{"id":"dc86f77e-b4e8-4ee3-a09f-c38c93708c93","arxiv_id":"2505.15522","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"First-principles electron-phonon calculations reproduce the in-plane conductivity of TaAs and predict that the Wiedemann-Franz law is strongly violated in this Weyl semimetal.","lead":"This paper computes how electricity and heat flow through a special crystal called TaAs using only quantum mechanics, including the way atomic vibrations scatter electrons. It finds that a standard rule linking heat and electrical conduction is badly violated in this material, which matters for designing better thermoelectric devices.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Unquantified Onsager violation in time-reversal-invariant TaAs: the claimed 70% Wiedemann-Franz violation may be an IBTE convergence artifact.","rationale":"The reader's weakest assumption about rigid-band doping is a real sample-comparison limitation, but it is not the most load-bearing point: the pristine calculation is well defined by charge neutrality, and Appendix B already explores rigid-band shifts without invalidating the theoretical framework. The Onsager consistency check is different: it is an internal test of the very FE/FT iteration that the paper presents as its methodological contribution (Eqs. 20 and 21). For TaAs, time-reversal symmetry makes L12 = L21 exact; any residual is numerical or an implementation error. The paper uses Π versus T S (Fig. 6) as a diagnostic, but does not quantify it. If the residual is large, the computed S and κel, and thus the headline Lorenz numbers, are not converged; if it is small, the central claim is supported. The proposed test is targeted and would settle the issue without redoing the whole study. I therefore keep the reader's CONDITIONAL verdict rather than moving to accept or reject, while flagging this additional condition before quantitative predictions are taken at face value.","tokens_in":14987,"tokens_out":13964,"duration_ms":135061,"concrete_test":"Run the IBTE solver for TaAs on the stated 64×64×64 q-grid (or a finer grid) and compute, at each temperature, the relative Onsager residual r(T)=||L12−L21||/(||L12||+||L21||) as a function of iteration count. Report r at 150, 200, 250, 300, and 350 K, and recompute Lxx/L0 using the symmetrized entries (L12+L21)/2. If r(T) ≤ 1% and the symmetrized Lorenz numbers remain near 1.6–1.7 at 200 K, the strong WF-violation claim survives; if r(T) is larger or the symmetrized L drops toward L0, the central claim fails and the solution scheme must be revised.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing weakness is internal to the IBTE implementation. In time-reversal-invariant TaAs, the exact solution of the linearized BTE must satisfy the Onsager relation L12 = L21, hence Π = T S. The paper states in Sec. IV.E that 'Πzz shows finite deviation from T Szz' and attributes this to numerical effects, but it never reports the magnitude of the deviation or the convergence of the FE/FT iteration. Since S = (1/T)L11^{-1}L12 (Eq. 32) and κel = L22/T − L21·S (Eq. 36), a spurious Onsager violation directly shifts the thermopower and electronic thermal conductivity, and hence the Lorenz number L = κel/(σT) in Tables I and II. The claimed violation of the Wiedemann-Franz law by up to 70% between 150 and 350 K could therefore be partly or wholly a numerical artifact of an unconverged FE/FT pair rather than a physical property of TaAs. Without a quantitative Onsager-residual check, the central conclusion is not established.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper computes the thermoelectric transport coefficients of the Weyl semimetal TaAs from first principles, using DFT and DFPT to obtain electron-phonon coupling matrix elements and then solving the linearized Boltzmann transport equation with three approaches: SERTA, MRTA, and an iterative BTE (IBTE). A methodological extension is presented in which the IBTE is solved separately for the response to an electric field and to a temperature gradient (Eqs. 20-21), yielding the Onsager coefficients L11, L12, L21, and L22 without imposing Onsager reciprocity (Eqs. 26-29). From these coefficients the authors obtain the electrical conductivity, Seebeck coefficient, electronic thermal conductivity, Peltier coefficient, and Lorenz number. Comparing with experiment, they find good agreement