Crossover from Conventional to Unconventional Superconductivity in 2M-WS2

Brian M. Leonard; Jifa Tian; Jinke Tang; John Ackerman; Joseph McBride; Kenji Watanabe; Piumi Samarawickrama; Sabin Gautam; Takashi Taniguchi; Wenyong Wang

REVIEW 3 major objections 5 minor 5 references

Crossover from Conventional to Unconventional Superconductivity in 2M-WS2

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict A worthwhile thickness series whose headline SOPC crossover is likely propped up by a wrong in-plane Bc2 extrapolation. read the letter →

arxiv 2412.06612 v1 pith:Y2NL6ECN submitted 2024-12-09 cond-mat.mes-hall cond-mat.supr-con

Piumi Samarawickrama , Joseph McBride , Sabin Gautam , ZhuangEn Fu , Kenji Watanabe , Takashi Taniguchi , Wenyong Wang , Jinke Tang

show 3 more authors

John Ackerman Brian M. Leonard Jifa Tian

This is my paper · ORCID

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

keywords 2M-WS2topologicalsuperconductorunconventionalsuperconductivityspin-orbit-paritycouplinguppercriticalfieldPaulilimit2Dsurfacestates

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

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

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.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

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.

What 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.

The 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.

The 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.

The 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.

Who 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.

Referee Report

3 major / 5 minor

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.

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 (3)

[Fig. 4b and the paragraph beginning 'Given the linearity of the BC2/BP versus TC curves...'] 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.
[Paragraph beginning 'We also rule out multi-band superconductivity...'] 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.
[Same paragraph, sentence 'We note that determining whether the orbital effect plays a role requires further…] 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.

minor comments (5)

[Fig. 4b] 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.
[Summary paragraph] The text contains the typo 'upper crucial field'; it should read 'upper critical field'.
[Section on Fig. 4b fitting] 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.
[Methods/Figure S3b] 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.
[Discussion of ref. 26] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the crossover claim rests on measured transport data and externally published GL/Pauli-limit/SOPC theory; self-citations concern only sample preparation.

full rationale

The paper's derivation chain is empirical and self-contained. The central observation—sub-20 nm samples show Bc2^||/B_P > 1 with a thickness- and carrier-density-dependent slope—comes from magnetotransport data and from extrapolating Bc2^||(T) to zero temperature using a linearized GL form. That extrapolation choice could be questioned, especially because the same samples are fitted with the 2D Tinkham angular form, but it is not circular: the extrapolated values are not used as inputs to define the fit. The SOPC interpretation is imported from external theory (refs. 6 and 26) and independent 2M-WS2 experiments (refs. 17–25), not from the authors' own prior results. The only self-citations (refs. 27, 28) concern sample preparation and phase metastability and do not carry the crossover claim. The paper's own concession that 'determining whether the orbital effect plays a role requires further experimental studies' is a limitation, not circular reasoning. No load-bearing step reduces, by construction, to its own inputs.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new entities. Its central claim rests on several fitted or borrowed items: Hall carrier densities from a single-band fit, upper critical field slopes and zero-temperature extrapolations from a chosen GL fit, the standard Pauli limit benchmark, and the assumption that band structure and sample quality are thickness-independent below 20 nm. These are the main costs the central claim carries.

free parameters (3)

Hall carrier density = 2D n from about 4.2e14 cm^-2 (3 nm) to 4.8e15 cm^-2 (40 nm) at 10 K
Extracted from a single-band linear fit to Hall resistance (Fig. S2) and used as the central variable for the SOPC correlation.
Slope dBC2/dTC from linearized GL fit = Increases about 3x from 50 nm to 6 nm; exact values not listed
Used to quantify the in-plane upper critical field enhancement and to correlate it with carrier density in Fig. 4c.
Zero-temperature in-plane upper critical field BC2(0) = Reported to exceed the Pauli limit for samples below 20 nm; values not tabulated
Extrapolated using the linearized GL formula after rejecting the 2D GL form; the claim of exceeding the Pauli limit depends on this fit.

assumptions (5)

domain assumption Single-band Hall model accurately describes the transport.
Used to convert Hall slopes to carrier density and to infer the Fermi-level dependence of SOPC (Figs. 2a and S2).
domain assumption Pauli paramagnetic limit BP = 1.84 TC is the correct conventional benchmark.
Central benchmark for classifying conventional vs unconventional superconductivity; standard but model-dependent.
ad hoc to paper Linearized GL formula, not the conventional 2D GL sqrt formula, is the correct form for the in-plane upper critical field in these thin samples.
Chosen because the standard 2D GL form does not fit the data; the extrapolated BC2(0) depends on this choice.
ad hoc to paper Band structure and sample quality do not change significantly below 20 nm.
Stated without direct measurement in the paragraph where multiband, disorder, and finite-momentum pairing are dismissed; load-bearing for the SOPC attribution.
domain assumption The SOPC theory for 2M-WS2 from refs 6 and 26 applies to the measured samples.
The paper borrows the SOPC mechanism from prior theoretical and experimental work rather than deriving it from the present data.

