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REVIEW 3 major objections 4 minor 60 references

Inhomogeneity identification by measuring magnetic quantum oscillations

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A spatially non-uniform dopant concentration in Cr-doped NbSb2 produces an asymmetric effective Fermi-energy distribution that shifts the dHvA phase and bends the Dingle plot, so inhomogeneity can be mistaken for a nontrivial Berry phase.

desk verdict A genuinely useful cautionary protocol for dHvA on inhomogeneous samples, but the central quantitative claim about asymmetric Fermi-energy distributions rests on an under-validated multi-Lorentzian fit. read the letter →

arxiv 2507.23246 v1 pith:X5OWL6EN submitted 2025-07-31 cond-mat.mtrl-sci

Sang-Eon Lee , Myung-Hwa Jung This is my paper · ORCID
classification cond-mat.mtrl-sci PACS 71.18.+y
keywords deHaas-vanAlpheneffectmagneticquantumoscillationssampleinhomogeneitynon-uniformdopingFermienergydistributionDingleplotBerryphaseNbSb2
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 sets out to establish that magnetic quantum oscillations can identify spatial inhomogeneity in a conductor, specifically a non-uniform dopant composition, and that such inhomogeneity can look like a nontrivial Berry phase. The authors compare Bi-doped and Cr-doped NbSb2, argue from grinding experiments that the Bi sample is homogeneous while the Cr sample is inhomogeneous on the millimeter scale, and find that only the Cr sample's $\beta$ oscillations deviate from the Lifshitz-Kosevich form: a nonlinear Dingle plot and a Landau-fan intercept far from the expected $-0.125$. They account for the deviation with an effective Fermi-energy distribution $D(\mu)$ that is asymmetric and non-Lorentzian for Cr and symmetric Lorentzian for Bi. If the interpretation is right, dHvA measurements become a bulk diagnostic for non-uniform composition and a safeguard against mistaking inhomogeneity-induced phase shifts for topological signals.

What carries the argument

The carrier of the argument is the effective Fermi-energy distribution $D(\mu)$: the observed quantum oscillations are written as a superposition of Lifshitz-Kosevich oscillations over different Fermi energies, $\Delta M \propto \int D(\mu) R_T \sin[2\pi F(\mu)/B + \pi/4]\,d\mu$, and for the inhomogeneous sample this distribution is modeled by a normalized sum of three Lorentzians, Eq. (2). The same object converts the familiar Dingle temperature, $T_D = \Delta\mu/\pi k_B$, into a width of a Lorentzian for homogeneous samples, so a nonlinear Dingle plot and a shifted phase become readouts of an asymmetric, non-Lorentzian $D(\mu)$. The Landau-fan intercept and the Onsager relation $F = \hbar S_F/(2\pi e)$ connect these distribution widths to Fermi-surface area variations.

What would settle it

Spatially resolve the local Cr concentration across the unground Cr-doped crystal with a compositional mapping technique and compare the inferred Fermi-energy spread with the fitted three-Lorentzian distribution; a uniform composition map, or a measured distribution that is symmetric, would invalidate the claimed mechanism.

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Extended reading notes

Core claim

The authors' central claim is that the inhomogeneous Cr-doped crystal's dHvA signal is a superposition of oscillations coming from regions with different local Fermi energies, so the effective distribution $D(\mu)$ is a weighted sum of Lorentzians rather than a single Lorentzian. From the $\beta$ oscillations they extract weights $A_i/\sum_i A_i = 0.4322$, $0.0755$, $0.4923$ at frequencies $F(\mu_{0i}) = 710.9$, $713.3$, $716.4$ T with widths $\Delta\mu = 1.55$, $0.88$, $1.43$ meV; the Bi-doped sample needs only one Lorentzian with $F = 708.7$ T and $\Delta\mu = 0.40$ meV. This asymmetry shifts the Landau-fan intercept from the theoretical $\gamma = -0.125$ to $\gamma = -0.46$, while pristine and Bi-doped samples stay near $-0.11$ and $-0.10$. The paper further shows that grinding away part of the Cr crystal restores a nearly linear Dingle plot and an intercept $\gamma = -0.07$, consistent with removing the inhomogeneous region.

Load-bearing premise

The load-bearing premise is that the weighted sum of three Lorentzian Fermi-energy components in Eq. (2) is the actual Fermi-energy distribution of the Cr-doped crystal, since the paper fits that shape to the very oscillations whose phase it is meant to explain and offers no independent spatial or spectroscopic measurement of the distribution.

