric 2M-WS2, supporting the coexistence of bulk s-wave pairing and surface topological superconductivity.","marker":"[23]"},{"why":"Shows nodeless s-wave superconductivity in bulk 2M-WS2, the conventional pairing from which the thin flakes depart.","marker":"[19]"},{"why":"Reports the scotch-tape preparation of 2D 2M-WS2 nanolayers used as the sample platform in this study.","marker":"[28]"}],"fun_headline_variants":["Thin 2M-WS2 superconducts beyond Pauli limit","Crossover to unconventional superconductivity at 20 nm","2M-WS2 flakes under 20 nm break Pauli limit","Thickness unlocks unconventional superconductivity in 2M-WS2"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise, asserted in the paragraph ruling out multiband superconductivity, is that band structure and sample quality do not change below 20 nm; if they do, the enhanced in-plane critical field could have a more conventional explanation.","fun_headline_variants_meta":{"raw":{"variants":["Thin 2M-WS2 superconducts beyond Pauli limit","Crossover to unconventional superconductivity at 20 nm","2M-WS2 flakes under 20 nm break Pauli limit","Thickness unlocks unconventional superconductivity in 2M-WS2"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000198,"raw_usage":{"total_tokens":1369,"prompt_tokens":946,"completion_tokens":423,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":562,"completion_tokens_details":{"reasoning_tokens":349}},"tokens_in":562,"tokens_out":423,"duration_ms":4152,"temperature":1.0,"reasoning_tokens":349,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T19:28:14.261074+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Electrostatically gate a single sub-20 nm flake at fixed thickness and measure $B_{C2}^{\\parallel}$ as a function of carrier density: the SOPC picture predicts the enhancement to track the Fermi level toward the band crossing, whereas a thickness-dependent disorder or band-structure explanation predicts little or no gate response. Alternatively, surface-sensitive probes such as tunneling spectroscopy or angle-resolved photoemission of flakes above and below 20 nm would directly show whether the topological surface band and its crossing move as thickness decreases.","supporting_citations":[],"review_version":1}