{"id":"a8f55f84-45e8-4d2a-8de0-ed8c75ffd411","arxiv_id":"2501.04498","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Closed-form electric, thermoelectric, and thermal conductivities up to third order in magnetic field are derived for pseudospin-1 triple-point semimetals, including out-of-plane anomalous Hall and Lorentz-force currents.","lead":"This paper derives formulas for how electricity and heat flow through a class of crystals where three electron bands meet at points, when a weak magnetic field is present. The results could help experimentalists interpret planar Hall and thermal Hall measurements in multifold semimetals such as CoSi.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The flat band's nonzero orbital magnetic moment is dropped without proof, although Eq. (7) plus Eq. (9) implies an OMM-induced Fermi surface for positive chemical potential, so the completeness claim is not yet established.","rationale":"The reader's weakest-assumption analysis identifies the flat-band OMM neglect as the core gap, and my independent reading agrees. The paper explicitly computes a nonzero OMM for the flat band in Eq. (7), then drops the band with a one-sentence remark that applies only when the OMM is zero. In the presence of the OMM, the effective dispersion xi_0 = -B.m_0 is not zero, and because the bare dispersion is exactly zero, the OMM energy is not a small perturbation anywhere on the band. For the simplest J=1 node, xi_0 has the form of a dipolar potential in k-space, so the equation xi_0=mu has solutions for any mu>0 and B>0; this means the flat band is not simply empty. The paper's completeness assertion therefore rests on an unproven cancellation. This is a concrete, checkable assumption rather than a stylistic or consensus-based objection. The proposed numerical integral of the flat-band Boltzmann term is a direct test: a nonzero result would require revising the claimed completeness, while a zero result (or a principled reason that the flat band is outside the semiclassical regime) would close the gap. For these reasons I retain the reader's CONDITIONAL verdict and do not adjust it.","tokens_in":25034,"tokens_out":7206,"duration_ms":78255,"concrete_test":"Evaluate the flat-band contribution to the longitudinal magnetoconductivity at O(B^2) from Eq. (16) without expanding f0 in B: compute sigma_xx^(s=0) = -e^2 tau integral d^3k/(2pi)^3 (w_0)_x (w_0)_x f'_0(xi_0), where xi_0 = -B.m_0 with m_0 from Eq. (7) and w_0 = grad(xi_0), for the J=1, chi=1 node with v_z=v_perp=1, mu=1, B=0.01 along x, and T=0.01. If this integral is nonzero (or diverges), the flat-band neglect is unjustified and the response tensors are incomplete. If the authors instead claim the semiclassical OMM dispersion is invalid for an exactly flat band, that claim should be stated and justified explicitly, since the paper currently offers no such argument.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is that all nonzero components of the linear-response tensors are computed up to O(B^3). This requires the s=0 flat band to contribute nothing. The only justification, given after Eq. (7), is that the flat band has zero dispersion and zero Berry curvature, so it gives zero conductivity when the OMM is ignored; the band is then 'neglected' for all subsequent linear-response calculations. That inference does not follow once the OMM is included, because Eq. (7) assigns the flat band a nonzero OMM, twice that of the dispersive bands, and this OMM enters the effective dispersion via Eq. (9), xi_0(k) = -B.m_0(k). Since epsilon_0(k)=0 identically, the weak-field condition |epsilon_m| << |epsilon_s| in Eq. (12) is violated on the entire flat band, so the perturbative expansion in B used elsewhere is not controlled here. More concretely, for the J=1, chi=1 case, m_0 is proportional to -k/k^2, giving xi_0 = v B.k/k^2. For any positive chemical potential mu and any nonzero B, the surface xi_0(k)=mu exists, i.e. the OMM shifts part of the flat band below the chemical potential, creating a Fermi surface of size set by B/mu. The Boltzmann integrands in Eq. (16) then contain w_0 = grad(xi_0) ~ B/k^2 and the occupation derivative f'_0(xi_0) peaked on this surface; the paper provides no argument that these integrals vanish. Since the completeness claim is the strongest assertion in the paper, this gap is load-bearing. The later sentence in Sec. VI, 'we have omitted their contributions, if any,' explicitly acknowledges that the flat-band contribution was not evaluated.