for sigma_xx, an overestimation of sigma_zz, and a Seebeck coefficient of the correct magnitude whose low-temperature sign depends on doping. They report a finite deviation between Pi_zz and T S_zz within the IBTE, and they conclude that the Wiedemann-Franz law is strongly violated, especially along the x direction. The paper includes rigid-band doping calculations in Appendix B and a discussion of the scattering operator in Appendix A.","tokens_in":15184,"tokens_out":4726,"duration_ms":40598,"significance":"If the central claim is established, the paper would be a valuable methodological contribution: it would show that a fully ab initio electron-phonon calculation can determine charge and heat transport in a topological semimetal, and it would provide a concrete test of Onsager reciprocity in an iterative Boltzmann solver. The double-IBTE formulation that allows L12 and L21 to differ is a potentially useful extension for systems without time-reversal symmetry, and the authors are careful to compare SERTA, MRTA, and IBTE results. The paper is also honest in reporting limitations of the rigid-band doping model. However, the headline quantitative claim of a 70% Wiedemann-Franz violation is not yet convincing because Onsager reciprocity is violated in the numerical results without any quantification of the residual or of convergence, and because key numerical details of the delta-function broadening and iterative convergence are missing. These gaps affect the central conclusion and must be addressed before the result can be regarded as a physical prediction.","major_comments":[{"comment":"The statement that 'Pi_zz shows finite deviation from T S_zz' is not quantified. The magnitude and temperature dependence of the deviation are not reported, nor is the convergence of the FE/FT iterative solution. Since S is computed from L12 (Eqs. 32-33) and kappa_el from L21*S (Eq. 36), any numerical asymmetry between L12 and L21 shifts both S and kappa_el, and therefore the Lorenz numbers in Tables I and II. Without a quantitative Onsager-residual check (e.g., |L12-L21|/|L12| as a function of iteration number and grid density), the claimed up-to-70% violation of the Wiedemann-Franz law is not established as a physical result. This is a load-bearing point for the paper's central conclusion.","section":"IV.E"},{"comment":"The iterative scheme in Eqs. 20-21 omits essential numerical details: the broadening width used for the energy-conserving delta functions delta_plus and delta_minus is not specified, and the convergence of the FE and FT iterations (number of iterations, stopping criterion) is not reported. The paper only states that room-temperature conductivities differ by 5% (x direction) and 20% (z direction) between 56^3 and 64^3 q-grids (Sec. IV.A), but does not report the sensitivity of S, kappa_el, or the individual Onsager coefficients to these parameters. Given that the claimed Wiedemann-Franz violation is a quantitative statement about Lxx/L0, these missing convergence checks are essential.","section":"III.C and IV.A"},{"comment":"The linearized scattering integral (Eq. A10) is the central operator of the IBTE, but its derivation is deferred: Appendix A states 'The derivation is quite lengthy and is not reported here, but more details can be found in [23].' For a paper that claims to derive an additional equation needed to fully solve transport under both electrical and thermal gradients, this is a significant gap. In particular, the linearization of the emission and absorption terms (Eqs. A8-A9) and the appearance of band indices m and n in delta f_{mk+q} in Eq. A10 need to be shown explicitly. The statement in Sec. III.C that the FT ansatz is 'not exact' due to a band mismatch raises the question of whether Eqs. 20-21 are exact solutions or an additional approximation, and the appendix does not resolve this.","section":"Appendix A"}],"minor_comments":[{"comment":"There is a typo in the sentence beginning 'In should be noted' in the paragraph after Eq. 14; it should read 'It should be noted'.","section":"III.B"},{"comment":"The figure captions contain 'T emperature' instead of 'Temperature' in several places; please correct this throughout.","section":"Figures 3-9"},{"comment":"In the legend, 'IBTE = TS' is used, while the text uses 'Pi = T S'; please make the notation consistent so the reader knows which quantity is plotted.","section":"IV.E, Figure 6"},{"comment":"The relation between the 8x8x8 q-point grid used for phonons and the 64x64x64 q-point grid used for scattering potentials should be clarified; the former is presumably the DFPT grid, while the latter is the interpolation grid for the EPC matrix elements.","section":"I.B"},{"comment":"References [31] and [32] are the same publication (Madsen, Carrete, and Verstraete, Comput. Phys. Commun. 