Editorial extensions

If this is right

  • A nonlinear Dingle plot in a metallic crystal becomes a warning sign for non-uniform composition rather than only for magnetic scattering or dislocations.
  • Extracting the effective Fermi-energy distribution from dHvA oscillations gives a bulk-sensitive homogeneity check that does not require surface spectroscopy.
  • Phase shifts obtained from Landau fan diagrams should not be assigned to a Berry phase until inhomogeneity is excluded by comparing before and after grinding or by checking Dingle-plot linearity.
  • Grinding away part of an inhomogeneous crystal and re-measuring the oscillations characterizes the length scale of the composition variation.
  • The same analysis can be extended to thin films and two-dimensional materials, as the paper suggests, where dopant distributions could be imaged independently.

Reading between the lines

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

  • Beyond the paper, the inversion could be pushed further: instead of assuming three Lorentzians, one could extract an unconstrained $D(\mu)$ from a full dHvA spectrum, turning the method into a quantitative compositional profiler whenever $F(\mu)$ is known.
  • Beyond the paper, the results imply that any claim of a Berry-phase shift from a single Landau-fan intercept in a doped material should be checked against a linear Dingle plot and a grinding test before being accepted.
  • Beyond the paper, a testable extension is to grow samples with controlled composition gradients and verify that the fitted asymmetry tracks the gradient direction and magnitude, which would independently validate the mechanism.
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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 paper reports de Haas-van Alphen (dHvA) measurements on pristine, Bi-doped, and Cr-doped NbSb2 single crystals. The Bi-doped sample behaves homogeneously, while the Cr-doped sample shows clear millimeter-scale inhomogeneity, demonstrated by the large change in dHvA oscillations after grinding. The Cr sample exhibits a nonlinear Dingle plot and a Landau fan intercept of -0.46, far from the expected -0.125. The authors attribute these anomalies to an asymmetric, non-Lorentzian effective Fermi energy distribution and model the oscillations using a sum of three Lorentzian distributions (Eq. 2). They conclude that dHvA analysis can identify non-uniform dopant composition and prevent misinterpreting phase shifts as topological Berry-phase signals.

Significance. The qualitative observations—the grinding comparison, the nonlinear Dingle plot, and the phase shift—are direct and reproducible and strongly support the identification of inhomogeneity. The exclusion of magnetic-impurity effects, the measurement of a common cyclotron mass, and the explicit comparison with a homogeneous Bi-doped sample are all valuable. If the quantitative inversion to an asymmetric D(μ) were rigorously established, the paper would have broader implications for interpreting quantum oscillations in inhomogeneous topological materials. However, the central quantitative claim is not yet convincing because it rests on an underdetermined fit and lacks independent validation. The paper is honest about the approximate nature of the fit, but it overstates the certainty of the asymmetric distribution and the 'violation' of the Lifshitz-Kosevich formula.

major comments (3)
  1. [3.1, Eq. (2), Fig. 3(a)] The central claim of an asymmetric, non-Lorentzian Fermi energy distribution D(μ) for the Cr sample is obtained from an eight-parameter fit of the multi-Lorentzian model in Eq. (2). With three weights, three frequencies, and three widths (modulo normalization), this functional form is flexible enough to reproduce essentially any smooth phase and amplitude envelope present in the data. The paper does not show that a symmetric multi-Lorentzian distribution, or a single LK oscillation with a field-dependent phase, gives a significantly worse fit. Moreover, the same fitted waveform contains the phase shift that the asymmetric distribution is then invoked to explain, so the explanation is partly a restatement of the fit. The authors should perform a quantitative model comparison (e.g., symmetric versus asymmetric fits with uncertainty quantification) or provide an independent measurement of the local Fermi energy distribution (for instance, an EPMA line scan across the sample) to support the asymmetry claim.
  2. [Abstract, Section 1, Eq. (2)] The phrase 'violation of the Lifshitz-Kosevich formula' overstates the result. Equation (2) is itself a superposition of LK oscillations with different frequencies and damping factors. The nonlinear Dingle plot and the phase shift observed in the Cr sample arise naturally from interference among these components within the LK framework; they do not indicate a breakdown of the LK theory. The wording should be softened to 'deviation from a single-component LK fit' or 'departure from the standard LK description for a homogeneous sample.' This is not merely a semantic issue, as the abstract and introduction frame the paper around this claimed violation.
  3. [3.1, Fig. 2(d), Fig. 3(a)] The Landau fan intercept for the Cr sample is reported as -0.46 with no uncertainty estimate. Because the integer assignment N is chosen to force the intercept into the range -0.5 to 0, the result may not be unique for such a large phase deviation. The paper should demonstrate that γ is stable under different reasonable integer assignments and field windows, or use an alternative phase-extraction method that does not rely on this assignment. In addition, the fit shown in Fig. 3(a) visibly does not capture the data perfectly, yet no goodness-of-fit metric or noise level is given. The small oscillation amplitude of ~1 μemu is mentioned qualitatively, but the authors should quantify the noise and report parameter uncertainties so the reader can judge the significance of the extracted asymmetry.
minor comments (4)
  1. [Throughout] The manuscript text contains many scanning/OCR artifacts, including the apparent title on the first page and numerous garbled words in equations and body text. The authors should provide a clean, correctly typeset version, as the current text is difficult to read.
  2. [Fig. 3 caption vs. Section 3.1] The figure caption lists the fitted widths for the Cr sample as Δμ = 1.55, 8.84, and 1.43 meV, while the text reports 1.55, 0.88, and 1.43 meV. These are inconsistent and must be corrected.
  3. [Fig. 2(a) caption] The bandpass filter range used to isolate the β oscillations is not specified. The grey area in Fig. 2(a) should be described in the caption, including the lower and upper frequency bounds of the filter.
  4. [Fig. 1 caption] The caption is duplicated: the second 'Fig. 1' heading should be 'Fig. 2.' In the same caption, 'for visality' should be 'for visibility,' and the phrase 'the size or cyclotron orbits' should read 'the size of cyclotron orbits.'

