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REVIEW 3 major objections 6 minor 51 references

Violation of the Wiedemann-Franz law and ultra-low thermal conductivity of Ti$_3$C$_2$T$_x$ MXene

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Using scanning thermal microscopy, this paper establishes that isolated Ti$_3$C$_2$T$_x$ MXene flakes have an effective thermal conductivity of $0.78\pm0.21$ W m$^{-1}$ K$^{-1}$ at room temperature, a value low enough that the measured…

desk verdict A useful new thermal-conductivity measurement for Ti3C2Tx flakes, but the headline WF 'violation' number uses the geometric-mean κ instead of the in-plane value, so the magnitude is overstated even though a violation likely survives. read the letter →

arxiv 2412.01546 v1 pith:K5G6237K submitted 2024-12-02 cond-mat.mtrl-sci cond-mat.mes-hall

Yubin Huang , Jean Spiece , Tetiana Parker , Asaph Lee , Yury Gogotsi , Pascal Gehring This is my paper · ORCID
classification cond-mat.mtrl-scicond-mat.mes-hall PACS 66.70.-f72.15.Eb07.79.-v
keywords MXeneTi3C2TxthermalconductivityWiedemann-Franzlawscanningmicroscopyelectron-phononcouplinginsulationinfraredstealth
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

This paper sets out to measure the intrinsic thermal conductivity of isolated Ti$_3$C$_2$T$_x$ MXene flakes and to test whether the Wiedemann-Franz law holds in a material with metallic conductivity and strong electron-phonon coupling. Using scanning thermal microscopy on flakes from monolayer to tens of layers, it finds an effective thermal conductivity of $0.78\pm0.21$ W m$^{-1}$ K$^{-1}$, an unusually low value for an electrically conductive 2D material. Because the same flakes show an electrical conductivity of $4.43\times10^5$ S m$^{-1}$, the implied Lorenz number is only $0.25L_0$, a strong violation of the Wiedemann-Franz prediction. The authors attribute this to strong electron-phonon interactions, particularly electron coupling to transverse optical phonons, which suppresses the electronic heat current while preserving charge transport. If the result holds, it would make MXenes promising for thermal insulation, infrared stealth, and thermoelectric applications, where low heat conduction and high electric conduction are usually contradictory.

What carries the argument

The load-bearing tool is a scanning thermal microscope (SThM) whose resistive Pd probe acts as both heater and thermometer, combined with a diffusive thermal transport model for orthotropic (direction-dependent) thermal spreading in a layered flake. The total resistance is written as $R_{\rm th} = R_{\rm tip} + R_{\rm int} + R_{\rm spr}$, where $R_{\rm spr}$ is the spreading resistance given by an analytical integral expression (Eq. 2) that depends on flake thickness, tip radius, in-plane conductivity $\kappa_i$, cross-plane conductivity $\kappa_c$, the substrate conductivity, and an interface resistivity $r_{\rm int}$. Since the tip radius ($\approx75$ nm) is much larger than the flake thickness ($\lesssim10$ nm), heat flow through thin flakes is assumed nearly vertical, so the cross-plane value is fitted first with an isotropic model, then the orthotropic model is used on thicker flakes. The central identity is the effective conductivity $\kappa_{\rm eff} = \sqrt{\kappa_i \kappa_c}$; comparing it with the electrical conductivity through the Lorenz number $L = \kappa/(\sigma T)$ is what produces the claimed violation.

What would settle it

Measure the same flakes with a technique that does not rely on the tip-sample contact model, for example time-domain thermoreflectance on a flake stack or a suspended-device thermal transport measurement, and check whether the thermal conductivity and Lorenz number reproduce at $\kappa_{\rm eff}=0.78$ W m$^{-1}$ K$^{-1}$ and $L=0.25L_0$.

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Extended reading notes

Core claim

The central discovery is that single-crystal Ti$_3$C$_2$T$_x$ MXene flakes combine high electrical conductivity with ultra-low thermal conductivity, violating the Wiedemann-Franz law at room temperature. From the thickness dependence of the thermal resistance measured by SThM, the paper extracts anisotropic in-plane and cross-plane thermal conductivities of $\kappa_i = 0.85$ to $1.56$ W m$^{-1}$ K$^{-1}$ and $\kappa_c = 0.38$ to $0.63$ W m$^{-1}$ K$^{-1}$, giving an effective isotropic value of $\kappa_{\rm eff} = 0.78 \pm 0.21$ W m$^{-1}$ K$^{-1}$. With $\sigma = 4.43 \times 10^5$ S m$^{-1}$ measured on the same type of flake, the Wiedemann-Franz expectation is $\kappa_{\rm WF} = 3.17$ W m$^{-1}$ K$^{-1}$, so the effective Lorenz number is $L = 0.25L_0$. The paper interprets the violation as evidence that strong electron-phonon coupling, previously inferred from ultrafast spectroscopy, suppresses the electronic contribution to heat transport, and argues that the low thermal conductivity also limits the phonon channel through local defects and inelastic scattering.

