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arxiv: 2605.13323 · v1 · pith:NNAZSNVUnew · submitted 2026-05-13 · ❄️ cond-mat.mes-hall

Thermoelectric enhancement from an asymmetric spectral-conductivity cusp in spin-1 chiral fermions

Risako Kikuchi , Junya Endo , Ai Yamakage This is my paper

Pith reviewed 2026-05-14 18:31 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords thermoelectric enhancementspectral conductivity cuspspin-1 chiral fermionsSeebeck coefficientfigure of meritimpurity scatteringself-consistent Born approximation
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The pith

An asymmetric cusp in spectral conductivity from impurity scattering enhances the Seebeck coefficient and figure of merit in spin-1 chiral fermions at low temperatures.

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

Spin-1 chiral fermion systems consist of two linearly dispersing bands plus one trivial band. Impurity scattering in these systems generates an asymmetric cusp in the spectral conductivity. Linear-response calculations within the self-consistent Born approximation show that this cusp produces clear low-temperature increases in both the Seebeck coefficient and the electronic figure of merit. The enhancement becomes stronger when the trivial band is given larger curvature, even though the density of states smooths out. A minimal model of the cusp alone reproduces the boost when the feature is sharp, strongly asymmetric, and sits at an energy where spectral conductivity remains small.

Core claim

In spin-1 chiral fermion systems composed of two linearly dispersing bands and one trivial band, impurity scattering produces an asymmetric cusp in the spectral conductivity that markedly enhances the electronic thermoelectric response, with low-temperature gains in the Seebeck coefficient and electronic figure of merit; the gains grow larger as the curvature of the trivial band is increased.

What carries the argument

asymmetric cusp in spectral conductivity induced by impurity scattering in the self-consistent Born approximation

If this is right

  • The Seebeck coefficient exhibits low-temperature enhancement due to the cusp.
  • The electronic figure of merit improves from the same conductivity feature.
  • Larger curvature of the trivial band strengthens the enhancement even as the density of states smooths.
  • The boost is largest for a sharp, strongly asymmetric cusp where spectral conductivity at the cusp energy is small.

Where Pith is reading between the lines

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

  • Materials hosting spin-1 fermions may achieve better thermoelectric performance by deliberately tuning trivial-band curvature rather than maximizing density of states.
  • Scattering-induced conductivity cusps offer an alternative route to thermoelectric optimization that does not rely on smooth band features.
  • Analogous asymmetric cusps could appear in other multi-band chiral systems once impurity scattering is treated at the same level.
  • The effect is expected to be observable only at sufficiently low temperatures where thermal broadening does not erase the cusp.

Load-bearing premise

The self-consistent Born approximation fully captures impurity scattering without higher-order corrections, and the model with one trivial band adequately represents real materials at low temperatures.

What would settle it

Direct measurement of spectral conductivity or thermoelectric coefficients in a candidate spin-1 chiral material that shows neither the predicted cusp nor the low-temperature enhancement in Seebeck coefficient would falsify the central claim.

Figures

Figures reproduced from arXiv: 2605.13323 by Ai Yamakage, Junya Endo, Risako Kikuchi.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: shows the temperature dependence of the electrical and thermal conductivities in the spin-1 chiral fermion system. Both conductivities are strongly sup￾pressed in the vicinity of ϵc ∼ 0.096q0ℏv, leaving a clear remnant of the cusp. As temperature increases, the elec￾trical conductivity becomes progressively smoother in en￾ergy, reflecting a thermal smearing of the cusp structure. Appendix B: Detailed Resul… view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
read the original abstract

A recent study showed that, in spin-1 chiral fermion systems composed of two linearly dispersing bands and one trivial band, impurity scattering produces an asymmetric cusp in the spectral conductivity. We demonstrate that this asymmetric cusp markedly enhances the electronic thermoelectric response. Using linear-response theory within the self-consistent Born approximation, we find low-temperature enhancements in both the Seebeck coefficient and the electronic figure of merit. Increasing the curvature of the trivial band further strengthens this cusp-induced enhancement, even though the corresponding density of states becomes smoother. To clarify this mechanism, we introduce a minimal cusp model for the spectral conductivity and show that the enhancement is most pronounced when the cusp is sharp and strongly asymmetric, and when the spectral conductivity at the cusp energy is small.

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

3 major / 3 minor

Summary. The manuscript presents a study of thermoelectric transport in spin-1 chiral fermion systems consisting of two linearly dispersing bands and one trivial band. It shows that impurity scattering, treated within the self-consistent Born approximation, generates an asymmetric cusp in the spectral conductivity. This feature leads to enhancements in the Seebeck coefficient and the electronic figure of merit at low temperatures. The authors introduce a minimal model of the spectral conductivity to elucidate the conditions under which the cusp produces the strongest enhancement.

