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arxiv: 2604.11527 · v1 · submitted 2026-04-13 · ❄️ cond-mat.mes-hall · quant-ph

Semiclassical theory of frequency dependent linear magneto-optical transport in Weyl semimetals

Azaz Ahmad , Pankaj Bhalla , Snehasish Nandy , Tanay Nag This is my paper

Pith reviewed 2026-05-10 15:25 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall quant-ph
keywords Weyl semimetalsmagneto-optical conductivitychiral anomalyintervalley scatteringorbital magnetic momentBoltzmann transportAC conductivity
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The pith

Strong intervalley scattering reverses the sign of longitudinal magneto-optical conductivity in untilted Weyl semimetals under weak AC driving when orbital magnetic moment is present.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a semiclassical Boltzmann transport theory for how alternating electric fields interact with electrons in Weyl semimetals placed in a static magnetic field. It incorporates orbital magnetic moment, possible tilting of the Weyl cones, and scattering both within and between valleys using a scattering-matrix treatment of relaxation. The central result is that, for untilted cones with orbital magnetic moment included, strong intervalley scattering causes the longitudinal magneto-optical conductivity to change sign in the low-frequency regime. This sign reversal cancels the contribution from the chiral anomaly. At high frequencies the scattering cannot readjust the populations within one cycle of the drive, so the sign reversal vanishes. Tilt of the cones changes the field-angle dependence of the conductivity in characteristic ways.

Core claim

For untilted WSMs with orbital magnetic moment, strong intervalley scattering in the weak ac regime induces a sign reversal of the longitudinal magneto-optical conductivity (LMOC), thereby suppressing the chiral anomaly. In contrast, in the strong ac regime, intervalley scattering fails to neutralize the chiral imbalance within a driving cycle, and no sign reversal is observed. Orbital magnetic moment induces linear magnetic-field contributions, while the chiral anomaly yields quadratic response accompanied by expected angular profiles. Tilt direction and orientation strongly affect LMOC: transverse tilt gives symmetric non-monotonic behavior, whereas parallel tilt leads to asymmetric, nearl

What carries the argument

Semiclassical Boltzmann equation solved with a scattering-matrix approach that encodes momentum-dependent relaxation times arising from intravalley and intervalley processes, together with the orbital magnetic moment term in the equations of motion.

If this is right

  • The chiral anomaly contribution to AC conductivity is suppressed only when intervalley scattering is strong enough and the drive frequency is low enough for population imbalance to relax within each cycle.
  • Orbital magnetic moment produces a linear-in-B term in the conductivity tensor while the anomaly produces a quadratic term with distinct angular dependence.
  • Transverse tilt of the Weyl cones produces symmetric non-monotonic LMOC versus magnetic field, while parallel tilt produces asymmetric nearly monotonic response.
  • Negative LMOC appears intrinsically when the tilt is parallel to the magnetic field, but requires the orbital magnetic moment when the tilt is transverse.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Frequency-dependent magneto-optical measurements could therefore serve as a direct probe of the chiral relaxation time scale in real materials.
  • The same semiclassical framework might be extended to compute higher-harmonic responses or nonlinear magneto-optical effects at stronger driving amplitudes.
  • Connecting these results to dc magnetotransport data on the same samples would test whether the extracted intervalley scattering rates are consistent across frequency regimes.

Load-bearing premise

The semiclassical Boltzmann equation with a scattering-matrix treatment of momentum-dependent relaxation remains valid across the weak-to-strong AC regimes and correctly captures the interplay between orbital magnetic moment, Weyl cone tilt, and intervalley scattering without higher-order quantum corrections.

What would settle it

An experiment that measures the longitudinal magneto-optical conductivity of an untilted Weyl semimetal as a function of AC frequency and identifies the precise frequency at which the sign reversal disappears for a sample with independently characterized intervalley scattering rate.

Figures

Figures reproduced from arXiv: 2604.11527 by Azaz Ahmad, Pankaj Bhalla, Snehasish Nandy, Tanay Nag.