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript derives closed-form semiclassical linear-response expressions for electric, thermoelectric, and thermal transport in planar-Hall and planar-thermal-Hall setups for pseudospin-1 triple-point semimetals. The calculation includes Berry curvature and orbital magnetic moment on equal footing, expands in powers of the weak magnetic field up to O(B^3), and gives explicit results for longitudinal, in-plane transverse, and out-of-plane anomalous-Hall/Lorentz-force components of the conductivity, together with formulas for the magnetothermoelectric conductivity and magnetothermal coefficient and for internode-scattering contributions. The results are compared with earlier results for Weyl/multi-Weyl and Rarita-Schwinger-Weyl semimetals.","tokens_in":25360,"tokens_out":9714,"duration_ms":103960,"significance":"If the completeness claims were fully justified, the paper would provide a useful analytic reference for magnetotransport experiments on multifold fermion materials, particularly in connection with the recent experiment cited as Ref. [8]. The paper's strengths are its systematic use of a standard Boltzmann formalism, explicit closed-form coefficients, and direct comparisons with the Weyl/multi-Weyl and Rarita-Schwinger-Weyl cases; no fitting to data is involved, and the Mott-relation and Wiedemann-Franz checks for the in-plane components are a valuable internal consistency test. However, the announced completeness is weakened by two gaps: the flat band is dismissed without a controlled argument once the OMM is included, and the thermoelectric/thermal tensors are only given for the in-plane, non-anomalous, non-Lorentz-force parts. These gaps affect the central claim that 'all nonzero components' have been chalked out.","major_comments":[{"comment":"The flat-band omission is not justified once the orbital magnetic moment is included. Eq. (7) gives Omega_0=0 but m_0(k) nonzero, with G_0=2, so Eq. (9) yields xi_0(k) = -B.m_0(k) while epsilon_0(k)=0. The weak-field condition |epsilon^{(m)}| << |epsilon_s| in Eq. (12) is therefore violated on the entire flat band, and the expansion in Eq. (13) has no controlled small parameter there. For J=1 the shift xi_0(k) is direction-dependent and independent of |k| for fixed direction, so the equilibrium Fermi factor f_0(xi_0) is not confined to small |k|, and no symmetry argument is supplied to show that the integrals in Eq. (16) vanish for s=0. The text after Eq. (7) only proves that the flat band gives zero conductivity when the OMM is ignored, which is precisely the case not under study. Since Sec. VI explicitly concedes that flat-band contributions were 'omitted ... if any', the claim to have computed all nonzero components up to O(B^3) is not established. Please either evaluate the flat-band contribution using Eqs. (16)-(19) with s=0 and a regularization/cutoff, or rigorously prove that it vanishes, or explicitly restrict the claim to the dispersive bands.","section":"Sec. II A, Eq. (7), Eq. (9), Eq. (12), Sec. VI"},{"comment":"The abstract and Sec. VI claim that all nonzero components of the linear-response tensors have been determined, but the paper explicitly limits the magnetothermoelectric conductivity and magnetothermal coefficient to in-plane components. The sentence after Eq. (21) states that only the in-plane components 'which arise from the non-anomalous-Hall and non-Lorentz-force parts' will be shown, and Eqs. (39)-(42) contain no out-of-plane alpha or ell components. The Mott-relation and Wiedemann-Franz verification in Sec. IV C is likewise restricted to the in-plane tensors. Thus the completeness claim for alpha and ell is not supported by the presented results. The authors should either compute the missing out-of-plane and anomalous/Lorentz-force contributions to alpha and ell, or revise the wording of the abstract and summary so that the claim matches what is actually derived.","section":"Sec. II C, Sec. IV, Sec. VI"},{"comment":"The paper announces results correct up to O(B^3), but the expansion displayed in Eq. (13) stops at O(B^2) for the distribution function, showing only the quadratic term in epsilon^{(m)}. The cubic term involving f'''_0 is introduced later, in Sec. III C, when the anomalous-Hall contribution is computed. This is not a fatal error, but it makes the order-by-order bookkeeping difficult to follow and should be reconciled, either by including the f'''_0 term in Eq. (13) or by explicitly labeling Eq. (13) as the expansion needed for the in-plane even-in-B response.","section":"Eq. (13), Sec. III C"}],"minor_comments":[{"comment":"There is a typo