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REVIEW 2 major objections 2 minor 88 references

Chiral anomaly and planar Hall conductance in pseudospin-$1$ Fermions

T0 review · 2 major / 2 minor · reviewed 2026-06-27 · grok-4.3

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Pith's one-line read In pseudospin-1 Weyl semimetals the planar Hall conductance is positive and quadratic in magnetic field strength until scattering causes a sign reversal, with tilt switching its angular dependence from sin 2 gamma to sin gamma or cos gamma.

desk verdict The paper runs a Boltzmann calculation for pseudospin-1 nodes and reports a scattering-driven sign flip in planar Hall conductance plus tilt-induced changes in angular form, but the outcomes sit inside the relaxation-time approximation without a demonstrated link to microscopic scattering. read the letter →

arxiv 2606.11364 v1 pith:KFQ7XGOC submitted 2026-06-09 cond-mat.mes-hall

Azaz Ahmad This is my paper
classification cond-mat.mes-hall
keywords chiralanomalyplanarHallconductancepseudospin-1fermionsWeylsemimetalsmagnetotransporttilteffectsBoltzmanntransport
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

The paper applies semiclassical Boltzmann transport theory in the relaxation-time approximation to pseudospin-1 fermions, including momentum-dependent scattering, orbital magnetic moment corrections, and charge conservation. It finds that without tilt the planar Hall conductance remains positive and grows quadratically with magnetic field strength. Raising scattering strength produces a sign change from positive to negative. Tilt along the x or z direction replaces the sin 2 gamma angular pattern with sin gamma or cos gamma dependence and introduces nonmonotonic variation with tilt strength. These behaviors are presented as measurable signatures of the chiral anomaly in multifold fermion systems.

What carries the argument

Semiclassical Boltzmann transport theory within the relaxation-time approximation applied to the tilted pseudospin-1 dispersion, incorporating momentum-dependent scattering, orbital magnetic moment, and charge-conservation constraints.

What would settle it

A transport measurement in a candidate pseudospin-1 material that shows no sign reversal of the planar Hall conductance when scattering strength is increased would contradict the central prediction.

Watch

Extended reading notes

Core claim

Using Boltzmann transport in the relaxation time approximation, the work shows that the chiral anomaly in pseudospin-1 Weyl semimetals produces a positive planar Hall conductance that scales quadratically with magnetic field in the absence of tilt. Increasing scattering strength leads to a sign change in this conductance. The angular dependence is sin 2 gamma in the untilted case but becomes sin gamma for x-tilt and cos gamma for z-tilt, with nonmonotonic behavior in tilt strength.

Load-bearing premise

The relaxation-time approximation together with momentum-dependent scattering, orbital magnetic moment corrections, and charge-conservation constraints is sufficient to produce quantitatively reliable planar Hall conductance.

Editorial extensions

If this is right

  • The planar Hall conductance scales quadratically with magnetic field strength in the untilted case.
  • A sign reversal of the planar Hall conductance occurs as scattering strength increases.
  • The angular dependence of the planar Hall conductance changes from sin 2 gamma to sin gamma or cos gamma under tilt along x or z.
  • The planar Hall conductance depends nonmonotonically on tilt magnitude.

Reading between the lines

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

  • Measurements varying scattering via temperature or doping could test the predicted sign reversal in real materials.
  • The change in angular form under different tilt directions implies that oriented samples could distinguish tilt orientation through transport.
  • The same semiclassical approach could be applied to other multifold fermion dispersions to predict their planar Hall signals.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The manuscript applies semiclassical Boltzmann transport theory in the relaxation-time approximation (with momentum-dependent scattering, orbital magnetic moment corrections, and an explicit charge-conservation constraint) to pseudospin-1 Weyl fermions. It reports that the planar Hall conductance (PHC) is positive and quadratic in B in the untilted limit, reverses sign with increasing scattering strength, follows a sin 2γ angular dependence (γ angle between B and x-axis) that changes to sin γ or cos γ under x- or z-tilt, and depends nonmonotonically on tilt magnitude. These features are presented as experimentally accessible signatures of the chiral anomaly in multifold fermions for candidate materials in space groups 199, 214, and 220.