Figure 1
Figure 1. Figure 1: (a) A possible experimental setup to test [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: We show the variation of characteristic time scale [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: LMOC namely, the real part of the quantity [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: We repeat Fig [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: We show the angular variation of LMOC and [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: We show the variation of LMOC for the tilt direction perpendicular to the applied magnetic field i.e., [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: We repeat Fig [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: We show the imaginary part of LMOC δσzz(B)/σzz(0) = Im[σzz(B ̸= 0)/σzz(0) − 1] in (a,b,c) for weak, moderate and strong ac regimes, respectively under linearly polarized irradiation in the presence of OMM. The negative response even for strong intervalley scattering in weak ac limit, is a signature of the reactive part of LMOC. and, ωe = −iω + 1/τ . Here, R k = R d 3k (2π) 3 . Using the band velocity vµ,k … view at source ↗
Figure 9
Figure 9. Figure 9: We repeat Fig [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: We show the angular variation of the real part [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: We repeat Fig [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
read the original abstract

We develop a semiclassical Boltzmann theory for frequency-dependent magneto-optical transport in Weyl semimetals (WSMs), incorporating momentum-dependent relaxation via a scattering matrix approach. The interplay of orbital magnetic moment, Weyl cone tilt, intervalley scattering, and electromagnetic driving is analyzed to obtain the full conductivity tensor in the presence of a static magnetic field. For untilted WSMs with orbital magnetic moment, strong intervalley scattering in the weak ac regime induces a sign reversal of the longitudinal magneto-optical conductivity (LMOC), thereby suppressing the chiral anomaly. In contrast, in the strong ac regime, intervalley scattering fails to neutralize the chiral imbalance within a driving cycle, and no sign reversal is observed. Orbital magnetic moment induces linear magnetic-field contributions, while chiral anomaly yields quadratic response accompanied by expected angular profiles. Tilt direction and orientation strongly affect LMOC such as, transverse tilt gives symmetric non-monotonic behavior, whereas parallel tilt leads to asymmetric, nearly monotonic response. Notably, negative LMOC arises intrinsically for parallel tilt, but requires orbital magnetic moment for transverse tilt. These results highlight frequency-dependent conductivity as a sensitive probe of chiral relaxation in MHz-THz magneto-optical experiments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript develops a semiclassical Boltzmann theory for frequency-dependent linear magneto-optical transport in Weyl semimetals, using a scattering-matrix treatment of momentum-dependent relaxation. It computes the full conductivity tensor in a static magnetic field, incorporating orbital magnetic moment, Weyl cone tilt, and intervalley scattering. Key claims are that strong intervalley scattering induces a sign reversal of the longitudinal magneto-optical conductivity (LMOC) in the weak AC regime for untilted WSMs (suppressing the chiral anomaly), while no reversal occurs in the strong AC regime; tilt direction affects LMOC symmetry and negativity; orbital moment gives linear B contributions and chiral anomaly quadratic ones with expected angular profiles.

Significance. If the central claims hold, this provides a frequency-dependent probe of chiral relaxation and anomaly suppression in MHz-THz magneto-optical experiments on WSMs. Strengths include the scattering-matrix approach for relaxation, the full tensor derivation, and the systematic analysis of tilt and orbital-moment effects on LMOC. The distinction between weak-AC reversal and strong-AC absence is a potentially falsifiable prediction.

major comments (2)
  1. [strong AC regime analysis] The headline distinction between sign reversal in the weak AC regime and its absence in the strong AC regime (abstract and strong-AC discussion) rests on the semiclassical Boltzmann equation remaining valid when driving frequency becomes comparable to cyclotron or inter-Landau-level energies. The manuscript provides no estimates, comparisons to quantum limits, or error analysis showing that Landau-level mixing and interband transitions do not alter the effective intervalley scattering rate or chiral imbalance; this is load-bearing for the claim that intervalley scattering 'fails to neutralize the chiral imbalance within a driving cycle.'
  2. [conductivity tensor derivation] The abstract states that the full conductivity tensor is obtained via the Boltzmann solution, yet the manuscript lacks explicit step-by-step derivations of the conductivity expressions, error estimates on the relaxation-time approximation, or direct comparisons to known limiting cases (DC limit, zero-frequency, zero-tilt, or zero-orbital-moment). Without these, it is impossible to verify whether the reported sign reversal and angular profiles are robust outcomes or sensitive to post-hoc choices in the scattering matrix.
minor comments (3)
  1. [Abstract] The abstract sentence 'Tilt direction and orientation strongly affect LMOC such as, transverse tilt gives symmetric non-monotonic behavior...' is grammatically awkward and should be rephrased for clarity.
  2. Figure captions and legends should explicitly list all parameter values (scattering rates, tilt angles, frequency regimes) used in the plotted LMOC curves to allow reproducibility.
  3. Add a brief discussion or reference to prior semiclassical Boltzmann treatments of magneto-transport in WSMs to clarify the incremental advance.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review of our manuscript. The comments raise important points about the validity of our semiclassical approach and the transparency of our derivations. We address each major comment below and will revise the manuscript to incorporate additional analysis and details as outlined.