in Appendix A: 'checmical potential' should be 'chemical potential'.","section":"Appendix A"},{"comment":"The headings 'T erms originating...' and 'Wiedemann-F ranz law' contain spacing typos; 'Terms' and 'Wiedemann-Franz' are intended.","section":"Appendix B, Sec. IV"},{"comment":"The caption contains 'under the actional of a nonquantizing magnetic field'; 'action' is intended.","section":"Fig. 1 caption"},{"comment":"The phrase 'we have omitted their contributions, if any' is in tension with the earlier categorical statement that the flat band is neglected; please resolve this ambiguity, ideally after performing the flat-band check requested above.","section":"Sec. VI"},{"comment":"In the discussion of sign changes, the statement 'for all values of J, the addition of the OMM does not change the sign of the overall response' is immediately followed by a case in which the OMM flips the sign for J=1; the text should clarify that the first statement refers to the B_x^2 term and the second to the B_y^2 term.","section":"Sec. III A"}],"recommendation":"major_revision","confidential_remarks":"The underlying Boltzmann calculation for the dispersive bands appears sound and incremental in the best sense, but the paper's completeness claims need to be brought in line with what is actually computed. The flat-band OMM issue is the one I would treat as load-bearing: the manuscript itself flags the omission only in passing, and the released text gives no symmetry argument. The missing out-of-plane alpha/ell components are a second, more easily fixable scope issue. I would be comfortable with acceptance after these points are resolved, but not before."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nHere's my take on arXiv:2501.04498. It is a competent, incremental extension of the authors' earlier Boltzmann-transport analysis to pseudospin-1 triple-point semimetals. The new content that matters is the inclusion of the orbital magnetic moment in the planar Hall and thermal Hall tensors, the out-of-plane anomalous-Hall and Lorentz-force components, and the internode-scattering result for two opposite-chirality TSM nodes. The in-plane formulas are structural analogues of the Weyl/multi-Weyl results, which is expected given the same semiclassical framework. The derivations are standard, and the final expressions are plausible; the appendices give enough intermediate steps for a specialist to follow, though several final integrals are asserted without being shown.\n\nThe real problem is the flat band. Equation (7) gives the s=0 band an OMM twice that of the dispersive bands. The effective dispersion is xi_0 = -B.m_0, which is not zero. For any positive chemical potential and any nonzero B, the surface xi_0 = mu exists, so the flat band acquires a Fermi surface whose size is set by B/mu. The paper drops the flat band after Eq. (7) with the argument that zero dispersion and zero Berry curvature give zero conductivity when the OMM is ignored. That argument stops working once the OMM is present. The summary section even says 'we have omitted their contributions, if any,' which concedes the point. Because the paper's central claim is completeness—'all the nonzero components'—this is a load-bearing gap. The weak-field condition of Eq. (12) is not satisfied on the flat band, since epsilon_0=0, so the perturbative expansion is not controlled there. A referee should ask for an explicit estimate of the flat-band contribution, or a symmetry/selection-rule argument that it vanishes, before accepting the completeness claim.\n\nThe citation pattern is heavily self-referential, but that is not a flaw here because the framework genuinely comes from their own prior work. No code or numerical check is included; that lowers confidence in the final integrals but is not disqualifying for an analytical paper.\n\nVerdict: this deserves refereeing, not desk rejection. The in-plane dispersive-band results are likely usable, and experimental groups working on multifold fermions (CoSi etc.) will want to cite them. But the current version overstates completeness, and the flat-band question must be resolved in revision.