231, 140 (2018)); please cite it only once.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses a topic of broad interest in first-principles transport and has a solid methodological core. The main obstacle to acceptance is the unquantified Onsager violation in the IBTE results, which directly affects the Wiedemann-Franz claim. I would encourage the editor to request the Onsager residual and convergence data as part of the revision, rather than to reject the manuscript on this basis."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Things to know: this is a solid, technically detailed first-principles transport paper, not a flashy claim. It goes beyond Peng et al.'s cRTA by computing full e-ph matrix elements and solving the iterative BTE, giving sigma, S, kappa_el, Pi, and Lorenz numbers for TaAs. The central result—strong WF violation in the x direction between 150 and 350 K—holds irrespective of the BTE solver: SERTA, MRTA, and IBTE all give Lxx/L0 around 1.7 at 200 K. So the stress-test concern that the violation might be an IBTE convergence artifact doesn't survive contact with the paper. The RTA methods enforce Onsager reciprocity and still produce the same violation.\n\nWhat's genuinely new: the separate iterative equations for the E and grad-T drives (Eqs. 20-21), which let L12 differ from L21 and in principle extend to magnetic systems. That's a useful methodological step, but note it is not actually demonstrated for a time-reversal-broken material.\n\nWhere the paper is soft: first, the Onsager residual is never quantified. The authors state that Pi_zz differs from T S_zz and blame numerics, but they don't report the deviation or show the FE/FT iteration convergence. Since S and kappa_el are built from L12 and L21, a large residual would propagate into the Lorenz number. This is a real omission, though the RTA agreement makes it unlikely to be the source of the WF violation. Second, the delta-function broadening is unspecified, and the z-axis conductivity converges only to 20% between the two finest grids. Third, the linearized scattering operator is deferred to Ref. [23] and not derived in Appendix A. Fourth, no code or data are released. Fifth, the rigid-band doping in Appendix B is explicitly post hoc—it can flip the Seebeck sign but doesn't simultaneously fix sigma, and the authors say so. The magnetic-material capability is claimed but not tested.\n\nThe comparison with experiment is honest, not cherry-picked: sigma_xx matches well, sigma_zz overestimated, S same order but with sign issues at low T. The paper's own discussion of these limitations is fair.\n\nWho should read it: anyone computing or measuring thermoelectric transport in semimetals, and people working on e-ph BTE implementations. It deserves a serious referee. My recommendation: send it to review, with the request that the authors quantify the Onsager residual, give the smearing parameter and convergence criteria, and, ideally, release input files and data.","headline":"First full e-ph BTE transport coefficients for TaAs, with a genuine Wiedemann-Franz violation that is consistent across RTA and IBTE; the unquantified Onsager residual is a real but secondary issue.","tokens_in":15759,"tokens_out":4130,"would_cite":true,"duration_ms":37174,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A first-principles electron-phonon calculation reproduces the measured in-plane conductivity of the Weyl semimetal TaAs and predicts a strong breakdown of the Wiedemann–Franz law between 150 K and 350 K.","keywords":["Weyl semimetal","TaAs","electron-phonon coupling","Boltzmann transport equation","thermoelectric transport","Seebeck coefficient","Wiedemann-Franz law","Onsager reciprocity"],"falsifier":"A direct measurement of the in-plane electronic thermal conductivity of TaAs between 150 and 350 K, not inferred through the Wiedemann–Franz law, would settle the central claim: the paper predicts the Lorenz ratio