pith. machine review for the scientific record. sign in

arxiv: 2604.11738 · v1 · submitted 2026-04-13 · ❄️ cond-mat.supr-con

Recognition: unknown

Reduced pair breaking from extended disorder in unconventional superconductors: implications to 4Hb-TaS₂

Yuval Tsur , Mark H. Fischer , Jonathan Ruhman
Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:03 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords unconventional superconductivitydisorderpair breakingtransition metal dichalcogenides4Hb-TaS2extended impuritiesspin-orbit couplingmultiband model
0
0 comments X

The pith

Extended impurity potentials reduce pair-breaking rates in unconventional superconductors by matching the gap's momentum structure.

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

The paper examines how common defects in materials like 4Hb-TaS2 affect unconventional superconductivity. It shows that extended impurity potentials from chalcogen vacancies or ad-atoms lead to a pair-breaking rate that is only about one-third of the transport scattering rate. This happens because the potential's momentum dependence overlaps with the superconducting gap, suppressing the scattering processes that destroy Cooper pairs. As a result, unconventional pairing can survive in samples with high resistivity, contrary to standard Abrikosov-Gor'kov expectations. The finding provides a direct explanation for the observed robustness of superconductivity in disordered transition metal dichalcogenides.

Core claim

Using a multiband model with spin-orbit coupling for H-phase TMDs and an impurity potential that mimics extended defects such as chalcogen vacancies, the authors compute the disorder-dressed pairing susceptibility and find that the pair-breaking rate Γ satisfies Γ τ_D ∼ 1/3 over a wide parameter range. This reduction arises because the momentum structure of the extended disorder potential partially matches the internal structure of the superconducting gap, thereby suppressing pair-breaking processes relative to the momentum-relaxation rate.

What carries the argument

The momentum-dependent form factor of the extended impurity potential, which partially overlaps with the superconducting gap's variation to suppress pair-breaking scattering channels.

If this is right

  • Unconventional superconducting states become significantly more stable against disorder from extended defects than predicted by standard theory.
  • High-resistivity samples of 4Hb-TaS2 and similar TMDs can still host unconventional pairing without contradiction.
  • The conventional link between momentum relaxation and pair breaking breaks down when the impurity potential has extended spatial structure.
  • Similar reductions in pair breaking should appear in other H-phase TMD superconductors that share the same class of lattice defects.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Varying the spatial extent of introduced defects in TMD samples could tune the stability of unconventional superconductivity in a controlled way.
  • The same momentum-matching mechanism may help explain resilient unconventional pairing in other disordered materials beyond TMDs.
  • Device designs that deliberately use extended defects could protect desired pairing symmetries from scattering.

Load-bearing premise

That chalcogen vacancies or ad-atoms produce an extended potential whose momentum dependence accurately represents real defects and that the multiband model with spin-orbit coupling captures the essential physics of the material.

What would settle it

Direct measurement of the ratio between the pair-breaking rate extracted from the suppression of the superconducting transition temperature and the transport scattering rate from resistivity, yielding a value near one-third rather than order one in controlled samples of 4Hb-TaS2.

Figures

Figures reproduced from arXiv: 2604.11738 by Jonathan Ruhman, Mark H. Fischer, Yuval Tsur.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematic of the 1H-TaS [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) The sum of Feynman diagrams leading to [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Two of the eigenvalues of the susceptibility ma [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) The product [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The weights of the channel [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
read the original abstract