Load-bearing premise

The extracted thermal conductivity assumes heat flows diffusively from the probe tip through the flake into the substrate, so any water meniscus, contamination layer, or non-continuum size effect would shift the fitted numbers.

Editorial extensions

If this is right

  • If the central claim is right, Ti$_3$C$_2$T$_x$ MXenes break the usual trade-off: thermal insulation and electrical conduction can coexist in one 2D material, opening a path to sub-micrometer thermal barriers and infrared stealth coatings.
  • The reported heat loss from Ti$_3$C$_2$T$_x$ is two orders of magnitude smaller than from gold, aluminium, and steel, so MXene foils or coatings could reduce radiative and conductive heat losses in electronic and industrial equipment.
  • The low $\kappa_{\rm eff}$ combined with $\sigma = 4.43\times10^5$ S m$^{-1}$ implies that the Wiedemann-Franz ratio is violated by a factor of four, which would make MXenes an experimental testbed for non-Fermi-liquid or strongly coupled transport in 2D metals.
  • The anisotropic values $\kappa_i = 0.85$ to $1.56$ W m$^{-1}$ K$^{-1}$ and $\kappa_c = 0.38$ to $0.63$ W m$^{-1}$ K$^{-1}$ provide reference data against which future calculations of phonon and electron transport in MXenes can be checked.
  • The low interface resistivity ($r_{\rm int} = 1.0\times10^{-8}$ K m$^2$ W$^{-1}$) near that of graphene/SiO$_2$ means that substrate effects are small, strengthening the conclusion that the measured conductivity is intrinsic to the flakes.

Reading between the lines

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

  • A testable extension: the diffusive-contact assumption could be checked by varying the SThM tip radius or by measuring in vacuum, since a water meniscus or contamination layer would change the fitted $\kappa$; if the extracted value moved, the WF violation would need revision.
  • An independent cross-check, such as time-domain thermoreflectance on stacked flakes or suspended-device electrical heating, would confirm whether $L=0.25L_0$ is intrinsic or an artifact of the spreading-resistance model.
  • The same measurement strategy could be applied to other MXene chemistries (e.g., Nb$_2$C or V$_2$C) to see whether the suppressed Lorenz number is a general MXene feature or specific to Ti$_3$C$_2$T$_x$ and its surface terminations.
  • If the phonon contribution is not negligible, the electronic part $\kappa_e$ would be even lower than $\kappa_{\rm eff}$, which would strengthen the WF violation but would also require a more elaborate separation of $\kappa_e$ and $\kappa_{\rm ph}$ than the paper's assumption that $\kappa_{\rm eff}\approx\kappa_e$.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper reports scanning thermal microscopy (SThM) measurements on Ti3C2Tx MXene single flakes of varying thickness and fits a diffusive orthotropic spreading-resistance model to extract the in-plane (κi = 0.85–1.56 W m^-1 K^-1) and cross-plane (κc = 0.38–0.63 W m^-1 K^-1) thermal conductivities. The authors define an effective thermal conductivity κeff = sqrt(κi κc) = 0.78 ± 0.21 W m^-1 K^-1 and combine this with a two-terminal electrical conductivity measurement (σ = 4.43 × 10^5 S m^-1) to obtain a Lorenz number L = 0.25 L0, which they interpret as a strong violation of the Wiedemann-Franz law driven by strong electron-phonon coupling. They further claim that the ultralow thermal conductivity and low emissivity make Ti3C2Tx promising for thermal insulation, thermoelectric, and infrared stealth applications.