\n\nBest.","headline":"Competent incremental transport theory for pseudospin-1 semimetals, but the flat band's nonzero OMM breaks the completeness claim.","tokens_in":25969,"tokens_out":3318,"would_cite":true,"duration_ms":32339,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"For pseudospin-1 triple-point semimetals, this paper derives all weak-field electric, thermoelectric, and thermal response tensors to third order in the magnetic field, including Berry curvature, orbital magnetic moment, anomalous-Hall…","keywords":["planar Hall effect","planar thermal Hall effect","pseudospin-1 fermions","triple-point semimetal","Berry curvature","orbital magnetic moment","anomalous Hall effect","internode scattering"],"falsifier":"Evaluate the flat-band (s=0) terms in the Boltzmann integrals of Eqs. (16)-(21) using the orbital magnetic moment from Eq. (7), and look for any nonzero component through O($B^{3}$); finding one would refute the paper's claim that all nonzero linear-response tensors for a pseudospin-1 node have been enumerated.","tokens_in":24765,"feed_emoji":"🧲","tokens_out":11909,"duration_ms":107266,"temperature":0.7,"pith_summary":"The paper sets out to establish that, for a single pseudospin-1 triple-point node — a three-dimensional semimetal point where three bands cross — every linear-response coefficient appearing in the planar-Hall and planar-thermal-Hall geometries is known explicitly through third order in a weak magnetic field. It treats the Berry curvature and the orbital magnetic moment on equal footing in a semiclassical Boltzmann calculation, and it includes the out-of-plane anomalous-Hall and Lorentz-force currents plus the effect of scattering between nodes of opposite chirality. A sympathetic reader would take the central claim to be completeness: for the pseudospin-1 case, the nonzero components of the magnetoelectric, magnetothermoelectric, and magnetothermal tensors are now listed component by component. The payoff is a set of analytic formulas with which angular-resolved magnetotransport data on multifold semimetals can be compared directly.","feed_headline":"All planar-Hall response tensors for three-band nodes are now explicit","feed_subtitle":"All nonzero electric, thermoelectric, and thermal coefficients are given through third order in the magnetic field.","key_machinery":"The load-bearing object is the pseudospin-1 Hamiltonian $H_\\chi(\\mathbf{k}) = \\mathbf{d}(\\mathbf{k})\\cdot\\mathbf{S}$, whose spin-1 representation gives three bands with energies $\\varepsilon_s = s\\,\\epsilon_k$ for $s=-1,0,1$, including a dispersionless flat band. The machinery is the semiclassical Boltzmann linear-response formalism: a phase-space factor $D_\\chi = (1 + e\\,\\mathbf{B}\\cdot\\boldsymbol{\\Omega}_\\chi)^{-1}$, an orbital-magnetic-moment-shifted dispersion $\\xi = \\varepsilon - \\mathbf{B}\\cdot\\mathbf{m}$, the correspondingly modified group velocity, the anomalous-Hall current built from $\\mathbf{E}\\times\\boldsymbol{\\Omega}$, and the Lorentz-force operator $\\check{L} = (\\mathbf{w}\\times\\mathbf{B})\\cdot\\nabla_k$ iterated to third order. These ingredients are expanded in $B$, integrated with Sommerfeld expansions, and assembled into the three response tensors $\\sigma_\\chi$, $\\alpha_\\chi$, and $\\ell_\\chi$, with the flat band neglected after Eq. (7).","core_discovery":"The paper's central result is a full enumeration, to $O(B^3)$, of the nonzero components of the electric, thermoelectric, and thermal response tensors for a pseudospin-1 node described by $H_\\chi(\\mathbf{k}) = \\mathbf{d}(\\mathbf{k})\\cdot\\mathbf{S}$ with $\\mathbf{d}(\\mathbf{k}) = (\\alpha_J k_\\perp^J \\cos(J\\phi), \\alpha_J k_\\perp^J \\sin(J\\phi), \\chi v_z k_z)$. The in-plane parts contain only even powers of $B$ and receive $B^2$ corrections from the Berry curvature and the orbital magnetic moment, whose coefficients are given as functions of the integer $J=1,2,3$; these two corrections can oppose each other, and for $J=1$ the orbital-moment term flips the sign of the $B_y^2$ longitudinal coefficient. The out-of-plane parts are odd in $B$ and combine the intrinsic anomalous-Hall current with the Lorentz-force Hall current, and internode scattering between conjugate nodes adds $B_x^2$ and $B_x B_y$ components proportional to the difference between the internode and intranode relaxation times. The paper also verifies that the Mott relation and the Wiedemann-Franz law hold within the computed tensors.","pith_inferences":["An implicit next step the paper does not take is to include the flat band's nonzero orbital magnetic moment, twice that of the dispersive bands, in the same Boltzmann integrals; a nonzero current there would alter the claimed complete tensors.","The same expansion machinery would likely produce linear-in-B in-plane terms if the node were tilted or strained, as the paper notes for related semimetal classes; that would be a testable extension of the present formulas.","The sign patterns of the derived