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Nernst power factor and figure of merit in compensated semimetal ScSb

T0 review · 3 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

Pith's one-line read ScSb, a topologically trivial compensated semimetal, reaches a Nernst thermopower of 47 µV/K at 12 K and 14 T, with PF_N ≈ 35×10⁻⁴ W m⁻¹ K⁻² and z_N ≈ 28×10⁻⁴ K⁻¹, matching topological semimetals; the paper argues topology is thus not…

desk verdict Solid Nernst measurements on ScSb with a new high-value result, but the Berry-curvature conclusion is a logical leap the data do not support. read the letter →

arxiv 2504.15450 v1 pith:SL2UCHS5 submitted 2025-04-21 cond-mat.mtrl-sci cond-mat.other

classification cond-mat.mtrl-scicond-mat.other
keywords Nernsteffectthermomagneticrefrigerationelectron-holecompensationphonondragsemimetalpowerfactorfigureofmerittopologicallytrivial
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 reports that ScSb, a semimetal with ordinary, topologically trivial electronic bands, shows a Nernst thermopower of about $47\,\mu\mathrm{V}/\mathrm{K}$ at 12 K in a 14 T field. From that signal the authors derive a Nernst power factor $PF_N \approx 35 \times 10^{-4}\,\mathrm{W\,m^{-1}\,K^{-2}}$ and a Nernst figure of merit $z_N \approx 28 \times 10^{-4}\,\mathrm{K^{-1}}$, values comparable to those of topological semimetals such as Cd$_3$As$_2$, ZrTe$_5$, and TbPtBi. The authors attribute the large signal to near-perfect electron-hole compensation, demonstrated by Hall measurements, angle-resolved photoemission spectroscopy, and density functional theory, combined with phonon drag. The significance is that it challenges the assumption that Berry curvature or nontrivial topology is required for strong thermomagnetic performance.

What carries the argument

The load-bearing objects are the semiclassical two-carrier model, equations (1) and (2) of the paper, which fit the field-dependent longitudinal and Hall conductivities to extract separate hole and electron densities and mobilities; and the measured and calculated Fermi surface showing three nested $\Gamma$-centered hole pockets and three pairs of $X$-centered electron ellipsoids with no band inversion. The two-carrier model demonstrates near-perfect compensation ($n_h/n_e \approx 1.05$), and the Fermi-surface maps establish the topologically trivial character. The performance metrics are then built from the measured $S_{xy}$, $\sigma_{yy}$, and $\kappa_{xx}$ through $PF_N = S_{xy}^2\,\sigma_{yy}$ and $z_N = S_{xy}^2\,\sigma_{yy}/\kappa_{xx}$, with the low thermal conductivity at 12 K (about $1.5\,\mathrm{W\,m^{-1}\,K^{-1}}$) making $z_N$ large.

What would settle it

Measure the Nernst thermopower in ScSb samples whose electron-hole ratio is deliberately shifted away from unity by slight Sb deficiency or doping: if the 12 K peak and the large power factor survive, compensation is not the controlling mechanism; a quantitative transport calculation that includes phonon drag and uses the measured carrier densities and mobilities should reproduce the ~$47\,\mu\mathrm{V}/\mathrm{K}$ peak, and if it cannot, the phonon-drag attribution is unsupported.

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Extended reading notes

Core claim

On its own terms the paper's central claim is that high Nernst performance does not require topological bands. In ScSb, which the authors classify as topologically trivial from the absence of band inversion, they measure a Nernst peak of about $47\,\mu\mathrm{V}/\mathrm{K}$ at 12 K and 14 T, a maximum Nernst power factor of about $35 \times 10^{-4}\,\mathrm{W\,m^{-1}\,K^{-2}}$, and a Nernst figure of merit of about $28 \times 10^{-4}\,\mathrm{K^{-1}}$. They attribute the peak to the combination of strong phonon drag and nearly equal electron and hole densities, with $n_h/n_e \approx 1.05 \pm 5\%$ from transport measurements, while density functional theory Fermi-surface volumes give about 1.31, a difference they trace to a Fermi-level shift of roughly $0.04\,\mathrm{eV}$. Because ScSb is a trivial compensated semimetal, they conclude that the Berry-curvature anomalous Nernst effect is not the primary contributor to the enhanced thermomagnetic performance seen in topological semimetals.