Significance. If the reported thermal conductivity and the WF violation are quantitatively robust, this work would be significant for both fundamental transport physics in strongly correlated 2D metals and for applications in thermal management. The experimental dataset—thickness-resolved SThM on single flakes down to monolayer thickness—is valuable and extends the limited thermal-transport literature on MXenes. The paper also makes a clear, falsifiable prediction (effective Lorenz number far below L0) that can be tested by independent methods. However, the strength of the claim currently depends on the choice of the scalar conductivity used in the WF comparison and on the reliability of the fitted parameters, which are not fully supported by the presented uncertainty analysis.

major comments (3)
  1. [Results and discussion, Eq. (1) and Table 1] The WF comparison uses κeff = sqrt(κi κc) in L = κ/(σT), while the measured electrical conductivity is an in-plane quantity. The directionally matched comparison would use κi, which gives L/L0 ≈ 0.27 for the lower bound of κi (0.85 W m^-1 K^-1) and ≈ 0.49 for the upper bound (1.56 W m^-1 K^-1), not the reported 0.25. The abstract, introduction, and conclusion all state L = 0.25 L0 as the 'strong violation' result. The authors must either use κi for the WF comparison or provide a physical justification for why κeff, a geometric mean defined for the spreading-resistance calculation, is the appropriate conductivity for a directional WF test.
  2. [Diffusive thermal transport model and Table 1] The uncertainty ±0.21 on κeff is not derived from the reported fit procedure. The parameters κi, κc, rint, and Rtip are obtained in a two-step fit (first an isotropic model for κc, then an orthotropic model for κi, rint, and Rtip), and the table lists only ranges for κi and κc while rint and Rtip are given as single values. No covariance matrix, confidence intervals, or propagation of the measurement errors in the thermal resistance histograms is provided. A Monte Carlo or residual-bootstrap analysis is needed to support the claimed uncertainty and to establish that the WF conclusion is not an artifact of parameter degeneracies.
  3. [Diffusive thermal transport model, Eq. (2)] The extracted thermal conductivities rest on the assumption of purely diffusive, continuum heat spreading from a 75-nm-radius tip with no water meniscus or contaminant layer and no ballistic or size effects. SThM in ambient conditions is susceptible to a water meniscus at the tip–sample contact, which would change the effective contact area and the measured thermal resistance. The authors should provide a sensitivity analysis (e.g., varying the tip radius or adding a parasitic contact resistance) to show that the fitted κ values—and hence the WF violation—are robust against plausible deviations from the assumed thermal circuit.
minor comments (6)
  1. [Discussion] The sentence 'we can assume that the total thermal conductivity is dominated by electron contributions (κe = κeff = 0.78 W m−1 K−1)' conflates the total effective thermal conductivity with the electronic contribution; this should be phrased as 'assuming κph ≪ κe, we identify κe with κeff'.
  2. [Eq. (2)] The symbol K is used for the reflection coefficient in the spreading-resistance integral, which is easy to confuse with kelvin or with the thermal conductivity ratio; a different symbol (e.g., Γ) would improve readability.
  3. [Table 1] The interface thermal resistivity rint is reported as a single value (1.0 × 10^-8 K m^2 W^-1) without an uncertainty, even though it is a fit parameter; please provide a confidence interval or state why it is fixed.
  4. [Figure 4a and Introduction] The claim of a 'record low' thermal conductivity among the 2D materials compared in Figure 4a should be reconciled with the WSe2 value of 0.048 W m^-1 K^-1 cited in the Introduction; if WSe2 is excluded from the comparison set, the exclusion should be stated.
  5. [Experimental Section] There is a typographical error: 'Bruke Dimension Icon' should be 'Bruker Dimension Icon'.
  6. [General] A data-availability statement is missing; the authors should state whether the SThM maps and fit code are available to readers.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the thermal conductivity is fit to independent SThM thickness-dependent data and the Wiedemann-Franz comparison uses a separately measured electrical conductivity; self-citations to prior SThM work are methodological provenance, not load-bearing circularity.

full rationale

The derivation chain begins with measured SThM thermal-resistance maps and 2D histograms (Fig. 3a). Equation (2) is a stated spreading-resistance model (attributed to Muzychka et al., ref 51) with explicitly listed assumptions (diffusive, orthotropic, tip radius 75 nm much larger than flake thickness). Fitting it to the thickness dependence yields κ_i, κ_c, r_int, and R_tip; κ_eff = sqrt(κ_i κ_c) is then defined as a derived quantity, not an input. The Wiedemann-Franz step is a comparison: the electrical conductivity σ = 4.43×10^5 S/m comes from an independent two-terminal I-V measurement (Note S4), and κ_WF = L0 σ T = 3.17 W/mK is computed from that independent σ, not extracted from the thermal fit. Therefore L = 0.25 L0 is not a fitted parameter renamed as a prediction; it is a ratio of two independent measurements under an assumption about which κ to use. The possible directional mismatch (using the geometric-mean κ_eff rather than in-plane κ_i) is a scientific-correctness issue about the appropriate transport coefficient, not a circularity, since κ_eff is not defined in terms of σ or L. The paper cites the authors' prior SThM work (refs 21–24) for the measurement and fitting approach, but the central model and equations are stated in the paper and the fit is to new data; no uniqueness theorem or forbidden alternative is imported from the self-citations, so the self-citation is minor and not load-bearing. No internal limitation passage or omitted proof changes this assessment.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central thermal conductivity values are not derived from first principles; they are outputs of a fitted spreading-resistance model with four free parameters. The model also relies on domain assumptions about diffusive, orthotropic continuum heat transport in few-layer flakes and about the representativeness of a single electrical measurement. No new physical entities are introduced.

