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First-principles calculations of transport coefficients in Weyl semimetal TaAs

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2505.15522 v1 pith:7D7Z4LXK submitted 2025-05-21 cond-mat.mtrl-sci cond-mat.other

Guillaume E. Allemand , Matteo Giantomassi , Matthieu J. Verstraete This is my paper · ORCID
classification cond-mat.mtrl-scicond-mat.other
keywords WeylsemimetalTaAselectron-phononcouplingBoltzmanntransportequationthermoelectricSeebeckcoefficientWiedemann-FranzlawOnsagerreciprocity
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 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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

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

  • 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.
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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 / 5 minor

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.

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 (3)
  1. [IV.E] 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.
  2. [III.C and IV.A] 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.
  3. [Appendix A] 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.
minor comments (5)
  1. [III.B] 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'.
  2. [Figures 3-9] The figure captions contain 'T emperature' instead of 'Temperature' in several places; please correct this throughout.
  3. [IV.E, Figure 6] 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.
  4. [I.B] 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.
  5. [References] References [31] and [32] are the same publication (Madsen, Carrete, and Verstraete, Comput. Phys. Commun. 231, 140 (2018)); please cite it only once.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: transport coefficients are computed ab initio with no fitted parameters; self-citations are methodological and not load-bearing.

full rationale

Walking the derivation chain: the paper computes electron-phonon matrix elements from DFPT, solves the linearized BTE in SERTA, MRTA, and IBTE, and forms the Onsager coefficients via Eqs. 26-29. The transport coefficients S, kappa_el, and Pi are then obtained from the defining relations in Eqs. 30-38. Nothing in this chain is fitted to the experimental sigma, S, or kappa_el values used for comparison; experimental data enter only after the calculations as benchmarks. The rigid-band doping shifts in Appendix B are exploratory: the paper chooses two concentrations and explicitly concludes that rigid-band doping cannot simultaneously explain S and sigma, so the doping study is not a fitted input renamed as a prediction. Self-citations to the ABINIT EPH module (Refs. 21, 22) and to prior work on cRTA failure (Ref. 8) support the numerical methodology but are not used to justify the central physical claim; the implementation is open-source and the electronic and phonon band structures are checked against independent calculations and experiments. The paper also discloses the two limitations that a circularity critique would target: the IBTE Onsager residual in Sec. IV.E, where it states that differences 'could be caused by numerical effects,' and the fact that the experimental kappa_el of Ref. 3 assumes the Wiedemann-Franz law. These are accuracy caveats, not circular reasoning. No step reduces, by construction, to its own input.

Assumptions & free parameters 3 free parameters · 7 assumptions · 0 invented entities

The central calculation leans on standard BTE and DFPT machinery, but the quantitative claims inherit several unverified modeling choices: GGA-PBE band structure, e-ph-only scattering, equilibrium phonons, rigid-band doping, and an unspecified smearing width. Of these, the rigid-band doping is the only ingredient tuned post hoc to data, used to rationalize the experimental Seebeck sign.