Load-bearing premise

The load-bearing premise is that the 12 K Nernst peak in ScSb is produced by phonon drag acting on nearly perfectly compensated electrons and holes; if that attribution fails, the proposed mechanism loses its support, although the measured values themselves remain valid.

Editorial extensions

If this is right

  • If correct, the result removes topology as a prerequisite for a strong Nernst response: ordinary compensated semimetals with phonon drag become candidate thermomagnetic refrigerators.
  • Because ScSb is cubic, the same performance should appear in polycrystalline form, and suppressing grain-boundary electron scattering while increasing boundary phonon scattering could raise $z_N$ further.
  • Tuning the carrier balance toward perfect compensation, for instance by shifting the Fermi level to match the density functional theory prediction, is a concrete lever for pushing the Nernst power factor higher.
  • The comparison implies that part of the large Nernst signal in topological semimetals may be non-topological, so measurements on trivial members of the same families are needed to separate the contributions.

Reading between the lines

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

  • The peak-value comparison against topological semimetals mixes samples measured at different temperatures and fields; a fairer comparison would map $S_{xy}(T,B)$ on the same grid or normalize by carrier density.
  • A direct test of the phonon-drag attribution would be isotope substitution: replacing Sb with a heavier isotope should shift the phonon-drag peak in temperature while leaving the electronic structure essentially unchanged, and the Nernst peak should move with it.
  • If compensation is the controlling factor, doping ScSb away from $n_h = n_e$ should suppress the Nernst peak; this prediction is measurable and would separate compensation from phonon drag.
  • The same logic suggests a search strategy for other topologically trivial, highly compensated semimetals, which could yield inexpensive thermomagnetic materials without the band-structure engineering needed for topological semimetals.
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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 / 4 minor

Summary. The manuscript reports transport, ARPES, and DFT measurements on the cubic semimetal ScSb, which the authors classify as topologically trivial. They observe a Nernst thermopower Sxy of about 47 µV/K at 12 K and 14 T, a Nernst power factor PFN of about 35 × 10^-4 W m^-1 K^-2, and a Nernst figure of merit zN of about 28 × 10^-4 K^-1. The authors attribute the large Nernst signal to nearly perfect electron-hole compensation, supported by two-carrier fits to Hall and longitudinal conductivity, ARPES Fermi-surface mapping, and DFT band-structure calculations. They compare PFN and zN with values reported for topological semimetals and argue that, since ScSb is topologically trivial and reaches comparable values, the Berry-curvature-induced anomalous Nernst effect is not the primary contributor to the enhanced thermomagnetic performance of topological semimetals.

Significance. If the conclusions are properly bounded, this is a valuable experimental contribution. It demonstrates that a topologically trivial, well-compensated semimetal can exhibit Nernst power factors and figures of merit in the range previously associated with topological semimetals, which is relevant for thermomagnetic cooling applications and for understanding the role of band topology in the Nernst effect. The paper's strengths include the internal consistency among transport, ARPES, and DFT; the direct measurement of Sxy, PFN, and zN rather than derivation from a fitted model; and the explicit comparison of Fermi-surface shapes and carrier densities. The main weakness is that the broad conclusion about Berry curvature in topological semimetals goes beyond what the data can establish, and the phonon-drag attribution is not quantitatively tested. With a revised interpretation and proper uncertainty propagation, the paper would be a solid and useful addition to the field.