Unconventional superconductivity is generally expected to be strongly suppressed by nonmagnetic disorder, as captured by Abrikosov--Gor'kov (AG) theory. However, several materials, including transition metal dichalcogenides, exhibit signatures of unconventional pairing despite relatively high resistivities, suggesting a breakdown of the conventional relation between momentum relaxation and pair breaking. Here, we study this problem in H-phase transition metal dichalcogenides by computing the disorder-dressed pairing susceptibility. We employ a multiband model with spin-orbit coupling and include an impurity potential that mimics a common lattice defect, namely a chalcogen vacancy or site ad-atom. This yields to an extended impurity potential, which we compare with the commonly considered on-site (point defect) potential. We evaluate the momentum-relaxation rate and the pair-breaking rate on equal footing. We find that extended impurity potentials lead to a parametrically reduced pair-breaking rate compared to the transport scattering rate, with $\Gamma \tau_D \sim 1/3$ over a wide parameter range. This reduction originates from the momentum structure of the disorder potential, which partially matches the internal structure of the superconducting gap and suppresses pair-breaking processes. As a result, unconventional pairing states are significantly more robust than predicted by standard AG theory. Our results provide a natural explanation for the persistence of unconventional superconductivity in systems with strong disorder and substantially alleviate the apparent conflict between high resistivity and unconventional pairing in materials such as 4Hb-TaS$_2$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that in H-phase TMDs, an extended impurity potential (mimicking chalcogen vacancies or ad-atoms) yields a parametrically reduced pair-breaking rate relative to the transport scattering rate, with Γτ_D ∼ 1/3 over a wide parameter range. This is obtained by computing the disorder-dressed pairing susceptibility in a multiband model with SOC, comparing extended vs. on-site potentials; the reduction arises because the momentum structure of the extended potential partially overlaps the internal structure of the superconducting gap, suppressing pair-breaking processes. The result implies unconventional superconductivity is more robust to disorder than AG theory predicts, offering an explanation for its persistence in high-resistivity materials such as 4Hb-TaS₂.

Significance. If the central numerical result is robust, the work supplies a concrete mechanism—momentum-space filtering by extended defects—to reconcile high resistivities with unconventional pairing in TMDs. The equal-footing extraction of 1/τ_D and Γ from the same disorder-dressed susceptibility is a methodological strength, as is the explicit contrast between point-like and extended potentials.

major comments (2)
  1. [Impurity potential modeling] The reported ratio Γτ_D ∼ 1/3 is load-bearing for the central claim yet depends on the precise spatial form chosen for the extended impurity potential. The manuscript must demonstrate that this form reproduces the momentum dependence of realistic chalcogen vacancies or site ad-atoms in 4Hb-TaS₂ (e.g., via comparison to ab initio defect potentials), because the suppression of pair-breaking originates from the Fourier components of the potential overlapping the gap structure.
  2. [Methods / Numerical implementation] The abstract states the method and the numerical result but supplies no equations, numerical procedures, convergence checks, or error estimates for the pairing-susceptibility calculation. Without these details the support for the specific factor of ∼1/3 cannot be assessed, even though the claim is presented as the direct output of the computation.
minor comments (1)
  1. The sentence 'This yields to an extended impurity potential' contains a grammatical error and should read 'This yields an extended impurity potential'.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Impurity potential modeling] The reported ratio Γτ_D ∼ 1/3 is load-bearing for the central claim yet depends on the precise spatial form chosen for the extended impurity potential. The manuscript must demonstrate that this form reproduces the momentum dependence of realistic chalcogen vacancies or site ad-atoms in 4Hb-TaS₂ (e.g., via comparison to ab initio defect potentials), because the suppression of pair-breaking originates from the Fourier components of the potential overlapping the gap structure.

    Authors: We agree that the momentum-space structure of the impurity potential is central to the reported suppression. In the manuscript we model the extended potential as a spatially broadened defect (chosen to represent the typical range of chalcogen vacancies or ad-atoms in H-phase TMDs) and show that the resulting Fourier components produce a partial overlap with the gap structure, yielding Γτ_D ≈ 1/3. While a direct ab-initio extraction of the defect potential for 4Hb-TaS₂ is not performed here, the reduction is a generic consequence of any extended potential whose Fourier transform is narrower than the Brillouin zone. In the revised manuscript we will add an explicit discussion of the chosen functional form, demonstrate the robustness of the ratio under reasonable variations of the potential range and shape, and note that the same qualitative filtering effect is expected for any realistic extended defect. A full ab-initio defect calculation lies outside the present scope but would be a natural extension. revision: partial

  2. Referee: [Methods / Numerical implementation] The abstract states the method and the numerical result but supplies no equations, numerical procedures, convergence checks, or error estimates for the pairing-susceptibility calculation. Without these details the support for the specific factor of ∼1/3 cannot be assessed, even though the claim is presented as the direct output of the computation.

