{"id":"9315b1d3-5e4a-422e-857d-1d852ffe5708","arxiv_id":"2412.01546","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"SThM measurements on Ti3C2Tx MXene single flakes give a thermal conductivity of 0.78 ± 0.21 W m-1 K-1, only about 25% of the Wiedemann-Franz expectation, implying strong electron-phonon coupling suppresses electronic heat flow.","lead":"This paper measures heat flow through single flakes of the conductive 2D material Ti3C2Tx MXene and reports an extremely low thermal conductivity of about 0.78 W m-1 K-1, far below what the Wiedemann-Franz law predicts for a metal with its high electrical conductivity. If correct, the result suggests MXenes could combine high electrical conductivity with strong thermal insulation, a combination useful for thermoelectrics, heat shielding, and infrared stealth.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The WF comparison uses the geometric-mean thermal conductivity κeff rather than the direction-matched in-plane κ_i, so the reported L=0.25L0 is not the Lorenz number for the measured conduction direction; with κ_i it is 0.27–0.49L0.","rationale":"The reader's conditional verdict identifies the SThM contact/model as the weak point. My independent pass found a different, more directly central problem: the WF ratio is evaluated with κeff rather than the direction-matched in-plane κ. This is not an external-consensus disagreement; it is an internal inconsistency in how Eq. 1 is applied to the paper's own measured σ and κ components. It does not by itself destroy the qualitative violation—using the in-plane bound still gives L≈0.27–0.49L0—but it changes the quantitative claim by up to a factor of two and weakens 'strong violation.' The paper does have independent strengths: the statistical 2D-histogram analysis, an established spreading-resistance framework, and a conservative (thick) flake thickness for σ. The requested recomputation with κ_i is straightforward and would settle whether the abstract's number should be revised. The reader's water-meniscus/diffusive-model concern remains valid, but I do not make it primary because the directional mismatch persists even if the thermal model is exactly correct.","tokens_in":11512,"tokens_out":9206,"duration_ms":87644,"concrete_test":"Recompute the Lorenz number using the in-plane thermal conductivity from Table 1, with the same σ=4.43×10^5 S/m and T=293 K: L_i/L0=κ_i/(σ T L0) for κ_i=0.85 and 1.56 W/mK. Compare with the paper's κeff-based value of 0.25. If L_i/L0 lies below 1 for both bounds, the qualitative WF violation survives but the headline 0.25L0 must be replaced by the directionally appropriate range; if either bound reaches or exceeds 1, the violation claim is not established and the verdict should be revised.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing step in the WF claim is the choice of a scalar thermal conductivity for Eq. 1. The electrical conductivity σ=4.43×10^5 S/m is measured in-plane via two-terminal indium contacts, while the thermal model returns an anisotropic pair (Table 1): κ_i=0.85–1.56 W/mK (in-plane) and κ_c=0.38–0.63 W/mK (cross-plane). The paper does not insert κ_i into L=κ/(σT); it inserts the geometric mean κeff=sqrt(κ_i κ_c)=0.78±0.21, defined for the spreading-resistance calculation, not as a transport coefficient for any physical direction. Because κ_c<κ_i, this lowers the numerator by a factor of roughly sqrt(κ_i/κ_c)≈1.5–2 and makes the violation look stronger than the directionally correct comparison. Recomputing with κ_i yields L/L0≈0.27 (κ_i=0.85) to ≈0.49 (κ_i=1.56), rather than 0.25. The qualitative conclusion that L<L0 may survive, but the specific quantitative claim in the abstract and the phrase 'strong violation' rest on a directionally mismatched comparison that should be corrected or justified.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":11802,"tokens_out":3134,"duration_ms":28726,"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":[{"comment":"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.","section":"Results and discussion, Eq. (1) and Table 1"},{"comment":"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.","section":"Diffusive thermal transport model and Table 1"},{"comment":"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.","section":"Diffusive thermal transport model, Eq. (2)"}],"minor_comments":[{"comment":"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'.","section":"Discussion"},{"comment":"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.","section":"Eq. (2)"},{"comment":"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.","section":"Table 1"},{"comment":"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.","section":"Figure 4a and Introduction"},{"comment":"There is a typographical error: 'Bruke Dimension Icon' should be 'Bruker Dimension Icon'.","section":"Experimental Section"},{"comment":"A data-availability statement is missing; the authors should state whether the SThM maps and fit code are available to readers.