free parameters (3)
  • Rigid-band p-type doping concentration = 0, +1e19, +5e19 cm^-3
    Applied in Appendix B to shift the chemical potential and test whether natural doping explains the experimental Seebeck sign; these levels are chosen post hoc to reproduce the observed positive Sxx at low T.
  • Energy window around the Fermi level = 0.25 eV
    Only Kohn-Sham states within this window are retained for EPC and transport; this filters the Brillouin zone to 3178 k-points and 4 bands and affects convergence.
  • Delta-function broadening width = not reported
    The energy-conserving delta functions in Eqs. 16, 20, and 21 require a finite smearing in numerical integration; the paper does not state its value, and transport coefficients are sensitive to it.
assumptions (7)
  • domain assumption Phonons stay in thermal equilibrium and follow the Bose-Einstein distribution n0(omega).
    Stated in Appendix A after Eq. A14; this excludes phonon drag and the coupled phonon Boltzmann equation, yet underpins the temperature dependence of all transport coefficients.
  • domain assumption Electron-phonon scattering is the only operative scattering mechanism.
    The scattering integral in Eq. A5 contains only e-ph coupling; impurity, defect, and electron-electron scattering are neglected, which is questionable at low temperature where measured transport is impurity-dominated.
  • domain assumption Quasiparticles are well defined: the spectral function is strongly peaked around epsilon_nk.
    Assumed at the start of Section III.A to justify the BTE; this breaks down if e-ph coupling is strong enough to produce broad spectral functions.
  • domain assumption GGA-PBE with spin-orbit coupling gives an accurate band structure and Fermi surface for TaAs.
    All velocities and EPC matrix elements derive from this band structure; the sigma_zz overestimate and anisotropic Hall coefficient indicate possible band-structure error beyond doping.
  • ad hoc to paper Doping only shifts the chemical potential and does not modify the band structure (rigid-band approximation).
    Used throughout Appendix B to simulate p-type doping; ignores screening, band renormalization, and impurity scattering.
  • domain assumption The iterative IBTE scheme converges to the solution of the linearized BTE.
    Rules 20-21 are iterated to self-consistency, but no convergence test for the iteration itself is reported; the initial FT guess is acknowledged not to be exact in the IBTE case.
  • standard math Fermi's golden rule applies to electron-phonon scattering.
    Used to derive the scattering rates in Eqs. 16-17 and A5.

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Pith. "Pith review of First-principles calculations of transport coefficients in Weyl semimetal TaAs." pith.science (2026). https://pith.science/paper/7D7Z4LXK

@misc{pith2026250515522,
  author       = {Pith},
  title        = {Pith review of: First-principles calculations of transport coefficients in Weyl semimetal TaAs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7D7Z4LXK}},
  note         = {Machine review of arXiv:2505.15522}
}
abstract

We study charge and heat transport from first-principles in the topological Weyl semimetal TaAs. Electron-phonon coupling matrix elements are calculated using density functional perturbation theory and used to derive the thermo-electric transport coefficients, including the electrical conductivity, Seebeck coefficient, electronic thermal conductivity and the Peltier coefficient. We compare the self-energy and momentum relaxation time approximations to the iterative solution of the Boltzmann Transport Equation, finding they give similar results for TaAs provided the chemical potential is treated accurately. For the iterative method, we derive an additional equation, which is needed to fully solve for transport under both thermal and an electrical potential gradients. Interestingly, the Onsager reciprocity between $S$ and $\Pi$ is no longer imposed, and we can deal with systems breaking time-reversal symmetry, in particular magnetic materials. We compare our results with the available experimental data for TaAs: the agreement is excellent for $\sigma_{xx}$, while $\sigma_{zz}$ is overestimated, probably due to differences in experimental carrier concentrations. The Seebeck coefficient is of the same order of magnitude in theory and experiments, and we find that its low-T behavior also strongly depends on the doping level.

Figures

Figures reproduced from arXiv: 2505.15522 by the authors.

Figure 1
Figure 1. Electronic band structure of TaAs within [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Phonon dispersion curve of TaAs. The green [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Temperature dependence of the xx and zz components of the electrical conductivity, calculated using RTA and IBTE methods. Experimental data come from [1] and [3] [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Temperature dependence of the xx and zz components of the Seebeck coefficient, calculated using RTA and IBTE methods. Experimental data come from [3]. The results are shown in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Temperature dependence of the xx and zz components of the electronic thermal conductivities, calculated using RTA and IBTE methods. Experimental data come from [3]. the IBTE framework, imposing ∇T = 0: Π = j Q j e = L21 · E − L22 · ∇T T L11 · E − L12 · ∇T T = L21 L11 .…
Figure 7
Figure 7. Figure 7: Temperature dependence of the xx and zz components of the electrical conductivity, calculated using RTA and IBTE methods, considering a simulated doping within the rigid band approximation of +1 1019 electronic charges per cm3 (p-type doping). Experimental data come fr…
Figure 8
Figure 8. Figure 8: Temperature dependence of the x component [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: Temperature dependence of the x component [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]

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