pith. sign in

arxiv: 2603.15915 · v2 · submitted 2026-03-16 · ❄️ cond-mat.str-el · cond-mat.mes-hall· cond-mat.mtrl-sci

Anomalous Thermal Transport Reveals Weak First-Order Melting of Charge Density Waves in 2H-TaSe2

Pith reviewed 2026-05-15 09:37 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.mes-hallcond-mat.mtrl-sci
keywords thermal conductivitycharge density waves2H-TaSe2weak first-order meltingCDW fluctuationsphonon scatteringthermal transporttransition metal dichalcogenides
0
0 comments X

The pith

V-shaped thermal conductivity in 2H-TaSe2 originates from scattering by local charge-density-wave correlations and signals weak first-order melting.

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

The paper establishes that thermal transport can serve as a sensitive probe for hidden, dynamic fluctuations in low-dimensional quantum materials. In 2H-TaSe2, the thermal conductivity exhibits a striking V-shaped temperature dependence that conventional phonon scattering cannot explain. This anomaly arises from scattering by persistent local charge-density-wave correlations, which the authors model phenomenologically by linking thermal transport to spatial CDW fluctuations. Electron and X-ray diffraction support the presence of short-range distortions and hysteresis, pointing to a dislocation- and fluctuation-driven weak first-order melting transition. This approach matters because it offers a way to resolve how ordered phases melt when fluctuations are charge-neutral and hard to detect directly.

Core claim

We show that the striking V-shaped temperature dependence of the thermal conductivity originates from scattering by persistent local charge-density-wave (CDW) correlations, consistent with our phenomenological model linking thermal transport to spatial CDW fluctuation. Electron diffraction reveals short-range periodic lattice distortions persisting to at least 300 K, while X-ray diffraction shows thermal hysteresis of the CDW wavevector. Together, these results reveal a dislocation- and fluctuation-driven weak first-order melting of the CDW state.

What carries the argument

phenomenological model linking thermal transport to spatial CDW fluctuation

Load-bearing premise

The observed V-shaped temperature dependence cannot be accounted for by conventional phonon-phonon scattering mechanisms.

What would settle it

A calculation or measurement showing that conventional phonon-phonon and electron-phonon scattering alone reproduces the V-shape without CDW fluctuations would falsify the claim.

read the original abstract

How ordered phases melt in low-dimensional quantum materials remain difficult to resolve because the relevant fluctuations are dynamic and charge neutral. In this work, we show that thermal transport provides a sensitive probe of these hidden fluctuations in the layered transition metal dichalcogenide 2H-TaSe2. We observe a striking V-shaped temperature dependence of the thermal conductivity that cannot be explained by conventional phonon-phonon scattering. Instead, it originates from scattering by persistent local charge-density-wave (CDW) correlations, consistent with our phenomenological model linking thermal transport to spatial CDW fluctuation. Electron diffraction reveals short-range periodic lattice distortions persisting to at least 300 K, while X-ray diffraction shows thermal hysteresis of the CDW wavevector. Together, these results reveal a dislocation- and fluctuation-driven weak first-order melting of the CDW state.

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 / 2 minor

Summary. The paper reports observation of a striking V-shaped temperature dependence in the thermal conductivity of 2H-TaSe2 that cannot be explained by conventional phonon-phonon scattering. Instead, it attributes this anomaly to scattering by persistent local charge-density-wave (CDW) correlations, supported by a phenomenological model linking transport to spatial CDW fluctuations. Electron diffraction shows short-range periodic lattice distortions up to at least 300 K, and X-ray diffraction reveals thermal hysteresis in the CDW wavevector, leading to the conclusion of a dislocation- and fluctuation-driven weak first-order melting of the CDW state.

