{"id":"47e491a2-e1c3-430a-8b7a-0abdba4eaac1","arxiv_id":"2507.23246","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":8,"one_line_summary":"Inhomogeneous Cr doping in NbSb2 produces a phase shift and nonlinear amplitude in de Haas-van Alphen oscillations that the authors model with an asymmetric Fermi-energy distribution.","lead":"This paper uses the wiggles in a crystal's magnetization, called magnetic quantum oscillations, to reveal whether dopant atoms are spread unevenly through the sample. It offers a practical warning that such sample flaws can masquerade as the Berry phase signals researchers look for in topological materials.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The asymmetric Fermi-energy distribution in Cr is extracted from an unvalidated 8-parameter Lorentzian fit to the same noisy oscillations whose phase shift it is meant to explain; a symmetric multi-component model could plausibly reproduce the data.","rationale":"The reader's weakest-assumption analysis identifies the same load-bearing risk: the three-Lorentzian model in Eq. (2) is assumed to represent the physical Fermi-energy distribution, and the fitted asymmetry is used to explain the phase shift contained in the same data without independent confirmation. My stress-test sharpens this into a concrete, testable non-uniqueness problem: the multi-Lorentzian ansatz has enough flexibility to absorb the observed phase anomaly even if the underlying distribution is symmetric, provided the symmetry constraint is not imposed. The grinding comparison is good evidence for inhomogeneity, and the exclusion of magnetic impurity effects is carefully argued, so the qualitative finding is plausible. However, the quantitative claim of an asymmetric distribution—and the associated warning about mimicking Berry phase—rests on a single overparameterized fit to a weak signal. The paper does not report uncertainties, raw data, or fitting code, so the stability of the three-Lorentzian decomposition cannot be checked from the manuscript alone. The proposed symmetry test would settle whether the asymmetry is required by the data rather than an artifact of model flexibility. Because the reader's conditional verdict already reflects the need for independent confirmation, I do not propose a change to that verdict.","tokens_in":13497,"tokens_out":6443,"duration_ms":77204,"concrete_test":"Refit the Cr Dosc data with a constrained symmetric model, e.g., two equal-weight, equal-width Lorentzians centered at F0 ± ΔF (or a symmetric Gaussian in frequency), using the same Dingle and normalization factors, and compare the fit to the unconstrained three-Lorentzian fit via an F-test, AIC/BIC, or bootstrap confidence intervals on an asymmetry parameter such as the first moment of D(μ). Additionally, inject synthetic data generated from a known symmetric two-region distribution with the reported noise level through the same filtering and fitting pipeline; if the symmetric model fits the Cr data within noise or the pipeline returns a spuriously asymmetric D(μ) from symmetric input, the asymmetric-distribution claim is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step for the central claim is the inversion from the Cr sample's Dosc to an asymmetric, non-Lorentzian effective Fermi-energy distribution D(μ) via Eq. (2). Because Eq. (2) is a sum of LK oscillations with a fixed intrinsic phase, any phase shift in the fit must be produced by the relative frequencies, widths, and weights of the three Lorentzians. With eight free parameters (three amplitudes, three frequencies, and three widths, modulo normalization) fitted to a roughly 1 μemu oscillation signal with unquantified noise, the fitted asymmetry is not established unless a symmetric multi-Lorentzian model is shown to be significantly worse. The paper fits the very oscillations whose phase anomaly is being explained, and no independent spatial or spectroscopic measurement of the Cr composition distribution is provided. The grinding comparison does robustly establish millimeter-scale inhomogeneity, and the exclusion of magnetic-impurity effects is reasonable, but neither step validates the specific asymmetric functional form used to explain the phase shift. The phrase 'violation of the Lifshitz-Kosevich formula' is also an overstatement because Eq. (2) is itself a superposition of LK terms.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":13754,"tokens_out":5068,"duration_ms":59591,"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":[{"comment":"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.","section":"3.1, Eq. (2), Fig. 3(a)"},{"comment":"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.","section":"Abstract, Section 1, Eq. (2)"},{"comment":"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.","section":"3.1, Fig. 2(d), Fig. 3(a)"}],"minor_comments":[{"comment":"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.","section":"Throughout"},{"comment":"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.","section":"Fig. 3 caption vs. Section 3.1"},{"comment":"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.","section":"Fig. 2(a) caption"},{"comment":"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.'","section":"Fig. 1 caption"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses an interesting question and the qualitative experimental comparison is solid. However, the central quantitative claim—the asymmetric Fermi-energy distribution—needs significantly stronger support. I recommend requiring a model comparison (symmetric vs. asymmetric fits, with uncertainties) or an independent spatial measurement of dopant distribution. If such support cannot be provided, the claims should be tempered to what the data actually show. The manuscript also needs substantial editorial cleanup. The paper fits the journal's scope in condensed matter and materials science."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The thing worth remembering from this paper is the grinding comparison: measuring dHvA before and after removing surface material is a simple, convincing way to detect millimeter-scale compositional inhomogeneity. The authors show a clear difference for the Cr-doped sample, a near-identical response for the Bi-doped one, and they make a fair case that magnetic impurity effects are not the cause. The nonlinear Dingle plot and the phase intercept of −0.46 in the Cr sample are real observations, and the demonstration that inhomogeneity can mimic a Berry-phase-like shift is a useful caution for the quantum oscillations community. So the qualitative core is solid.