Significance. If the results hold, this identifies an impurity-scattering-induced mechanism for boosting thermoelectric performance in systems with chiral fermions, which may be relevant for materials like certain topological semimetals. The use of both detailed SCBA calculations and a simplified cusp model is a positive aspect, allowing for mechanistic understanding. The finding that increasing trivial band curvature enhances the effect despite smoother DOS is intriguing and could guide material design.

major comments (3)
  1. [Section III] Section III (SCBA calculation of spectral conductivity): the paper does not address potential limitations of the self-consistent Born approximation such as neglect of vertex corrections or higher-order scattering effects. In linear-dispersion systems these can round or symmetrize the cusp when the scattering rate approaches the Fermi energy, directly affecting the claimed low-T enhancement.
  2. [Section IV] Section IV (minimal cusp model): this model is introduced after and parameterized from the SCBA results rather than derived independently. It therefore cannot serve as a cross-check and the enhancement mechanism remains tied to the same approximation whose validity is unverified.
  3. [Results] Results (e.g., Figure 3 and associated text): quantitative enhancements in Seebeck coefficient and electronic figure of merit are shown without error estimates, sensitivity analysis to impurity strength, or comparison to alternative approximations, leaving the robustness of the central claim unclear.
minor comments (3)
  1. [Abstract] The abstract could specify the temperature window and impurity concentration range over which the enhancement is observed.
  2. [Figures] Figure captions would benefit from explicit labels indicating the cusp energy and the measure of asymmetry used.
  3. [Introduction] A brief discussion of related SCBA studies in other linear-dispersion systems would improve context in the introduction.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Section III] Section III (SCBA calculation of spectral conductivity): the paper does not address potential limitations of the self-consistent Born approximation such as neglect of vertex corrections or higher-order scattering effects. In linear-dispersion systems these can round or symmetrize the cusp when the scattering rate approaches the Fermi energy, directly affecting the claimed low-T enhancement.

    Authors: We agree that the SCBA has limitations, including the neglect of vertex corrections and higher-order scattering. Our calculations are performed in the regime where the scattering rate remains much smaller than the Fermi energy at low temperatures, which preserves the cusp asymmetry. We will add an explicit discussion of these limitations and the validity condition in the revised Section III. revision: yes

  2. Referee: [Section IV] Section IV (minimal cusp model): this model is introduced after and parameterized from the SCBA results rather than derived independently. It therefore cannot serve as a cross-check and the enhancement mechanism remains tied to the same approximation whose validity is unverified.

    Authors: The minimal cusp model is introduced as a simplified phenomenological tool to isolate the role of cusp sharpness and asymmetry in driving the enhancement, rather than as an independent derivation or cross-check. We will revise the text in Section IV to clarify this purpose and its complementary role to the SCBA results. revision: partial

  3. Referee: [Results] Results (e.g., Figure 3 and associated text): quantitative enhancements in Seebeck coefficient and electronic figure of merit are shown without error estimates, sensitivity analysis to impurity strength, or comparison to alternative approximations, leaving the robustness of the central claim unclear.

    Authors: We will add a sensitivity analysis to impurity strength in the revised results section, including additional curves for varying impurity potential. We will also compare SCBA results to the non-self-consistent Born approximation to illustrate the effect of self-consistency. These additions will address the robustness of the reported enhancements. revision: yes

Circularity Check

0 steps flagged

Self-citation of cusp origin but independent calculation of thermoelectric response

full rationale

The derivation begins from the spin-1 chiral fermion model and applies linear-response theory plus SCBA to compute the Seebeck coefficient and figure of merit; the asymmetric cusp is imported from a cited prior study rather than derived anew here. A minimal cusp model is then introduced separately to illustrate mechanism dependence on sharpness and asymmetry, without any parameter fitting that would force the reported low-T enhancements to equal an input quantity by construction. No equation or step reduces the central thermoelectric claims to self-definition, renamed inputs, or a self-citation chain whose validity is presupposed inside the present work.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the applicability of linear-response theory and the self-consistent Born approximation to impurity scattering in the described band structure; no free parameters or invented entities are mentioned in the abstract.

axioms (2)
  • standard math Linear-response theory applies to the thermoelectric coefficients in the low-temperature regime.
    Invoked to compute Seebeck coefficient and figure of merit from spectral conductivity.
  • domain assumption Self-consistent Born approximation sufficiently describes impurity scattering effects.
    Used to generate the asymmetric cusp in spectral conductivity.

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