Significance. If the central interpretation holds, the work establishes thermal transport as a sensitive probe of dynamic, charge-neutral fluctuations in low-dimensional quantum materials, offering new insight into the melting of CDW order in 2H-TaSe2. The combination of transport data with diffraction evidence for persistent short-range order and hysteresis provides a coherent picture of weak first-order character driven by dislocations and fluctuations.

major comments (2)
  1. [Abstract and Results] Abstract and Results: The claim that the V-shaped κ(T) 'cannot be explained by conventional phonon-phonon scattering' is load-bearing for the CDW-fluctuation interpretation, yet no full Boltzmann transport equation (BTE) calculation with realistic anisotropic phonon dispersions (including flexural modes, Umklapp, boundary, and impurity channels) is presented to demonstrate incompatibility. In layered TMDs such profiles can arise from standard mechanisms alone; without this explicit exclusion the attribution to local CDW correlations remains unverified.
  2. [Phenomenological model] Phenomenological model section: The model is stated to be 'consistent with the data' rather than independently predictive. Clarification is required on whether the V-shape is reproduced with zero free parameters or via fitting; if the latter, the risk of circularity noted in the review must be addressed by showing the functional form derives from CDW fluctuation physics without adjustable parameters tuned to the anomaly.
minor comments (2)
  1. [Figures] Figure captions and text: Ensure all symbols in thermal conductivity plots are defined consistently with the model equations; add error bars or uncertainty estimates to the V-shaped feature to allow quantitative assessment of its robustness.
  2. [References] References: Include recent works on phonon BTE in TMDs (e.g., studies of flexural phonon contributions in TaSe2 or similar) to contextualize the exclusion of conventional scattering.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and have revised the manuscript to improve clarity and strengthen the supporting arguments.

read point-by-point responses
  1. Referee: [Abstract and Results] The claim that the V-shaped κ(T) 'cannot be explained by conventional phonon-phonon scattering' is load-bearing for the CDW-fluctuation interpretation, yet no full Boltzmann transport equation (BTE) calculation with realistic anisotropic phonon dispersions (including flexural modes, Umklapp, boundary, and impurity channels) is presented to demonstrate incompatibility. In layered TMDs such profiles can arise from standard mechanisms alone; without this explicit exclusion the attribution to local CDW correlations remains unverified.

    Authors: We agree that a full anisotropic BTE calculation would provide the most rigorous exclusion of conventional mechanisms. Such a calculation is computationally demanding and requires phonon dispersions and matrix elements that are not currently available for 2H-TaSe2 at the required level of detail. In the revised manuscript we have added a dedicated paragraph comparing our data to thermal conductivity measurements on isostructural TMDs (2H-NbSe2, 2H-TaS2) that lack the V-shaped feature, and we include a simple Callaway-model estimate showing that standard Umklapp scattering produces a monotonic 1/T decline rather than the observed upturn below ~150 K. We have also changed the abstract and results wording from “cannot be explained by” to “is difficult to reconcile with standard phonon-phonon scattering models,” thereby softening the claim while retaining the central interpretation. We view this as a partial but substantive response. revision: partial

  2. Referee: [Phenomenological model] The model is stated to be 'consistent with the data' rather than independently predictive. Clarification is required on whether the V-shape is reproduced with zero free parameters or via fitting; if the latter, the risk of circularity noted in the review must be addressed by showing the functional form derives from CDW fluctuation physics without adjustable parameters tuned to the anomaly.

    Authors: The referee correctly identifies the need for clarification. The phenomenological model is derived from the additional phonon scattering rate due to CDW fluctuations, with the temperature dependence set by the correlation length ξ(T) measured independently by electron diffraction. The functional form follows directly from the fluctuation-dissipation relation applied to the CDW order-parameter fluctuations and contains no adjustable parameters fitted to the thermal-conductivity data. In the revised manuscript we now present the explicit derivation in the main text and add a supplementary note that reproduces the V-shape using only the diffraction-derived ξ(T) and the known transition temperature as inputs. This demonstrates that the model is predictive on the basis of the fluctuation physics alone. revision: yes

Circularity Check

0 steps flagged

No significant circularity: phenomenological consistency claim does not reduce to input by construction

full rationale

The paper asserts that the observed V-shaped thermal conductivity cannot be explained by conventional phonon-phonon scattering and instead originates from CDW correlations, described as consistent with a phenomenological model. No equations, parameter-fitting procedure, or self-citation chain is quoted that would make the model output equivalent to its inputs by definition. The exclusion of standard scattering is presented as an empirical observation rather than a derived result that loops back on fitted values. The derivation chain therefore remains self-contained against external benchmarks and does not trigger any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The claim depends on the assumption that phonon scattering alone produces monotonic behavior and that the phenomenological model isolates CDW fluctuation scattering; no new entities are introduced.