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The core experiment is interesting and the thickness-dependent SThM dataset is a useful contribution. My main concern is that the headline WF violation is quantitatively overstated because it uses a geometric-mean conductivity against an in-plane electrical measurement. The two-step fitting procedure also does not currently provide a defensible uncertainty on the central value. These issues are fixable within the scope of a revision—recomputing the Lorenz number with κi and adding a proper uncertainty analysis—so I recommend major revision rather than rejection. I would also encourage the editor to seek a referee with SThM modeling expertise, since the validity of the diffusive spreading-resistance model is essential to the extraction."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear [Colleague],\n\nThe genuinely new thing here is the first measured thermal conductivity of isolated Ti3C2Tx flakes: SThM on flakes from monolayer to tens of layers, yielding anisotropic values (κ_i = 0.85–1.56, κ_c = 0.38–0.63 W/mK). The statistical processing of the thermal maps is careful, and the electrical conductivity used later is conservative (full AFM thickness). That part is worth publishing.\n\nThe soft spot is the WF analysis. The paper plugs κ_eff = √(κ_i κ_c) = 0.78 into L = κ/(σT) and reports L = 0.25 L0. But the electrical conductivity is measured in-plane, so the WF check should use the in-plane κ_i. With κ_i = 0.85–1.56, L/L0 is 0.27–0.49. So the violation remains but the \"strong violation\" headline is overstated. That is a load-bearing problem for the abstract and conclusion, and it needs to be fixed or justified.\n\nAdditional caveats: the four-parameter fit (κ_i, κ_c, r_int, R_tip) rests on a modest resistance contrast between flake and substrate, and the quoted uncertainty on κ_eff is not a propagated error from the fit. The diffusive continuum assumption for a thin flake with a 75 nm tip is reasonable but unverified for this material. The paper also assumes the total measured κ is electronic to make the WF comparison; that is an upper bound, fine for arguing a violation, but it should be stated more explicitly.\n\nThe \"record low\" phrasing in Figure 4 is debatable given the lower values reported for some other 2D materials, though those are often cross-plane or disordered films.\n\nNet: the experiment is a solid contribution and the qualitative WF breakdown is plausible, but the quantitative claim needs revision. This paper deserves a serious referee, and the directional mismatch in the Lorenz number should be the first thing the referee asks about.\n\nBest,","headline":"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.","tokens_in":12361,"tokens_out":4428,"would_cite":false,"duration_ms":38638,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["66.70.-f","72.15.Eb","07.79.-v"],"model":"deepseek-v4-flash","headline":"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…","keywords":["MXene","Ti3C2Tx","thermal conductivity","Wiedemann-Franz law","scanning thermal microscopy","electron-phonon coupling","thermal insulation","infrared stealth"],"falsifier":"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 $L=0.25L_0$.","tokens_in":11306,"feed_emoji":"🔥","tokens_out":6497,"duration_ms":48072,"temperature":0.7,"pith_summary":"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.","feed_headline":"MXene flakes carry heat four times worse than Wiedemann-Franz allows","feed_subtitle":"SThM measures L = 0.25 L0 at room temperature in Ti3C2Tx, pointing to strong electron-phonon coupling.