read point-by-point responses

  1. Referee: [strong AC regime analysis] The headline distinction between sign reversal in the weak AC regime and its absence in the strong AC regime (abstract and strong-AC discussion) rests on the semiclassical Boltzmann equation remaining valid when driving frequency becomes comparable to cyclotron or inter-Landau-level energies. The manuscript provides no estimates, comparisons to quantum limits, or error analysis showing that Landau-level mixing and interband transitions do not alter the effective intervalley scattering rate or chiral imbalance; this is load-bearing for the claim that intervalley scattering 'fails to neutralize the chiral imbalance within a driving cycle.'

    Authors: We acknowledge that the distinction between weak and strong AC regimes relies on the semiclassical Boltzmann framework remaining applicable. The manuscript assumes frequencies where inter-Landau-level transitions remain negligible, but we agree that explicit bounds are needed. In the revised version, we will add a new subsection in the discussion section providing estimates of the cyclotron energy ħω_c = e v_F² B / E_F for representative Weyl semimetal parameters (B ≈ 0.1–1 T, E_F ≈ 50–200 meV), and compare the driving frequency ω to both the intervalley scattering rate and Landau-level spacing. This will delineate the regime where our prediction of no sign reversal in the strong AC regime holds, while noting that quantum corrections may appear outside this window. revision: yes

  2. Referee: [conductivity tensor derivation] The abstract states that the full conductivity tensor is obtained via the Boltzmann solution, yet the manuscript lacks explicit step-by-step derivations of the conductivity expressions, error estimates on the relaxation-time approximation, or direct comparisons to known limiting cases (DC limit, zero-frequency, zero-tilt, or zero-orbital-moment). Without these, it is impossible to verify whether the reported sign reversal and angular profiles are robust outcomes or sensitive to post-hoc choices in the scattering matrix.

    Authors: We agree that more explicit derivations and validation checks would improve verifiability. In the revised manuscript, we will expand the theoretical methods section to include a step-by-step derivation of the conductivity tensor components from the linearized Boltzmann equation with the momentum-dependent scattering matrix. We will also add direct comparisons to the DC limit (recovering the known chiral-anomaly-induced negative magnetoconductivity), the zero-tilt case, and the zero-orbital-moment limit, along with a brief discussion of the relaxation-time approximation and its expected errors for the intervalley scattering model employed. These additions will confirm that the reported sign reversal and angular dependencies arise robustly from the scattering-matrix solution. revision: yes

Circularity Check

0 steps flagged

Semiclassical Boltzmann derivation is self-contained with no circular reduction

full rationale

The paper derives the frequency-dependent magneto-optical conductivity tensor by solving the semiclassical Boltzmann equation incorporating orbital magnetic moment, Weyl cone tilt, and a scattering-matrix treatment of intervalley scattering. The sign reversal of LMOC in the weak-AC regime and its absence in the strong-AC regime are obtained as direct outcomes of this solution under varying driving frequencies, not by redefining input parameters or fitting to the target observables. No self-citation chain, ansatz smuggling, or uniqueness theorem imported from prior author work is required to close the central claims; the results follow from applying the standard transport equation to the specified Hamiltonian terms and scattering rates. The derivation remains independent of the reported predictions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete. The central claim rests on the validity of the semiclassical Boltzmann equation, a momentum-dependent scattering matrix, and the separation of orbital-moment and chiral-anomaly contributions; no explicit free parameters or invented entities are named in the abstract.

axioms (2)
  • domain assumption Semiclassical Boltzmann transport equation remains valid for frequency-dependent response in the presence of static magnetic field and AC driving.
    Invoked to derive the conductivity tensor from the abstract description.
  • domain assumption Scattering matrix approach correctly encodes momentum-dependent intervalley relaxation.
    Used to incorporate intervalley scattering effects on chiral imbalance.

pith-pipeline@v0.9.0 · 5515 in / 1504 out tokens · 36095 ms · 2026-05-10T15:25:36.365926+00:00 · methodology

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