free parameters (1)
  • phenomenological model parameters
    The model linking thermal transport to spatial CDW fluctuation likely requires at least one fitted scale or coupling strength to reproduce the V-shape.
axioms (1)
  • domain assumption Conventional phonon-phonon scattering produces a monotonic temperature dependence of thermal conductivity in this temperature range
    Invoked to establish that the V-shape is anomalous and requires an additional scattering mechanism from CDW correlations.

pith-pipeline@v0.9.0 · 5513 in / 1312 out tokens · 42535 ms · 2026-05-15T09:37:16.103615+00:00 · methodology

discussion (0)

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

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Microscopic Theory of Acoustic Phonon Scattering by Charge-Density-Wave Fluctuations

    cond-mat.mes-hall 2026-04 unverdicted novelty 6.0

    A microscopic Green's function theory models acoustic phonon self-energy from CDW fluctuations via local-intensity and texture channels, linking to soft-mode spectroscopy and anomalous thermal transport.

Reference graph

Works this paper leans on

65 extracted references · 65 canonical work pages · cited by 1 Pith paper · 1 internal anchor

  1. [1]

    J. M. Kosterlitz, D. J. Thouless, Ordering, metastability and phase transitions in two- dimensional systems. Journal of Physics C: Solid State Physics 6, 1181–1203 (1973)

  2. [2]

    B. I. Halperin, D. R. Nelson, Theory of Two-Dimensional Melting. Physical Review Letters 41, 121–124 (1978)

  3. [3]

    Y. Kato, N. Nagaosa, Monte Carlo simulation of two-dimensional flux-line-lattice melting. Physical Review B 48, 7383–7391 (1993)

  4. [4]

    J. Hu, A. H. MacDonald, Two-dimensional vortex lattice melting. Physical Review Letters 71, 432–435 (1993)

  5. [5]

    J. A. Wilson, F. J. Di Salvo, S. Mahajan, Charge-density waves and superlattices in the metallic layered transition metal dichalcogenides. Advances in Physics 24, 117–201 (1975)

  6. [6]

    D. E. Moncton, J. D. Axe, F. J. DiSalvo, Neutron scattering study of the charge-density wave transitions in 2 H − Ta Se 2 and 2 H − Nb Se 2. Phys. Rev. B 16, 801–819 (1977)

  7. [7]

    Laverock, D

    J. Laverock, D. Newby, E. Abreu, R. Averitt, K. E. Smith, R. P. Singh, G. Balakrishnan, J. Adell, T. Balasubramanian, k -resolved susceptibility function of 2 H -TaSe 2 from angle- resolved photoemission. Phys. Rev. B 88, 035108 (2013)

  8. [8]

    D. S. Inosov, V. B. Zabolotnyy, D. V. Evtushinsky, A. A. Kordyuk, B. Büchner, R. Follath, H. Berger, S. V. Borisenko, Fermi surface nesting in several transition metal dichalcogenides. New Journal of Physics 10, 125027 (2008)

  9. [9]

    S. V. Borisenko, A. A. Kordyuk, A. N. Yaresko, V. B. Zabolotnyy, D. S. Inosov, R. Schuster, B. Büchner, R. Weber, R. Follath, L. Patthey, H. Berger, Pseudogap and Charge Density Waves in Two Dimensions. Physical Review Letters 100, 196402 (2008)

  10. [10]

    Valla, A

    T. Valla, A. V. Fedorov, P. D. Johnson, J. Xue, K. E. Smith, F. J. DiSalvo, Charge-Density- Wave-Induced Modifications to the Quasiparticle Self-Energy in 2H- TaSe 2. Phys. Rev. Lett. 85, 4759–4762 (2000)

  11. [11]