coefficients, such as the negative squared-field orbital-moment coefficient for all J, could serve as fingerprints in angular-resolved magnetotransport on candidate materials, which the paper motivates but does not itself perform.","The O(B^3) results set a quantitative baseline against which future strong-field Landau-level transport in triple-point semimetals can be compared, since the weak-field limit is the regime where the present semiclassical expansion applies."],"forward_implications":["If the paper is correct, the full angular dependence of the planar magnetoconductivity, thermoelectric conductivity, and thermal conductivity is known analytically for any J=1,2,3 pseudospin-1 node, not just its symmetry class.","The out-of-plane anomalous-Hall and Lorentz-force conductivities are odd in B and linear in the in-plane field component along y, so an in-plane field produces a z-directed voltage whose magnitude and sign depend on the node chirality and on J.","The orbital-magnetic-moment corrections can flip the sign of the squared-field longitudinal coefficient for J=1 but not for J=2 or 3, giving a specific material-dependent prediction.","Because the Mott relation and Wiedemann-Franz law survive, the thermal tensors can be inferred from the electric one, extending the usefulness of electrical measurements.","Internode scattering adds contributions proportional to the difference between internode and intranode relaxation times in the longitudinal and planar-Hall components, separating chiral-anomaly-driven transfer between nodes from intranode topological transport."],"supporting_citations":[{"why":"Supplies the Berry-curvature and orbital-magnetic-moment formulas that define Omega and m in Eq. (6).","marker":"[27, 87]"},{"why":"Provides the linear-response framework and the Rarita-Schwinger-Weyl node comparison against which the TSM results are checked.","marker":"[25]"},{"why":"Gives the generic in-plane response expressions, Sommerfeld-integral identities, and WSM/mWSM comparison values used throughout.","marker":"[33]"},{"why":"Earlier treatment of a quadratic (J=2) triple-component node without orbital magnetic moment that this paper extends to all J and to OMM effects.","marker":"[46]"},{"why":"Supplies the internode-scattering theory that Section V specializes to a pair of pseudospin-1 nodes.","marker":"[84]"},{"why":"Provides the standard Boltzmann and Sommerfeld identities used to evaluate the Fermi-surface integrals.","marker":"[89]"},{"why":"The experimental study of multifold fermions whose O(B^3) fitting motivates the truncation order and the practical relevance of the results.","marker":"[8]"}],"fun_headline_variants":["Planar-Hall tensors for pseudospin-1 nodes fully enumerated","All response tensors for three-band semimetals to third order in B","Out-of-plane and scattering effects now in planar-Hall response","Pseudospin-1 semimetal response tensors complete through B^3"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes the s=0 flat band produces no current up to third order in B even though its orbital magnetic moment is twice that of the dispersive bands, and it drops the band after Eq. (7) without proving the omission; if that current is nonzero, the reported response tensors are incomplete.","fun_headline_variants_meta":{"raw":{"variants":["Planar-Hall tensors for pseudospin-1 nodes fully enumerated","All response tensors for three-band semimetals to third order in B","Out-of-plane and scattering effects now in planar-Hall response","Pseudospin-1 semimetal response tensors complete through B^3"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000207,"raw_usage":{"total_tokens":1434,"prompt_tokens":1014,"completion_tokens":420,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":630,"completion_tokens_details":{"reasoning_tokens":341}},"tokens_in":630,"tokens_out":420,"duration_ms":4552,"temperature":1.0,"reasoning_tokens":341,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T21:31:58.249908+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Evaluate the flat-band (s=0) terms in the Boltzmann integrals of Eqs. (16)-(21) using the orbital magnetic moment from Eq. (7), and look for any nonzero component through O($B^{3}$); finding one would refute the paper's claim that all nonzero linear-response tensors for a pseudospin-1 node have been enumerated.","supporting_citations":[{"cited_title":"Avdoshkin, V","cited_arxiv_id":null,"evidence_quote":"Supplies the internode-scattering theory that Section V specializes to a pair of pseudospin-1 nodes."}],"review_version":1}