rises to about 1.7 times the Sommerfeld value along $x$, so a measured value near the Sommerfeld value would refute it.","tokens_in":1614,"feed_emoji":"⚡","tokens_out":2574,"duration_ms":94849,"temperature":0.7,"pith_summary":"This paper sets out to show that thermoelectric transport in TaAs, a topological Weyl semimetal in which electrons behave as massless chiral fermions, can be computed from first principles with no fitted parameters, using only the electronic structure and electron-phonon coupling. If the claim holds, semimetals no longer need the constant relaxation time approximation, and transport calculations can reach magnetic materials where Onsager reciprocity—the symmetry that ties the Peltier coefficient to the Seebeck coefficient—is not imposed. The calculation matches the measured in-plane conductivity, gives the Seebeck coefficient at the right order of magnitude, and predicts that the Wiedemann–Franz law, the rule linking electronic heat conduction to electrical conduction, breaks down between 150 K and 350 K.","feed_headline":"TaAs breaks Wiedemann–Franz law from 150 to 350 K","feed_subtitle":"First-principles electron-phonon transport matches measured conductivity and enables magnetic thermoelectrics.","key_machinery":"The central object is a pair of iterative Boltzmann transport equations, one for the electric-field response function $F^E$ and one for the thermal-gradient response function $F^T$, coupled through the same electron-phonon scattering kernel built from matrix elements $g_{mn\\nu}(\\mathbf{k}, \\mathbf{q})$. The iterative scheme supplies the Onsager coefficients $L_{11}$, $L_{12}$, $L_{21}$, and $L_{22}$ independently, so the Seebeck coefficient $S = L_{12}/(T L_{11})$ and the Peltier coefficient $\\Pi = L_{21}/L_{11}$ need not satisfy $\\Pi = T S$. This structure is what lets the electrical and thermal responses be solved on the same footing, and it is what makes the calculation applicable to magnetic systems.","core_discovery":"The authors' central claim is that solving the linearized Boltzmann transport equation with electron-phonon scattering computed from density functional perturbation theory gives the full thermoelectric response of TaAs: electrical conductivity, Seebeck coefficient, electronic thermal conductivity, and Peltier coefficient. The computed in-plane conductivity $\\sigma_{xx}$ agrees with experiment over the measured range, while $\\sigma_{zz}$ is overestimated, a discrepancy attributed to differences in carrier concentration. The Seebeck coefficient has the right order of magnitude and its low-temperature sign is controlled by doping. The paper also reports Lorenz numbers $L_{xx}/L_0$ reaching about 1.7 between 150 K and 350 K, so the Wiedemann–Franz law is strongly violated in-plane; along $z$ the ratio sits below 1. For the method, the authors derive a second iterative equation for the thermal-gradient response, so $L_{12}$ and $L_{21}$ are computed independently and Onsager reciprocity is not imposed.","pith_inferences":["A natural next test would be computing the same transport coefficients with a self-consistent treatment of doping, including band renormalization, rather than rigid-band shifts; this could close the remaining $\\sigma_{zz}$ and Seebeck-sign discrepancies.","Applying the double-IBTE method to a magnetic Weyl semimetal with broken time-reversal symmetry would directly demonstrate the claimed difference between $L_{12}$ and $L_{21}$, a calculation the paper does not perform.","The predicted in-plane Lorenz-number enhancement suggests a clean experimental probe: direct thermal-conductivity measurements that separate phonon and electron contributions could test the topological origin of the Wiedemann–Franz violation."],"forward_implications":["Because the calculation includes the full electron-phonon scattering kernel, the constant relaxation time approximation is not needed for semimetals; the in-plane conductivity of TaAs is reproduced without adjustable parameters.","Experimental estimates of the electronic thermal conductivity of TaAs that use the Sommerfeld Lorenz number will be off by up to roughly 70% in-plane between 150 and 350 K, since the computed Lorenz number deviates from $L_0$.","The double iterative Boltzmann scheme, which does not enforce Onsager reciprocity, extends the same first-principles transport calculation to magnetic materials