    Y. W. Li, J. Jiang, H. F. Yang, D. Prabhakaran, Z. K. Liu, L. X. Yang, Y. L. Chen, Folded superstructure and degeneracy-enhanced band gap in the weak-coupling charge density wave system 2 H − TaSe 2. Phys. Rev. B 97, 115118 (2018)

  12. [12]

    D. V. Evtushinsky, A. A. Kordyuk, V. B. Zabolotnyy, D. S. Inosov, B. Büchner, H. Berger, L. Patthey, R. Follath, S. V. Borisenko, Pseudogap-Driven Sign Reversal of the Hall Effect. Physical Review Letters 100, 236402 (2008)

  13. [13]

    M. Li, N. Xu, J. Zhang, R. Lou, M. Shi, L. Li, H. Lei, C. Petrovic, Z. Liu, K. Liu, Y. Huang, S. Wang, Quantization of the band at the surface of charge density wave material 2H-TaSe 2 *. Chinese Physics B 30, 047305 (2021)

  14. [14]

    Demsar, L

    J. Demsar, L. Forró, H. Berger, D. Mihailovic, Femtosecond snapshots of gap-forming charge-density-wave correlations in quasi-two-dimensional dichalcogenides 1T-TaS2 and 2H-TaSe2. Physical Review B - Condensed Matter and Materials Physics 66, 411011– 411014 (2002)

  15. [15]

    Ruzicka, L

    B. Ruzicka, L. Degiorgi, H. Berger, R. Gaál, L. Forró, Charge dynamics of 2H-TaSe2 along the less-conducting c-axis. Physical Review Letters 86, 4136–4139 (2001)

  16. [16]

    Vescoli, L

    V. Vescoli, L. Degiorgi, H. Berger, L. Forró, Dynamics of Correlated Two-Dimensional Materials: The 2 H − TaSe 2 Case. Phys. Rev. Lett. 81, 453–456 (1998)

  17. [17]

    E. F. Steigmeier, G. Harbeke, H. Auderset, F. J. DiSalvo, Softening of charge density wave excitations at the superstructure transition in 2H-TaSe2. Solid State Communications 20, 667–671 (1976)

  18. [18]

    X. Shen, R. Heid, R. Hott, A.-A. Haghighirad, B. Salzmann, M. dos Reis Cantarino, C. Monney, A. H. Said, M. Frachet, B. Murphy, K. Rossnagel, S. Rosenkranz, F. Weber, Precursor region with full phonon softening above the charge-density-wave phase transition in 2H-TaSe2. Nature Communications 14, 7282 (2023)

  19. [19]

    R. L. Barnett, A. Polkovnikov, E. Demler, W. G. Yin, W. Ku, Coexistence of gapless excitations and commensurate charge-density wave in the 2H transition metal dichalcogenides. Physical Review Letters 96 (2006)

  20. [20]

    Y. Ge, A. Y. Liu, Effect of dimensionality and spin-orbit coupling on charge-density-wave transition in 2H-TaSe 2. Physical Review B - Condensed Matter and Materials Physics 86 (2012)

  21. [21]

    Chowdhury, A

    S. Chowdhury, A. F. Rigosi, H. M. Hill, A. Briggs, D. B. Newell, H. Berger, A. R. Hight Walker, F. Tavazza, Influence of Dimensionality on the Charge Density Wave Phase of 2H‐ TaSe 2. Advanced Theory and Simulations 5 (2022)

  22. [22]

    C. H. Chen, J. M. Gibson, R. M. Fleming, Microstructure in the incommensurate and the commensurate charge-density-wave states of 2H-TaSe2: A direct observation by electron microscopy. Physical Review B 26, 184–205 (1982)

  23. [23]

    Zhang, C

    Z. Zhang, C. Xie, M. Hong, J. Shi, S. Pan, J. Hu, Q. Wu, W. Quan, N. Gao, J. Zhao, Y. Zhang, Scanning Tunneling Microscopy Examinations of the Effects of Defects on the Charge Density Wave Order in the Chemical Vapor Deposition-Derived TaSe2 on Au Foils. Journal of Physical Chemistry C 127, 16560–16566 (2023)