    Authors: We acknowledge that the abstract is necessarily concise. The full text already contains the multiband Hamiltonian, the expression for the disorder-dressed pairing susceptibility, and the numerical evaluation procedure. To make the technical support fully transparent we will expand the Methods section with the explicit integral expressions for the susceptibility, the momentum-space discretization and cutoff scheme, the convergence tests performed with respect to grid density and energy cutoff, and quantitative estimates of the numerical uncertainty in the extracted Γτ_D ratio. These additions will allow readers to reproduce and assess the factor of ∼1/3. revision: yes

Circularity Check

0 steps flagged

No significant circularity: direct computation of rates from model inputs

full rationale

The derivation computes the disorder-dressed pairing susceptibility in a multiband model with SOC, using an explicit extended impurity potential as input to obtain both the transport scattering rate 1/τ_D and pair-breaking rate Γ on equal footing. The reported ratio Γτ_D ∼ 1/3 is an output of the momentum-space overlap between the chosen potential and the gap, not a fitted parameter renamed as prediction nor a self-referential definition. No load-bearing self-citation, uniqueness theorem, or ansatz smuggling is indicated; the result follows from the stated model assumptions without reducing to its own inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of a multiband Hamiltonian with spin-orbit coupling for H-phase TMDs and on the specific momentum dependence chosen for the extended impurity potential that represents lattice defects.

free parameters (1)
  • impurity potential spatial range
    The extension length or functional form of the potential is selected to mimic vacancies or ad-atoms but is not numerically specified in the abstract.
axioms (1)
  • domain assumption The multiband model with spin-orbit coupling captures the essential low-energy physics of H-phase transition metal dichalcogenides.
    Invoked to justify studying disorder effects on pairing susceptibility in these materials.

pith-pipeline@v0.9.0 · 5577 in / 1468 out tokens · 70656 ms · 2026-05-10T16:03:23.135837+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

37 extracted references · 4 canonical work pages

  1. [1]

    M. R. Norman, The challenge of unconventional su- perconductivity, Science332, 196 (2011)

    2011

  2. [2]

    A.A.Abrikosov and L.P.Gork’ov, On the theory of su- perconducting alloys, Soviet Physics JETP35(1959)

    1959

  3. [3]

    Juskus, J

    D. Juskus, J. Ayres, R. Nicholls, and N. Hussey, In- sensitivity of t c to the residual resistivity in high-t c cuprates and the tale of two domes, Frontiers in Physics12, 1396463 (2024)

    2024

  4. [4]

    Y. S. Hor, A. J. Williams, J. G. Checkelsky, P. Roushan, J. Seo, Q. Xu, H. W. Zandbergen, A. Yazdani, N. P. Ong, and R. J. Cava, Supercon- ductivity in cuxbi2se3 and its implications for pairing in the undoped topological insulator, Phys. Rev. Lett. 104, 057001 (2010)

    2010

  5. [5]

    Novak, S

    M. Novak, S. Sasaki, M. Kriener, K. Segawa, and Y. Ando, Unusual nature of fully gapped supercon- ductivity in in-doped snte, Phys. Rev. B88, 140502 (2013)

    2013

  6. [6]

    Prozorov, M

    R. Prozorov, M. Ko´ nczykowski, M. A. Tanatar, A. Thaler, S. L. Bud’ko, P. C. Canfield, V. Mishra, and P. J. Hirschfeld, Effect of electron irradi- ation on superconductivity in single crystals of Ba(fe1−xrux)2as2 (x= 0.24), Phys. Rev. X4, 041032 (2014)

    2014

  7. [7]

    Teknowijoyo, K

    S. Teknowijoyo, K. Cho, M. A. Tanatar, J. Gonzales, A. E. B¨ ohmer, O. Cavani, V. Mishra, P. J. Hirschfeld, S. L. Bud’ko, P. C. Canfield, and R. Prozorov, En- hancement of superconducting transition temperature by pointlike disorder and anisotropic energy gap in fese single crystals, Phys. Rev. B94, 064521 (2016)

    2016

  8. [8]

    M. H. Fischer, P. A. Lee, and J. Ruhman, Mecha- nism forπphase shifts in little-parks experiments: Application to 4 hb-tas 2 and to 2 h-tas 2 interca- lated with chiral molecules, Physical Review B108, L180505 (2023)

    2023

  9. [9]

    Simon, H

    S. Simon, H. Yerzhakov, S. KP, A. Vakahi, S. Remen- nik, J. Ruhman, M. Khodas, O. Millo, and H. Stein- berg, The transition-metal-dichalcogenide family as a superconductor tuned by charge density wave strength, Nature Communications15, 10439 (2024)