Circularity Check

1 steps flagged · score 6.0 of 10

Cr's asymmetric Fermi-energy distribution is a fitted output of Eq. (2), then reused as the cause of the same observed phase shift; the central inference restates the fit.

  1. fitted input called prediction [Section 3.1, Eq. (2) and the subsequent three-Lorentzian fit; Fig. 3(a) and Fig. 4 discussion]
    "We fitted Dosc of the Cr sample by Eq. (2) with the three Lorentzian functions. ... From the fitting, we obtained A_i/Σ_i A_i = 0.4322, 0.0755, 0.4923, F(μ0i) = 710.9, 713.3, 716.4 T, and Δμ = 1.55, 0.88, 1.43 meV for Cr sample. ... The peak of the inhomogeneous Cr sample has a broader HWHM = 1.7 meV than that of Bi, asymmetric and non-Lorentzian, producing the phase deviation and the nonlinear Dingle plot."

    The D(μ) asymmetry is not measured independently; it is the fitted output of Eq. (2), and its parameters are chosen to reproduce the same Dosc waveform whose phase deviation and Dingle-plot curvature the paper then attributes to that asymmetry. With three amplitudes, three frequencies, and three widths, the multi-Lorentzian sum can absorb an arbitrary smooth envelope, so the phase shift is explained by construction rather than tested. No symmetric multi-Lorentzian fit is shown to be worse, and no spatial or spectroscopic determination of the Cr composition distribution is provided; the grinding comparison establishes only mm-scale inhomogeneity, not the specific asymmetric form.

full rationale

The derivation chain is partially circular. The inhomogeneity detection by grinding is independent: the Cr and Cr' oscillations differ, and Cr' returns toward the LK phase and linear Dingle plot, supporting mm-scale inhomogeneity as the cause. However, the specific central claim—that the Cr sample has an asymmetric, non-Lorentzian effective Fermi-energy distribution that 'produces' the phase shift—rests entirely on fitting Eq. (2) to the same β-oscillation data whose phase deviation is at issue. The multi-Lorentzian ansatz is flexible enough to reproduce the Dingle curvature and phase shift by adjusting three amplitudes, three frequencies, and three widths; no symmetric alternative is fit and rejected, and no independent spatial or spectroscopic measurement of the Cr distribution is presented. The causal statement is therefore a restatement of the fit parameters, not a consequence derived from independent first principles. The self-citation to ref. [28] for the reference phase −0.125 is standard LK theory and not load-bearing, so it does not add circularity. Overall score 6: the central asymmetric-distribution inference reduces by construction, while the grinding comparison provides independent, though not form-specific, support.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The central model depends on superposing LK oscillations over a distribution of Fermi energies. The only genuinely new ingredient, the multi-Lorentzian shape for the inhomogeneous sample, is chosen ad hoc and fitted to the data, which is why the parameter count is high. No new physical entities are postulated.