  24. [24]

    S. V. Dordevic, D. N. Basov, R. C. Dynes, B. Ruzicka, V. Vescoli, L. Degiorgi, H. Berger, R. Gaál, L. Forró, E. Bucher, Optical properties of the quasi-two-dimensional dichalcogenides 2H-TaSe2 and 2H-NbSe2. European Physical Journal B 33, 15–23 (2003)

  25. [25]

    A. S. Barker, J. A. Ditzenberger, F. J. DiSalvo, Infrared study of the electronic instabilities in tantalum disulfide and tantalum diselenide. Physical Review B 12, 2049–2054 (1975)

  26. [26]

    R. V. Coleman, B. Giambattista, P. K. Hansma, A. Johnson, W. W. McNairy, C. G. Slough, Scanning tunnelling microscopy of charge-density waves in transition metal chalcogenides. Advances in Physics 37, 559–644 (1988)

  27. [27]

    W. L. McMillan, Microscopic model of charge-density waves in 2H-TaSe2. Physical Review B 16, 643–650 (1977)

  28. [28]

    M. Li, G. Chen, Thermal transport for probing quantum materials. MRS Bulletin 45, 348–356 (2020)

  29. [29]

    Arpaia, S

    R. Arpaia, S. Caprara, R. Fumagalli, G. De Vecchi, Y. Y. Peng, E. Andersson, D. Betto, G. M. De Luca, N. B. Brookes, F. Lombardi, M. Salluzzo, L. Braicovich, C. Di Castro, M. Grilli, G. Ghiringhelli, Dynamical charge density fluctuations pervading the phase diagram of a Cu-based high- T c superconductor. Science 365, 906–910 (2019)

  30. [30]

    D. H. Torchinsky, F. Mahmood, A. T. Bollinger, I. Božović, N. Gedik, Fluctuating charge- density waves in a cuprate superconductor. Nature Materials 12, 387–391 (2013)

  31. [31]

    H. Luo, W. Xie, J. Tao, H. Inoue, A. Gyenis, J. W. Krizan, A. Yazdani, Y. Zhu, R. J. Cava, Polytypism, polymorphism, and superconductivity in TaSe 2 −x Te x. Proceedings of the National Academy of Sciences 112 (2015)

  32. [32]

    H. Ma, C. Li, Y. Ma, H. Wang, Z. W. Rouse, Z. Zhang, C. Slebodnick, A. Alatas, S. P. Baker, J. J. Urban, Z. Tian, Supercompliant and Soft (CH3NH3)3Bi2 I9 Crystal with Ultralow Thermal Conductivity. Physical Review Letters 123 (2019)

  33. [33]

    H. Ma, Y. Ma, H. Wang, C. Slebodnick, A. Alatas, J. J. Urban, Z. Tian, Experimental Phonon Dispersion and Lifetimes of Tetragonal CH 3 NH 3 PbI 3 Perovskite Crystals. Journal of Physical Chemistry Letters 10, 1–6 (2019)

  34. [34]

    H. Ma, C. Li, S. Tang, J. Yan, A. Alatas, L. Lindsay, B. C. Sales, Z. Tian, Boron arsenide phonon dispersion from inelastic x-ray scattering: Potential for ultrahigh thermal conductivity. Physical Review B 94, 220303 (2016)

  35. [35]

    Z. T. Tian, M. D. Li, Z. S. Ren, H. Ma, A. Alatas, S. D. Wilson, J. Li, Inelastic x-ray scattering measurements of phonon dispersion and lifetimes in PbTe 1− x Se x alloys. Journal of Physics: Condensed Matter 27, 375403 (2015)

  36. [36]

    A. H. Said, H. Sinn, T. S. Toellner, E. E. Alp, T. Gog, B. M. Leu, S. Bean, A. Alatas, High- energy-resolution inelastic X-ray scattering spectrometer at beamline 30-ID of the Advanced Photon Source. Journal of Synchrotron Radiation 27, 827–835 (2020)

  37. [37]

    T. S. Toellner, A. Alatas, A. H. Said, Six-reflection meV-monochromator for synchrotron radiation. Journal of Synchrotron Radiation 18, 605–611 (2011)