    2024

  10. [10]

    S. C. Holbæk, M. H. Christensen, A. Kreisel, and B. M. Andersen, Unconventional superconductivity protected from disorder on the kagome lattice, Phys- ical Review B108, 144508 (2023)

    2023

  11. [11]

    Hirschfeld, M

    P. Hirschfeld, M. Korshunov, and I. Mazin, Gap sym- metry and structure of fe-based superconductors, Re- ports on Progress in Physics74, 124508 (2011)

    2011

  12. [12]

    Ribak, R

    A. Ribak, R. M. Skiff, M. Mograbi, P. K. Rout, M. H. Fischer, J. Ruhman, K. Chashka, Y. Dagan, and A. Kanigel, Chiral superconductivity in the alter- nate stacking compound 4Hb-TaS2, Science Advances 6, 10.1126/sciadv.aax9480 (2020)

    work page doi:10.1126/sciadv.aax9480 2020

  13. [13]

    P. L. K.T. Law, 1T-TaS 2 as a quantum spin liquid, Proceedings of the National Academy of Sciences114, https://doi.org/10.1073/pnas.1706769114 (2017)

    work page doi:10.1073/pnas.1706769114 2017

  14. [14]

    Ribak, I

    A. Ribak, I. Silber, C. Baines, K. Chashka, Z. Salman, Y. Dagan, and A. Kanigel, Gapless excitations in the ground state of 1T-TaS 2, Phys. Rev. B96, 195131 (2017)

    2017

  15. [15]

    Almoalem, I

    A. Almoalem, I. Feldman, I. Mangel, M. Shlafman, Y. E. Yaish, M. H. Fischer, M. Moshe, J. Ruhman, and A. Kanigel, The observation ofπ-shifts in the little-parks effect in 4Hb-TaS 2, Nature Communica- tions15, 4623 (2024)

    2024

  16. [16]

    Persky, A

    E. Persky, A. V. Bjørlig, I. Feldman, A. Al- moalem, E. Altman, E. Berg, I. Kimchi, J. Ruhman, A. Kanigel, and B. Kalisky, Magnetic memory and spontaneous vortices in a van der waals superconduc- tor, Nature607, 692 (2022)

    2022

  17. [17]

    H. Wang, Y. Jiao, F. Meng, X. Zhang, D. Dai, C. Tu, C. Zhao, L. Xin, S. Huang, H. Lei, and S. Li, Evidence for multiband gapless superconductivity in the topological superconductor candidate 4Hb−tas 2, Phys. Rev. Lett.135, 126002 (2025)

    2025

  18. [18]

    A. K. Nayak, A. Steinbok, Y. Roet, J. Koo, G. Mar- galit, I. Feldman, A. Almoalem, A. Kanigel, G. A. Fi- ete, B. Yan, Y. Oreg, N. Avraham, and H. Beidenkopf, Evidence of topological boundary modes with topo- logical nodal-point superconductivity, Nature Physics 17, 1413 (2021). 9

    2021

  19. [19]

    Michaeli and L

    K. Michaeli and L. Fu, Spin-orbit locking as a pro- tection mechanism of the odd-parity¡? format?¿ su- perconducting state against disorder, Physical review letters109, 187003 (2012)

    2012

  20. [20]

    E. I. Timmons, S. Teknowijoyo, M. Ko´ nczykowski, O. Cavani, M. A. Tanatar, S. Ghimire, K. Cho, Y. Lee, L. Ke, N. H. Jo,et al., Electron irradiation ef- fects on superconductivity in pdte 2: An application of a generalized anderson theorem, Physical Review Research2, 023140 (2020)

    2020

  21. [21]

    Dentelski, V

    D. Dentelski, V. Kozii, and J. Ruhman, Effect of in- terorbital scattering on superconductivity in doped dirac semimetals, Physical Review Research2, 33302 (2020)

    2020

  22. [22]

    S. C. Holbæk, M. H. Christensen, A. Kreisel, and B. M. Andersen, Protection of unconventional super- conductivity from disorder (2026), arXiv:2601.20937 [cond-mat.supr-con]

    work page arXiv 2026

  23. [23]