major comments (3)
  1. [Section IV (Conclusions)] The concluding statement that "the anomalous Nernst effect driven by Berry curvature in topological semimetals is not the primary contributor to their enhanced thermomagnetic performance" is not supported by the presented data. The experiment shows that one trivial compensated semimetal can have PFN and zN values comparable to those of several topological semimetals, but it does not decompose the Nernst signal in Cd3As2, ZrTe5, PtSn4, or TbPtBi into normal and anomalous contributions. Those materials may achieve their peaks at different temperatures and fields and may be dominated by different mechanisms. I recommend reframing the conclusion as an existence statement: a topologically trivial semimetal can exhibit comparably large Nernst response, so large PFN/zN alone does not prove a Berry-curvature origin. A quantitative comparison of the normal Nernst contribution in the topological reference materials would be needed to support the stronger claim.
  2. [Section III (Results and discussion, around Fig. 1 and Fig. 2)] The attribution of the 12 K Nernst peak to phonon drag is inferred only from the coincident peak in Sxx and from the temperature dependence, without a quantitative model or a control experiment. The text states that "the same mechanism also boosts the Nernst thermopower," but no estimate of the phonon-drag contribution to Sxy is given, and alternatives such as ambipolar diffusion or inelastic scattering are not discussed. Since the mechanistic explanation of the large Nernst effect in ScSb depends on this attribution, the claim in the Conclusions that the values "arise from well compensated electron and hole carriers ... and a strong phonon drag effect" needs either quantitative support or a more cautious phrasing.
  3. [Section III (PFN and zN definitions, Fig. 3)] No uncertainties are reported for Sxy, σyy, κxx, PFN, or zN, so the statement that the ScSb values are "comparable" to those of topological semimetals is not quantitatively established. The only stated uncertainties are the ±5% errors on carrier densities and mobilities from the two-carrier fit. Given that the central claim rests on a quantitative comparison with literature values, I request error propagation from the measured quantities into PFN and zN, and, if possible, error bars in Fig. 3 so that the reader can assess whether the differences among materials are significant.
minor comments (4)
  1. [Section II (Methods)] There is a typo in "in a a JEOL JSM-7600F scanning electron microscope" and another in "exhange-correlation functional." Please correct these.
  2. [Section III (Fig. 3 and surrounding text)] The comparison in Fig. 3 lists maximum PFN and zN values for each material but does not specify the temperature and magnetic field at which each maximum was obtained. Since the peaks occur at different conditions, adding this information to the caption or text would make the comparison more meaningful.
  3. [Section III (Fig. 1c)] The statement that "the value of Sxx is nearly zero down to T = 100 K" is vague; please provide the approximate magnitude or a zoomed inset so that the reader can verify the near-zero behavior.
  4. [Section III (ARPES paragraph)] The notation "it is evident" appears as "its evident" in the text; please correct the grammar.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; measured Nernst values are direct outputs of transport measurements, not derived from fitted parameters.

full rationale

The central quantities Sxy, PF_N, and z_N are obtained directly from measurements: Sxy is measured as a function of temperature and field, sigma_yy is obtained from measured resistivity, and kappa_xx is measured; PF_N and z_N are then evaluated from their defining relations PF_N = Sxy^2*sigma_yy and z_N = PF_N/kappa_xx. The two-carrier model is used only to extract carrier densities and mobilities from Hall and longitudinal conductivity data; it is not used to compute or predict Sxy, PF_N, or z_N. The electron-hole compensation and phonon-drag narratives are interpretive explanations of the measured behavior, not equations that force the target results. The one self-citation (ref. [8], which includes co-authors Q. Li and N. Aryal) is used for a measurement-platform detail and for comparison values of NbSb2; even if that citation were removed, the ScSb data and the derived PF_N/z_N would stand unchanged. No fitted parameter is renamed as a prediction, no result is reduced to its own input by construction, and no load-bearing argument depends on an unverified self-citation. The paper is therefore not circular; any concern about the strength of the Berry-curvature conclusion is a matter of inference and scope, not circularity.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

No new physical entities are introduced. The main inputs are the semiclassical two-carrier model, the phonon drag interpretation, and the DFT band structure, all standard tools, but none directly produces the Nernst signal from first principles.