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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 $\\kappa_{\\rm eff}\\approx\\kappa_e$."],"forward_implications":["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."],"supporting_citations":[{"why":"Prior observation of the breakdown of the Wiedemann-Franz law in graphene; provides the precedent for a metallic 2D system where $L<L_0$.","marker":"[5]"},{"why":"Ultrafast spectroscopy evidence of strong electron-phonon coupling in MXenes; supports the mechanism proposed for the observed violation.","marker":"[10]"},{"why":"SThM methodology for nanoscale thermal transport in 2D materials; basis for the measurement protocol used here.","marker":"[21]"},{"why":"Cross-sectional SThM technique that quantifies thermal transport in buried nanostructures; underpins the thickness-dependent fitting.","marker":"[22]"},{"why":"Low thermal conductivity in franckeite heterostructures; source of the analytical spreading-resistance expression used for the fit.","marker":"[23]"},{"why":"Anisotropic in-plane thermal conductivity in few-layer black phosphorus; precedent for the orthotropic continuum model.","marker":"[25]"},{"why":"Extremely anisotropic van der Waals thermal conductors; supports the diffusive orthotropic treatment of layered flakes.","marker":"[26]"},{"why":"High electrical conductivity of individual monolayer Ti$_3$C$_2$T$_x$ flakes; provides the reference value used to compute $\\sigma$ and the Lorenz number.","marker":"[44]"},{"why":"Theoretical lattice thermal conductivity of monolayer Ti$_3$C$_2$T$_x$ with different surface terminations; the comparison that highlights the low measured value.","marker":"[49]"}],"fun_headline_variants":["MXene violates Wiedemann-Franz with ultra-low heat conduction","Ti3C2Tx MXene: thermal conductivity 4x below Wiedemann-Franz","MXene flakes defy Wiedemann-Franz law for heat transport","Low heat loss in MXene despite high electrical conductivity","Wiedemann-Franz fails in MXene: L = 0.25 L0"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["MXene violates Wiedemann-Franz with ultra-low heat conduction","Ti3C2Tx MXene: thermal conductivity 4x below Wiedemann-Franz","MXene flakes defy Wiedemann-Franz law for heat transport","Low heat loss in MXene despite high electrical conductivity","Wiedemann-Franz fails in MXene: L = 0.25 L0"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000729,"raw_usage":{"total_tokens":3328,"prompt_tokens":1075,"completion_tokens":2253,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":691,"completion_tokens_details":{"reasoning_tokens":2154}},"tokens_in":691,"tokens_out":2253,"duration_ms":13079,"temperature":1.0,"reasoning_tokens":2154,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T04:17:22.064526+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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 $L=0.25L_0$.","supporting_citations":[{"cited_title":"K.; Wang, K.; Liu, X.; Harzheim, A.; Lucas, A.; Sachdev, S.; Kim, P.; Taniguchi, T.; Watanabe, K.; Ohki, T","cited_arxiv_id":null,"evidence_quote":"Prior observation of the breakdown of the Wiedemann-Franz law in graphene; provides the precedent for a metallic 2D system where $L<L_0$."},{"cited_title":"Simultaneous Capturing Phonon and Electron Dynamics in MXenes","cited_arxiv_id":null,"evidence_quote":"Ultrafast spectroscopy evidence of strong electron-phonon coupling in MXenes; supports the mechanism proposed for the observed violation."},{"cited_title":"J.; Mucientes, M.; Mueller, T.; Lambert, C.; Sadeghi, H.; Kolosov, O","cited_arxiv_id":null,"evidence_quote":"SThM methodology for nanoscale thermal transport in 2D materials; basis for the measurement protocol used here."},{"cited_title":"J.; El Sachat, A.; Haenel, L.; Alonso, M","cited_arxiv_id":null,"evidence_quote":"Cross-sectional SThM technique that quantifies thermal transport in buried nanostructures; underpins the thickness-dependent fitting."},{"cited_title":"J.; Lulla, K.; Mueller, T.; Kolosov, O.; Sadeghi, H.; Evangeli, C","cited_arxiv_id":null,"evidence_quote":"Low thermal conductivity in franckeite heterostructures; source of the analytical spreading-resistance expression used for the fit."},{"cited_title":"P.; Lundstrom, M","cited_arxiv_id":null,"evidence_quote":"Anisotropic in-plane thermal conductivity in few-layer black phosphorus; precedent for the orthotropic continuum model."},{"cited_title":"E.; Mujid, F.; Rai, A.; Eriksson, F.; Suh, J.; Poddar, P.; Ray, A.; Park, C.; Fransson, E.; Zhong, Y.; Muller, D","cited_arxiv_id":null,"evidence_quote":"Extremely anisotropic van der Waals thermal conductors; supports the diffusive orthotropic treatment of layered flakes."},{"cited_title":"J.; Vorobeva, N","cited_arxiv_id":null,"evidence_quote":"High electrical conductivity of individual monolayer Ti$_3$C$_2$T$_x$ flakes; provides the reference value used to compute $\\sigma$ and the Lorenz number."},{"cited_title":"Effect of Surface Termination on the Lattice Thermal Conductivity of Monolayer Ti _3 C _2 T _z MXenes","cited_arxiv_id":null,"evidence_quote":"Theoretical lattice thermal conductivity of monolayer Ti$_3$C$_2$T$_x$ with different surface terminations; the comparison that highlights the low measured value."}],"review_version":1}