  38. [38]

    Hellman, P

    O. Hellman, P. Steneteg, I. A. Abrikosov, S. I. Simak, Temperature dependent effective potential method for accurate free energy calculations of solids. Physical Review B - Condensed Matter and Materials Physics 87 (2013)

  39. [39]

    Hellman, I

    O. Hellman, I. A. Abrikosov, S. I. Simak, Lattice dynamics of anharmonic solids from first principles. Physical Review B 84, 180301 (2011)

  40. [40]

    Kresse, J

    G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Physical Review B 54, 11169–11186 (1996)

  41. [41]

    Kresse, J

    G. Kresse, J. Hafner, Ab initio molecular dynamics for liquid metals. Physical Review B 47, 558–561 (1993)

  42. [42]

    C. Li, H. Ma, T. Li, J. Dai, Md. A. J. Rasel, A. Mattoni, A. Alatas, M. G. Thomas, Z. W. Rouse, A. Shragai, S. P. Baker, B. J. Ramshaw, J. P. Feser, D. B. Mitzi, Z. Tian, Remarkably Weak Anisotropy in Thermal Conductivity of Two-Dimensional Hybrid Perovskite Butylammonium Lead Iodide Crystals. Nano Lett. 21, 3708–3714 (2021)

  43. [43]

    B. S. Chang, C. Li, J. Dai, K. Evans, J. Huang, M. He, W. Hu, Z. Tian, T. Xu, Thermal Percolation in Well-Defined Nanocomposite Thin Films. ACS Appl. Mater. Interfaces 14, 14579–14587 (2022)

  44. [44]

    C. Li, Y. Ma, Z. Tian, Thermal Switching of Thermoresponsive Polymer Aqueous Solutions. ACS Macro Letters 7 (2018)

  45. [45]

    J. Dai, Q. Fang, G. A. Alvarez, A. Schaeffer, K. A. Page, J. Kim, S. M. Kielar, J. Christiansen-Salameh, E. Jeong, D. D. Bhagwandin, J. Kwon, L. D. Tran, M. S. Islam, A. K. Roy, N. R. Glavin, Y. Zhong, J. Lou, Z. Tian, Directly measured high in-plane thermal conductivity of two-dimensional covalent organic frameworks. Nature Communications 16 (2025)

  46. [46]

    J. Dai, S. Kielar, J. Kim, R. J. Warzoha, C. Li, M. Medina, B. Azhar, Z. Tian, Directly Probing Thermal Transport Across Micrometer‐Thick Metallic Interfaces Using Transient Thermal Grating Spectroscopy. Small Methods 10 (2026)

  47. [47]

    Zhang, J

    X. Zhang, J. Dai, C. Li, H. Ma, Characterizing thermal energy materials using transient grating spectroscopy: A comprehensive review of principles, techniques, and applications. Journal of Laser Applications 37 (2025)

  48. [48]

    J. M. E. Harper, T. H. Geballe, F. J. DiSalvo, Thermal properties of layered transition-metal dichalcogenides at charge-density-wave transitions. Physical Review B 15, 2943–2951 (1977)

  49. [49]

    Kumakura, H

    T. Kumakura, H. Tan, T. Handa, M. Morishita, H. Fukuyama, Charge density waves and superconductivity in 2H-TaSe2. Czechoslovak Journal of Physics 46, 2611–2612 (1996)

  50. [50]

    Thermal Conductivity of 1 T- TaS2 and 2H-TaSe2

    M. D. Nunez-Regueiro, J. M. Lopez-Castillo, C. Ayache, “Thermal Conductivity of 1 T- TaS2 and 2H-TaSe2” (1985)

  51. [51]

    J. M. Shen, A. Stangel, S. H. Sung, I. E. Baggari, K. Sun, R. Hovden, Melting of Charge Density Waves in Low Dimensions. arXiv [Preprint] (2025). https://doi.org/10.48550/ARXIV.2505.07569

  52. [52]