free parameters (8)
  • Cyclotron mass mc = 0.51 me
    Fitted from temperature-dependent dHvA amplitude with the thermal reduction factor; used in converting frequency shifts to Fermi-energy shifts.
  • Dingle temperature TD for pristine NbSb2 = 0.16 K
    Fitted from the linear Dingle plot slope; used as a scattering reference.
  • Dingle temperature TD for Bi-doped NbSb2 = 1.3 K
    Fitted from the linear Dingle plot slope; used as a scattering reference.
  • Bi sample beta frequency F = 708.7 T
    Fitted with a single damped oscillation; used to locate the Fermi-energy distribution of the homogeneous Bi sample.
  • Bi sample Lorentzian width delta-mu = 0.40 meV
    Fitted from the single-oscillation Dosc fit; represents relaxation-time broadening.
  • Cr multi-Lorentzian amplitude fractions A_i/sumA = 0.4322, 0.0755, 0.4923
    Fitted weights of the three Lorentzian components; together they define the shape of the inferred effective Fermi-energy distribution.
  • Cr component frequencies F(mu0i) = 710.9, 713.3, 716.4 T
    Fitted centers of the three Lorentzian components in frequency space.
  • Cr component widths delta-mu_i = 1.55, 0.88, 1.43 meV; Fig. 3 caption lists 8.84 for the middle value
    Fitted widths of the three Lorentzian components; the value inconsistency between text and caption is unresolved.
assumptions (5)
  • standard math The Lifshitz-Kosevich formula for a three-dimensional ellipsoidal Fermi surface, Eq. (1), describes each oscillatory component.
    Invoked from standard dHvA theory, Shoenberg [25], and prior NbSb2 analysis [28].
  • domain assumption The observed dHvA signal is the integral over Fermi energies of single-energy LK oscillations weighted by an effective distribution D(mu).
    Extends the standard thermal and Dingle reduction-factor idea to spatial Fermi-energy variation; no derivation that spatial regions add incoherently is given.
  • domain assumption Frequency and Fermi-energy shifts are related linearly by delta-mu approximately e-hbar-delta-F/mc.
    Assumes the Onsager relation and a constant cyclotron mass across the dopant variation.
  • ad hoc to paper A multi-Lorentzian form is an adequate trial shape for D(mu) of the inhomogeneous Cr sample.
    Introduced in Section 3.1 as a trial solution; its success is evaluated visually, with an acknowledged imperfect fit.
  • domain assumption Grinding removes material without changing the intrinsic electronic structure, so any dHvA difference before and after grinding is due to compositional inhomogeneity.
    Used in Section 3.1 to infer millimeter-scale inhomogeneity in the Cr sample.

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Pith. "Pith review of Inhomogeneity identification by measuring magnetic quantum oscillations." pith.science (2026). https://pith.science/paper/X5OWL6EN

@misc{pith2026250723246,
  author       = {Pith},
  title        = {Pith review of: Inhomogeneity identification by measuring magnetic quantum oscillations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/X5OWL6EN}},
  note         = {Machine review of arXiv:2507.23246}
}
abstract

This study explores the identification of sample inhomogeneity via magnetic quantum oscillations analysis in semimetal NbSb$_2$. By doping Bi and Cr, we obtained a homogeneous Bi-doped sample and an inhomogeneous Cr-doped sample, whose homogeneity was confirmed by comparing the magnetic quantum oscillation before and after grinding the samples. The magnetic quantum oscillations in the inhomogeneous sample exhibited a distinct phase shift and unusual field-dependent amplitude, believed to result from a non-uniform Fermi energy. The analysis of the magnetic quantum oscillations demonstrated that the homogeneous Bi-doped sample can be interpreted by the symmetric and Lorentzian effective Fermi energy distribution, while the inhomogeneous Cr-doped sample exhibited an asymmetric distribution, illustrating an unconventional violation of the Lifshitz-Kosevich formula. This research provides a novel method for identifying material inhomogeneity and mitigating potential misinterpretations of magnetic quantum oscillations' unusual phase, commonly seen as a nontrivial Berry phase indicator in topological materials studies.

Figures

Figures reproduced from arXiv: 2507.23246 by the authors.

Figure 1
Figure 1. Comparison of the dHvA oscillations before and after grinding mm-size samples. The dHvA oscillations were measured at 2 K. The ground samples are indicated by a prime. (a) The dHvA oscillations of Bi-doped NbSb2 before and after grinding. We vertically shifted Bi and Bi’ data for clarity (the dashed lines show the shifted M = 0 lines). There is no significant difference between the two, indicating homogeneity. (b) … view at source ↗

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