free parameters (4)
  • κi (in-plane thermal conductivity) = 0.85 to 1.56 W m-1 K-1
    Fitted using the orthotropic spreading-resistance model to the thickness-dependent thermal resistance data.
  • κc (cross-plane thermal conductivity) = 0.38 to 0.63 W m-1 K-1
    Fitted first with an isotropic model on thin flakes (<10 nm), then used as a fixed input for the orthotropic fit.
  • rint (MXene/SiO2 interface thermal resistivity) = 1.0e-8 K m2 W-1
    Fitted parameter in the total thermal resistance series Rth = Rtip + Rint + Rspr.
  • Rtip (SThM tip thermal resistance) = 3.54e6 K W-1
    Fitted as part of the series resistance; accounts for tip and contact contributions.
assumptions (5)
  • standard math The spreading-resistance integral solution (Eq. 2) for orthotropic systems is valid for Ti3C2Tx flakes.
    Taken from Muzychka et al. (ref 51) and prior SThM studies (refs 21-24).
  • domain assumption Heat transport in the flake is diffusive and can be described by continuum orthotropic thermal conductivities.
    Invoked in the 'Diffusive thermal transport model' section; size effects and ballistic phonon transport are neglected.
  • domain assumption For flakes thinner than 10 nm, the tip radius (75 nm) is much larger than the thickness, so heat flow is nearly vertical and an isotropic approximation can be used to fit κc.
    Stated in the 'Diffusive thermal transport model' section before the two-stage fitting procedure.
  • domain assumption The electrical conductivity measured on one flake is representative of the flakes used for thermal measurements.
    The WF comparison combines σ from a two-terminal device (Figure S5) with κ from SThM on other flakes.
  • domain assumption The total measured thermal conductivity can be set equal to the electronic contribution for the WF comparison.
    Stated in the Discussion: 'κe = κeff = 0.78 W m-1 K-1', despite the later argument that phonons are also suppressed.

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Cite this review

Pith. "Pith review of Violation of the Wiedemann-Franz law and ultra-low thermal conductivity of Ti$_3$C$_2$T$_x$ MXene." pith.science (2026). https://pith.science/paper/K5G6237K

@misc{pith2026241201546,
  author       = {Pith},
  title        = {Pith review of: Violation of the Wiedemann-Franz law and ultra-low thermal conductivity of Ti$_3$C$_2$T$_x$ MXene},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K5G6237K}},
  note         = {Machine review of arXiv:2412.01546}
}
abstract

The high electrical conductivity and good chemical stability of MXenes offer hopes for their use in many applications, such as wearable electronics, energy storage, or electromagnetic interference shielding. While their optical, electronic and electrochemical properties have been widely studied, the information on thermal properties of MXenes is scarce. In this study, we investigate the heat transport properties of Ti$_3$C$_2$T$_x$ MXene single flakes using scanning thermal microscopy and find exceptionally low anisotropic thermal conductivities within the Ti$_3$C$_2$T$_x$ flakes, leading to an effective thermal conductivity of 0.78$\pm$0.21 W m$^{-1}$ K$^{-1}$. This observation is in stark contrast to the predictions of the Wiedemann-Franz law, as the estimated Lorenz number is only 0.25 of the classical value. Due to the combination of low thermal conductivity and low emissivity of Ti$_3$C$_2$T$_x$, the heat loss from it is two orders of magnitude smaller than that from common metals. Our study explores the heat transport mechanisms of MXenes and highlights a promising approach for developing thermal insulation, two-dimensional thermoelectric, or infrared stealth materials.

Figures

Figures reproduced from arXiv: 2412.01546 by the authors.

Figure 1
Figure 1. (a) Schematic of the preparation process of Ti [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. (a) Schematic of the SThM setup for measuring local thermal transport properties [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. (a) Total 2D histogram combined with all different Ti [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: (a) Comparison of experimental results in thermal conductivity for several 2D ma [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.