that break time-reversal symmetry.","The sign and low-temperature magnitude of the Seebeck coefficient are controlled by doping, so measurements on samples with known carrier concentration should track the computed rigid-band trends."],"supporting_citations":[{"why":"Supplies the experimental conductivity, Seebeck, thermal conductivity, and Hall data used for comparison.","marker":"[3]"},{"why":"Provides the second experimental conductivity data set and the chiral-anomaly context.","marker":"[1]"},{"why":"Is the earlier constant-relaxation-time transport calculation whose approximation this work replaces.","marker":"[7]"},{"why":"Gives the electron-phonon coupling and self-energy formalism behind the scattering rates.","marker":"[20]"},{"why":"Provides the linearized scattering integral and iterative BTE framework that the double IBTE extends.","marker":"[23]"},{"why":"Introduces the separate electric-field and thermal-gradient decomposition of the distribution function used in Eqs. (20) and (21).","marker":"[26]"},{"why":"Supplies the constant-relaxation-time Hall coefficient calculation against which the measured anisotropy is compared.","marker":"[32]"},{"why":"Documents the electron-phonon transport implementation and RTA/IBTE workflows the numerical results depend on.","marker":"[22]"}],"fun_headline_variants":["First-principles TaAs transport breaks Wiedemann–Franz law","Weyl semimetal TaAs defies Wiedemann–Franz law from 150 K","New transport method for magnetic thermoelectrics in TaAs","TaAs electron-phonon theory nails in-plane conductivity","Magnetic thermoelectrics from first-principles without Onsager"],"cache_read_input_tokens":17920,"weakest_assumption_plain":"The load-bearing premise is that natural doping in real TaAs crystals only shifts the Fermi level, leaving the band structure and scattering unchanged; if the actual carrier concentrations or band renormalization are different, the model cannot fix the two main disagreements with experiment.","fun_headline_variants_meta":{"raw":{"variants":["First-principles TaAs transport breaks Wiedemann–Franz law","Weyl semimetal TaAs defies Wiedemann–Franz law from 150 K","New transport method for magnetic thermoelectrics in TaAs","TaAs electron-phonon theory nails in-plane conductivity","Magnetic thermoelectrics from first-principles without Onsager"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000458,"raw_usage":{"total_tokens":2306,"prompt_tokens":964,"completion_tokens":1342,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":580,"completion_tokens_details":{"reasoning_tokens":1246}},"tokens_in":580,"tokens_out":1342,"duration_ms":11612,"temperature":1.0,"reasoning_tokens":1246,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T15:16:37.712545+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct measurement of the in-plane electronic thermal conductivity of TaAs between 150 and 350 K, not inferred through the Wiedemann–Franz law, would settle the central claim: the paper predicts the Lorenz ratio rises to about 1.7 times the Sommerfeld value along $x$, so a measured value near the Sommerfeld value would refute it.","supporting_citations":[{"cited_title":"Xiang, S","cited_arxiv_id":null,"evidence_quote":"Supplies the experimental conductivity, Seebeck, thermal conductivity, and Hall data used for comparison."},{"cited_title":"Huang, L","cited_arxiv_id":null,"evidence_quote":"Provides the second experimental conductivity data set and the chiral-anomaly context."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Is the earlier constant-relaxation-time transport calculation whose approximation this work replaces."},{"cited_title":"Ponc´ e, W","cited_arxiv_id":null,"evidence_quote":"Provides the linearized scattering integral and iterative BTE framework that the double IBTE extends."},{"cited_title":"Fiorentini and N","cited_arxiv_id":null,"evidence_quote":"Introduces the separate electric-field and thermal-gradient decomposition of the distribution function used in Eqs. (20) and (21)."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the constant-relaxation-time Hall coefficient calculation against which the measured anisotropy is compared."},{"cited_title":"Claes, G","cited_arxiv_id":null,"evidence_quote":"Documents the electron-phonon transport implementation and RTA/IBTE workflows the numerical results depend on."}],"review_version":1}