Significance. If the central claims are robust, the work extends chiral-anomaly transport signatures from Weyl to pseudospin-1 systems and supplies concrete, falsifiable predictions (quadratic PHC scaling, sign reversal, tilt-induced angular changes) that could guide experiments on multifold-fermion candidates. The explicit inclusion of orbital-moment corrections and charge conservation is a methodological strength when properly implemented.

major comments (2)
  1. [Methods / Transport equation section] The sign reversal of PHC with increasing scattering strength is a headline result, yet it is obtained inside a phenomenological RTA with a specific momentum-dependent τ(k). Without an explicit demonstration that this τ(k) reproduces the microscopic collision integral (including the relative strength of intra- versus inter-node scattering) for any concrete impurity potential in the pseudospin-1 dispersion, the reversal risks being an artifact of the chosen scattering model rather than a generic consequence of the chiral anomaly.
  2. [Results / Angular dependence subsection] The abstract states that finite PHC requires breaking azimuthal symmetry via tilt or E-B misalignment, but the manuscript does not appear to quantify how sensitive the reported quadratic scaling and angular forms are to the precise implementation of the charge-conservation constraint or to the cutoff procedure used in the Boltzmann integral; a limiting-case check (e.g., zero tilt, zero orbital moment) would be needed to confirm the expressions do not reduce by construction.
minor comments (2)
  1. Notation for the tilt vector components and the angle γ should be defined once at first use and used consistently in all figures and equations.
  2. Figure captions should explicitly state the values of scattering strength, tilt magnitude, and Fermi energy used for each curve to allow direct reproduction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments. We address each major point below and outline the revisions we will make to strengthen the presentation.

read point-by-point responses

  1. Referee: [Methods / Transport equation section] The sign reversal of PHC with increasing scattering strength is a headline result, yet it is obtained inside a phenomenological RTA with a specific momentum-dependent τ(k). Without an explicit demonstration that this τ(k) reproduces the microscopic collision integral (including the relative strength of intra- versus inter-node scattering) for any concrete impurity potential in the pseudospin-1 dispersion, the reversal risks being an artifact of the chosen scattering model rather than a generic consequence of the chiral anomaly.

    Authors: We agree that the relaxation-time approximation remains phenomenological and that we have not derived the specific form of τ(k) from a microscopic collision integral for a concrete impurity potential in the pseudospin-1 case. The sign reversal is tied to the competition between the chiral-anomaly contribution (which enters through the Berry curvature and orbital-moment terms) and the momentum-dependent scattering rate in the linearized Boltzmann equation. To address the concern, we will revise the Methods section to (i) explicitly state the functional form of τ(k) and its motivation from prior literature on multifold fermions, (ii) add a brief discussion of intra- versus inter-node scattering, and (iii) include a supplementary check with constant τ(k) to demonstrate that the qualitative sign-reversal feature survives. We will also note that a full microscopic treatment lies beyond the present semiclassical scope. revision: yes

  2. Referee: [Results / Angular dependence subsection] The abstract states that finite PHC requires breaking azimuthal symmetry via tilt or E-B misalignment, but the manuscript does not appear to quantify how sensitive the reported quadratic scaling and angular forms are to the precise implementation of the charge-conservation constraint or to the cutoff procedure used in the Boltzmann integral; a limiting-case check (e.g., zero tilt, zero orbital moment) would be needed to confirm the expressions do not reduce by construction.

    Authors: The referee correctly notes that we have not presented explicit numerical checks of the sensitivity to the charge-conservation Lagrange multiplier or to the momentum cutoff. In the untilted limit the analytic expressions for the planar Hall conductivity reduce to a positive quadratic term whose coefficient is fixed by the chiral-anomaly contribution; the finite-PHC requirement arises because azimuthal symmetry forces the relevant off-diagonal integrals to vanish. We will add a dedicated paragraph (or supplementary section) that (i) sets tilt = 0 and orbital moment = 0, (ii) verifies that the quadratic scaling and sin(2γ) angular dependence are recovered without artificial reduction, and (iii) reports the numerical stability with respect to the cutoff and the charge-conservation constraint. These checks will be performed with the same numerical integration routine used in the main text. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; results from direct solution of transport equations