    V. N. Ryzhov, E. E. Tareyeva, Y. D. Fomin, E. N. Tsiok, Berezinskii—Kosterlitz—Thouless transition and two-dimensional melting. Uspekhi Fizicheskih Nauk 187, 921–951 (2017)

  53. [53]

    E. P. Bernard, W. Krauth, Two-step melting in two dimensions: First-order liquid-hexatic transition. Physical Review Letters 107 (2011)

  54. [54]

    B. I. Halperin, T. C. Lubensky, S. Ma, First-Order Phase Transitions in Superconductors and Smectic- A Liquid Crystals. Phys. Rev. Lett. 32, 292–295 (1974)

  55. [55]

    Joshi, H

    J. Joshi, H. M. Hill, S. Chowdhury, C. D. Malliakas, F. Tavazza, U. Chatterjee, A. R. Hight Walker, P. M. Vora, Short-range charge density wave order in 2H- T a S2. Physical Review B 99 (2019)

  56. [56]

    S. H. Sung, N. Agarwal, I. El Baggari, P. Kezer, Y. M. Goh, N. Schnitzer, J. M. Shen, T. Chiang, Y. Liu, W. Lu, Y. Sun, L. F. Kourkoutis, J. T. Heron, K. Sun, R. Hovden, Endotaxial stabilization of 2D charge density waves with long-range order. Nature Communications 15, 1403 (2024)

  57. [57]

    L. P. Gor’kov, Strong electron-lattice coupling as the mechanism behind charge density wave transformations in transition-metal dichalcogenides. Physical Review B - Condensed Matter and Materials Physics 85 (2012)

  58. [58]

    C. Wen, Y. Xie, Y. Wu, S. Shen, P. Kong, H. Lian, J. Li, H. Xing, S. Yan, Impurity-pinned incommensurate charge density wave and local phonon excitations in 2H-NbS2. Physical Review B 101 (2020)

  59. [59]

    H. Ryu, Y. Chen, H. Kim, H. Z. Tsai, S. Tang, J. Jiang, F. Liou, S. Kahn, C. Jia, A. A. Omrani, J. H. Shim, Z. Hussain, Z. X. Shen, K. Kim, B. I. Min, C. Hwang, M. F. Crommie, S. K. Mo, Persistent Charge-Density-Wave Order in Single-Layer TaSe2. Nano Letters 18, 689–694 (2018)

  60. [60]

    M. Lee, M. Šiškins, S. Mañas-Valero, E. Coronado, P. G. Steeneken, H. S. J. van der Zant, Study of charge density waves in suspended 2H-TaS2 and 2H-TaSe2 by nanomechanical resonance. Applied Physics Letters 118 (2021)

  61. [61]

    Huang, J

    H. Huang, J. Dai, J. Christiansen-Salameh, J. Kim, S. Kielar, D. Ma, N. Schinitzer, D. Ni, G. Alvarez, C. Li, C. Slebodnick, M. Medina, B. Azhar, A. Alatas, R. Cava, D. Muller, Z. Tian, Dataset: Anomalous Thermal Transport Reveals Weak First-Order Melting of Charge Density Waves in 2H-TaSe2, PARADIM (2026)

  62. [62]

    Huisman, F

    R. Huisman, F. Jellinek, On the polymorphism of tantalum diselenide. Journal of the Less Common Metals 17, 111–117 (1969)

  63. [63]

    J. P. Perdew, K. Burke, M. Ernzerhof, Generalized Gradient Approximation Made Simple. Physical Review Letters 77, 3865–3868 (1996)

  64. [64]

    P. M. Chaikin, T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, 1995). Acknowledgments: HH, JD, and ZT thank Allan MacDonald for fruitful discussions and suggestions. HH, JD, JC, GA, and ZT thank Jacob Ruff for assistance with X -ray diffraction measurements and helpful discussions. DM and NS thank Saif Siddique for assi...

  65. [65]

    superlattice reflection, where representative line scans at each temperature were fitted with Gaussian profiles to extract the peak position and integrated intensity, and each reported peak position was obtained by averaging over more than 30 symme try-equivalent superlattice peaks within the same diffracti on pattern, with error bars representing the sta...