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Cite this review

Pith. "Pith review of Crossover from Conventional to Unconventional Superconductivity in 2M-WS2." pith.science (2026). https://pith.science/paper/Y2NL6ECN

@misc{pith2026241206612,
  author       = {Pith},
  title        = {Pith review of: Crossover from Conventional to Unconventional Superconductivity in 2M-WS2},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Y2NL6ECN}},
  note         = {Machine review of arXiv:2412.06612}
}

read the original abstract

Leveraging reciprocal-space proximity effect between superconducting bulk and topological surface states (TSSs) offers a promising way to topological superconductivity. However, elucidating the mutual influence of bulk and TSSs on topological superconductivity remains a challenge. Here, we report pioneering transport evidence of a thickness-dependent transition from conventional to unconventional superconductivity in 2M-phase WS2 (2M-WS2). As the sample thickness reduces, we see clear changes in key superconducting metrics, including critical temperature, critical current, and carrier density. Notably, while thick 2M-WS2 samples show conventional superconductivity, with an in-plane (IP) upper critical field constrained by the Pauli limit, samples under 20 nm exhibit a pronounced IP critical field enhancement, inversely correlated with 2D carrier density. This marks a distinct crossover to unconventional superconductivity with strong spin-orbit-parity coupling. Our findings underscore the crucial role of sample thickness in accessing topological states in 2D topological superconductors, offering pivotal insights into future studies of topological superconductivity.

Figures

Figures reproduced from arXiv: 2412.06612 by the authors.

**Figure 1.** Raman spectroscopy and superconductivity of 2M-WS2 thin layers. (a) Top and side view of the lattice structure of 2M-WS2. (b) AFM image of a 3 nm-thick 2M-WS2 flake. Inset: the thickness profile of the flake along the white dotted line. (c) Optical image (left) of a 2M-WS2 flake with different thicknesses and Raman spectra (right) taken at different locations labeled with numbers “1” to “5” on the flake. (d) Longitu… view at source ↗

**Figure 2.** Thickness dependent superconductivity of 2M-WS2. (a) Temperature dependence of the 2D carrier density of 2M-WS2 flakes with various thicknesses. (b) The normalized sheet resistance as a function of temperature for 2M-WS2 flakes. (c) Transition temperature (TC) as a function of sample thickness. Inset: The corresponding thickness-dependent residual resistivity ratio (RRR) is calculated by dividing the sheet resistanc… view at source ↗

**Figure 3.** Berezinskii-Kosterlitz-Thouless transition and strong anisotropy in 2M-WS2. (a) I-V relationship of a 9 nm-thick 2M-WS2 device at various temperatures plotted in a log-log scale. The black dotted line represents the power law dependence V I with = 3. (b) The extracted values as a function of temperature for different samples. Dotted line represents = 3. The inset shows the extracted TBKT values for the corresponding… view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Thickness-dependent transition from conventional to SOPC superconductivity in 2M-WS2. (a) Angular dependence of the upper critical field for a 6 nm flake measured at 7 K. The results are fitted by both 2D Tinkham model (black curve) and 3D anisotropic GL model (green c…

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Reference graph

Works this paper leans on

5 extracted references · 5 canonical work pages

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Anisotropic Full-Gap Superconductivity in 2M-WS2 Topological Metal with Intrinsic Proximity Effect

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work page 2021

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

(1) Clarke, J.; Wilhelm, F. K. Superconducting Quantum Bits. Nature 2008, 453 (7198), 1031-1042. (2) Li, Y.; Xu, Z. -A. Exploring Topological Superconductivity in Topological Materials. Adv. Quantum Technol. 2019, 2 (9), 1800112. (3) Qiu, D.; Gong, C.; Wang, S.; Zhang, M.; Yang, C.; Wang, X.; Xiong, J. Recent Advances in 2D Superconductors. Adv. Mater. 20...

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[2] [50]

(20) Yuan, Y.; Pan, J.; Wang, X.; Fang, Y.; Song, C.; Wang, L.; He, K.; Ma, X.; Zhang, H.; Huang, F.; Li, W.; Xue, Q. -K. Evidence of Anisotropic Majorana Bound States in 2M -WS2. Nat. Phys. 2019, 15 (10), 1046-1051. (21) Wang, L. S.; Fang, Y. Q.; Huang, Y. Y.; Cheng, E. J.; Ni, J. M.; Pan, B. L.; Xu, Y.; Huang, F. Q.; Li, S. Y. Nodeless Superconducting G...

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M.; Saito, Y.; Ideue, T.; Nojima, T.; Iwasa, Y

(30) Itahashi, Y. M.; Saito, Y.; Ideue, T.; Nojima, T.; Iwasa, Y. Quantum and Classical Ratchet Motions of Vortices in a Two-dimensional Trigonal Superconductor. Phys. Rev. Res. 2020, 2 (2), 023127. (31) Yazdani, A.; Kapitulnik, A. Superconducting-Insulating Transition in Two-Dimensional a-MoGe Thin Films. Phys. Rev. Lett. 1995, 74 (15), 3037-3040. (32) T...

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C.; Lee, H

(34) Chiang, C. C.; Lee, H. C.; Lin, S. C.; Qu, D.; Chu, M. W.; Chen, C. D.; Chien, C. L.; Huang, S. Y. Unequivocal Identification of Spin-Triplet and Spin-Singlet Superconductors with Upper Critical Field and Flux Quantization. Phys. Rev. Lett. 2023, 131 (23), 236003. (35) Llovo, I. F.; Carballeira, C.; Só ñ ora, D.; Pereiro, A.; Ponte, J. J.; Salem -Sug...

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Anisotropic Full-Gap Superconductivity in 2M-WS2 Topological Metal with Intrinsic Proximity Effect

(24) Lian, C.-S.; Si, C.; Duan, W. Anisotropic Full-Gap Superconductivity in 2M-WS2 Topological Metal with Intrinsic Proximity Effect. Nano Lett. 2021, 21 (1), 709-715. (25) Cho, S.; Huh, S.; Fang, Y.; Hua, C.; Bai, H.; Jiang, Z.; Liu, Z.; Liu, J.; Chen, Z.; Fukushima, Y.; Harasawa, A.; Kawaguchi, K.; Shin, S.; Kondo, T.; Lu, Y.; Mu, G.; Huang, F.; Shen, ...

work page 2021