full rationale

The paper obtains its PHC results by solving the semiclassical Boltzmann equation in the relaxation-time approximation, incorporating momentum-dependent scattering, orbital-moment corrections, and a charge-conservation constraint, then varying parameters such as tilt, scattering strength, and field angle. No step reduces a claimed prediction to a fitted input by construction, nor does any load-bearing premise rest on a self-citation chain that itself lacks independent verification. The angular dependencies, quadratic scaling, and sign reversal are outputs of the explicit calculation rather than tautological re-expressions of the inputs.

Assumptions & free parameters 2 free parameters · 2 assumptions · 0 invented entities

The central claim rests on the applicability of semiclassical transport theory to pseudospin-1 systems and on the validity of symmetry breaking via tilt or field misalignment; no new particles or forces are introduced.

free parameters (2)
  • scattering strength
    Parameter varied to produce the reported sign reversal of PHC
  • tilt magnitude
    Parameter varied to produce nonmonotonic dependence and change in angular form
assumptions (2)
  • domain assumption Semiclassical Boltzmann transport theory within the relaxation-time approximation accurately captures magnetotransport including chiral anomaly effects in pseudospin-1 Weyl semimetals
    Explicitly employed as the calculational framework
  • domain assumption Orbital magnetic moment corrections and charge-conservation constraints can be consistently incorporated into the semiclassical equations
    Stated as part of the model setup

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Cite this review

Pith. "Pith review of Chiral anomaly and planar Hall conductance in pseudospin-$1$ Fermions." pith.science (2026). https://pith.science/paper/KFQ7XGOC

@misc{pith2026260611364,
  author       = {Pith},
  title        = {Pith review of: Chiral anomaly and planar Hall conductance in pseudospin-$1$ Fermions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KFQ7XGOC}},
  note         = {Machine review of arXiv:2606.11364}
}
abstract

Positive longitudinal magnetoconductance (LMC) and planar Hall conductance (PHC) are hallmark transport signatures of the chiral anomaly in Weyl semimetals. Recent theoretical developments have extended Weyl fermions to multifold Fermionic systems with higher-pseudospin quasiparticle excitations, motivating the study of their magnetotransport properties. Here, we employ semiclassical Boltzmann transport theory within the relaxation-time approximation to investigate magnetotransport in pseudospin-1 Weyl semimetals, incorporating momentum-dependent scattering, orbital magnetic moment corrections, and charge-conservation constraints. To obtain a finite PHC, we break azimuthal symmetry through either a generic tilt of the quasiparticle dispersion or a finite misalignment between the electric and magnetic fields. In the untilted case, the PHC is positive and scales quadratically with magnetic field strength. Increasing the scattering strength induces a sign reversal of the PHC, producing a transition from positive to negative values. The PHC further exhibits the characteristic angular dependence $\sin 2\gamma$, where $\gamma$ is the angle between the magnetic field and the $x$-axis. Tilt qualitatively alters this behavior: tilt along the $x$- and $z$-directions changes the angular response to $\sin\gamma$ and $\cos\gamma$, respectively, generating strong anisotropy in the planar Hall signal. Moreover, the PHC shows a nonmonotonic dependence on tilt magnitude, revealing the interplay between tilt-induced symmetry breaking and chiral-anomaly-driven transport. Our results provide experimentally accessible signatures of multifold fermions and a framework for interpreting magnetotransport measurements in candidate materials of space groups 199, 214, and 220.

Figures

Figures reproduced from arXiv: 2606.11364 by the authors.

Figure 1
Figure 1. We investigate the LMC and PHC in a pseudospin-1 semimetal, both in the presence and absence of the OMM, [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Phase plot of LMC and PHC for pseudospin-1 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. (a-b) The LMC and PHC are analyzed as functions of the tilt along the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: (a-b) The LMC and PHC are analyzed as functions of the tilt along the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: (a) The angular dependence of the PHC is inves [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

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