    Ramires, D

    A. Ramires, D. F. Agterberg, and M. Sigrist, Tailor- ing t c by symmetry principles: The concept of su- perconducting fitness, Physical Review B98, 024501 (2018)

    2018

  24. [24]

    Andersen, A

    L. Andersen, A. Ramires, Z. Wang, T. Lorenz, and Y. Ando, Generalized anderson’s theorem for super- conductors derived from topological insulators, Sci- ence advances6, eaay6502 (2020)

    2020

  25. [25]

    M¨ ockli and M

    D. M¨ ockli and M. Khodas, Robust parity-mixed su- perconductivity in disordered monolayer transition metal dichalcogenides, Physical Review B98, 144518 (2018)

    2018

  26. [26]

    M¨ ockli and M

    D. M¨ ockli and M. Khodas, Magnetic-field induced s+ if pairing in ising superconductors, Physical Review B99, 180505 (2019)

    2019

  27. [27]

    M¨ ockli and M

    D. M¨ ockli and M. Khodas, Ising superconductors: In- terplay of magnetic field, triplet channels, and disor- der, Physical Review B101, 014510 (2020)

    2020

  28. [28]

    In systems with strongly momentum-dependent or ex- tended impurity potentials, such corrections may fur- ther renormalize the effective pair-breaking rate

    The AG framework typically neglects vertex correc- tions in the impurity-averaged pairing interaction. In systems with strongly momentum-dependent or ex- tended impurity potentials, such corrections may fur- ther renormalize the effective pair-breaking rate

  29. [29]

    Almoalem, R

    A. Almoalem, R. Gofman, Y. Nitzav, I. Mangel, I. Feldman, J. Koo, F. Mazzola, J. Fujii, I. Vobornik, J. S´ anchez-Barriga,et al., Charge transfer and spin- valley locking in 4hb-tas2, npj Quantum Materials9, 36 (2024)

    2024

  30. [30]

    Di Salvo, B

    F. Di Salvo, B. Bagley, J. Voorhoeve, and J. Waszczak, Preparation and properties of a new polytype of tantalum disulfide (4hb-tas2), Journal of Physics and Chemistry of Solids34, 1357 (1973)

    1973

  31. [31]

    L. F. Mattheiss, Band structures of transition-metal- dichalcogenide layer compounds, Physical Review B 8, 3719 (1973)

    1973

  32. [32]

    Ritschel, J

    T. Ritschel, J. Trinckauf, K. Koepernik, B. B¨ uchner, M. v. Zimmermann, H. Berger, Y. I. Joe, P. Abba- monte, and J. Geck, Orbital textures and charge den- sity waves in transition metal dichalcogenides, Nature Physics11, 328 (2015)

    2015

  33. [33]

    Liu, W.-Y

    G.-B. Liu, W.-Y. Shan, Y. Yao, W. Yao, and D. Xiao, Three-band tight-binding model for monolayers of group-vib transition metal dichalcogenides, Physical Review B—Condensed Matter and Materials Physics 88, 085433 (2013)

    2013

  34. [34]

    J. Yu, Y. Jiang, Y. Xu, D. C˘ alug˘ aru, H. Hu, H. Guo, S. Sajan, Y. Wang, M. M. Ugeda, F. De Juan,et al., Quantum geometry in the nbse 2 family i: Ob- structed compact wannier function and new perturba- tion theory, arXiv preprint arXiv:2507.02047 (2025)

    work page arXiv 2025

  35. [35]

    S. C. De la Barrera, M. R. Sinko, D. P. Gopalan, N. Sivadas, K. L. Seyler, K. Watanabe, T. Taniguchi, A. W. Tsen, X. Xu, D. Xiao,et al., Tuning ising superconductivity with layer and spin–orbit coupling in two-dimensional transition-metal dichalcogenides, Nature communications9, 1427 (2018)

    2018

  36. [36]

    W. Wang, Z. Jiang, X. Zhang, J. Zheng, H. Du, and Z. Zhang, A theoretical study of lifshitz transition for 2H-TaS2, Phys. Chem. Chem. Phys.26, 15868 (2024)

    2024

  37. [37]

    H. J. Monkhorst and J. D. Pack, Special points for brillouin-zone integrations, Physical Review B13, 5188 (1976)

    1976