free parameters (5)
  • hole density n_h(T) = around 10^20 cm^-3 (temperature dependent)
    Free parameter in the two-carrier fit to Hall conductivity; central to the compensation claim.
  • electron density n_e(T) = around 10^20 cm^-3 (temperature dependent)
    Free parameter in the two-carrier fit; the n_h/n_e ratio is about 1.05.
  • hole mobility mu_h(T) = around 10^3 cm^2/V/s
    Free parameter in the two-carrier fit.
  • electron mobility mu_e(T) = around 10^3 cm^2/V/s
    Free parameter in the two-carrier fit.
  • Fermi level offset = about 0.04 eV
    Introduced to reconcile the DFT carrier ratio (1.31) with the experimental ratio (1.05).
assumptions (4)
  • domain assumption Semiclassical two-carrier model (Eq. 1 and 2) with field-independent densities and mobilities
    Used to extract n_h, n_e, mu_h, and mu_e from Hall and longitudinal conductivity; assumes independent parabolic bands with a single relaxation time per carrier.
  • domain assumption Phonon drag produces the low-temperature peaks in Sxx and Sxy
    Attributed by analogy with the 12 K peak in Seebeck data, not verified by a dedicated measurement or calculation.
  • domain assumption Cubic symmetry makes rho_xx = rho_yy and kappa_xx = kappa_yy in a magnetic field
    Used to compute PF_N and z_N from a single longitudinal direction; reasonable for a cubic crystal but not explicitly verified in the measured sample.
  • domain assumption GGA-PBE DFT with spin-orbit coupling correctly describes the Fermi surface of ScSb
    Used to interpret the Fermi pockets and the carrier ratio; standard approximation, but the observed deviation from experiment is handled by a Fermi level offset.

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Cite this review

Pith. "Pith review of Nernst power factor and figure of merit in compensated semimetal ScSb." pith.science (2026). https://pith.science/paper/SL2UCHS5

@misc{pith2026250415450,
  author       = {Pith},
  title        = {Pith review of: Nernst power factor and figure of merit in compensated semimetal ScSb},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SL2UCHS5}},
  note         = {Machine review of arXiv:2504.15450}
}
abstract

Recently, topological semimetals have emerged as strong candidates for solid state thermomagnetic refrigerators due to their enhanced Nernst effect. This enhancement arises from the combined contributions of the Berry curvature induced anomalous Nernst coefficient associated with topological bands and the normal Nernst effect resulting from synergistic electron-hole compensation. Generally, these two effects are intertwined in topological semimetals, making it challenging to evaluate them independently. Here, we report the observation of high Nernst effect in the electron hole compensated semimetal ScSb with topologically trivial electronic band structures. Remarkably, we find a high maximum Nernst power factor of $PF_N \sim 35 \times 10^{-4}$ W m$^{-1}$ K$^{-2}$ in ScSb. The Nernst thermopower ($S_{xy}$) exhibits a peak of $\sim$ 47 $\mu$V/K at 12 K and 14 T, yielding a Nernst figure of merit ($z_N$) of $\sim 28 \times 10^{-4}$ K$^{-1}$. Notably, despite its trivial electronic band structure, both the $PF_N$ and $z_N$ values of ScSb are comparable to those observed in topological semimetals with Dirac band dispersions. The origin of the large Nernst signal in ScSb is explained by well compensated electron and hole carriers, through Hall resistivity measurements, angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations.

Figures

Figures reproduced from arXiv: 2504.15450 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Cubic crystal structure of ScSb. (b) Schematic [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 4
Figure 4. FIG. 4. (a) Longitudinal resistivity ( [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. FIG. 5. Electronic structure of ScSb. (a) Band structure of along a labeled high-symmetry path. Labels for the Fermi pockets [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figures from the paper (1 more)
Figure 6
Figure 6. Figure 6: FIG. 6. Electronic structure of ScSb probed using ARPES at 20 K. (a) Primitive 3D Brillouin zone (BZ) of ScSb (bottom) and [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Large non-saturating Nernst thermopower and magnetoresistance in compensated semimetal ScSb

    cond-mat.mtrl-sci 2025-07 conditional novelty 6.0 of 10

    Polycrystalline, cubic ScSb shows a Nernst thermopower of 128 µV/K at 30 K and 14 T and a Nernst power factor of 240e-4 W m^-1 K^-2, exceeding single-crystal ScSb due to improved electron-hole compensation.

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