\n\nThe soft spot is the quantitative step that turns those observations into an asymmetric, non-Lorentzian effective Fermi-energy distribution. That distribution is the output of an eight-parameter sum of three Lorentzians fitted to a roughly 1 μemu oscillation signal. The fit is then used to explain the very phase shift contained in the same data. It is a circular restatement unless a symmetric three-Lorentzian model is shown to fit substantially worse, which the paper never does. There is also no independent spatial or spectroscopic measurement of the Cr distribution. The statement that the result illustrates a 'violation of the Lifshitz-Kosevich formula' overstates things, because Eq. (2) is itself a superposition of LK terms.\n\nI would not dismiss the paper. The grinding protocol and the qualitative observations are new enough to be valuable, and the writing is clear about what was done. But the central mechanistic claim about asymmetric D(μ) needs much stronger support. A serious referee should ask for the raw data and fitting code, uncertainty estimates for the fit parameters, a comparison against a symmetric three-component model, and a softened or better-supported conclusion. The claim about preventing misidentified Berry phases is plausible and well worth publishing once the quantitative inversion is either confirmed or replaced with a more conservative interpretation. This deserves peer review, not desk rejection; the authors have the right idea and a good experimental handle, just a load-bearing analysis step that is currently under-supported.","headline":"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.","tokens_in":14311,"tokens_out":1029,"would_cite":true,"duration_ms":15441,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["71.18.+y"],"model":"deepseek-v4-flash","headline":"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.","keywords":["de Haas-van Alphen effect","magnetic quantum oscillations","sample inhomogeneity","non-uniform doping","Fermi energy distribution","Dingle plot","Berry phase","NbSb2"],"falsifier":"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.","tokens_in":13235,"feed_emoji":"🧲","tokens_out":10707,"duration_ms":115033,"temperature":0.7,"pith_summary":"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.","feed_headline":"Uneven doping mimics a topological Berry phase in quantum oscillations","feed_subtitle":"dHvA analysis shows uniform and uneven doping can be told apart before phase shifts are read as topology.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"It supplies the Lifshitz-Kosevich formula and the reduction-factor framework that the analysis applies and then extends.","marker":"[25]"},{"why":"It provides Onsager's relation between oscillation frequency and Fermi-surface cross-section, which is why a spatially varying Fermi energy changes the local dHvA frequency.","marker":"[38]"},{"why":"It gives the original Lorentzian Fermi-energy distribution that produces a linear Dingle plot for homogeneous samples, the baseline against which the Cr sample is judged.","marker":"[43]"},{"why":"It establishes the expected phase $\\gamma = -0.125$ for the $\\beta$ oscillations in NbSb2, the reference value used to flag the Cr sample's phase shift.","marker":"[28]"},{"why":"It documents the dHvA oscillations of NbSb2 that the paper uses to identify the observed frequencies.","marker":"[46]"},{"why":"It provides the magnetoresistance and Shubnikov-de Haas behavior of NbSb2 used to place the present dHvA results.","marker":"[47]"},{"why":"It is the s-d coupling study used to rule out magnetic impurity scattering as the origin of the Cr sample's anomalous Dingle plot and phase.","marker":"[57]"}],"fun_headline_variants":["Uneven doping mimics Berry phase in quantum oscillation data","Quantum oscillations expose inhomogeneity, dodging false Berry phase","Distinguishing uneven doping from topological Berry phase in dHvA","Inhomogeneous doping distorts quantum oscillation phase, not topology"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Uneven doping mimics Berry phase in quantum oscillation data","Quantum oscillations expose inhomogeneity, dodging false Berry phase","Distinguishing uneven doping from topological Berry phase in dHvA","Inhomogeneous doping distorts quantum oscillation phase, not topology"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000451,"raw_usage":{"total_tokens":2276,"prompt_tokens":952,"completion_tokens":1324,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":568,"completion_tokens_details":{"reasoning_tokens":1254}},"tokens_in":568,"tokens_out":1324,"duration_ms":11924,"temperature":1.0,"reasoning_tokens":1254,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T10:54:50.155829+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Shoenberg, F","cited_arxiv_id":null,"evidence_quote":"It supplies the Lifshitz-Kosevich formula and the reduction-factor framework that the analysis applies and then extends."},{"cited_title":"Dingle, Some magnetic properties of metals II","cited_arxiv_id":null,"evidence_quote":"It gives the original Lorentzian Fermi-energy distribution that produces a linear Dingle plot for homogeneous samples, the baseline against which the Cr sample is judged."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It establishes the expected phase $\\gamma = -0.125$ for the $\\beta$ oscillations in NbSb2, the reference value used to flag the Cr sample's phase shift."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It documents the dHvA oscillations of NbSb2 that the paper uses to identify the observed frequencies."},{"cited_title":"Guo, Y .K","cited_arxiv_id":null,"evidence_quote":"It provides the magnetoresistance and Shubnikov-de Haas behavior of NbSb2 used to place the present dHvA results."},{"cited_title":"Fermi surface magnetization of Fe-doped NbSb$_2$ investigated by magnetic quantum oscillations","cited_arxiv_id":"2104.07948","evidence_quote":"It is the s-d coupling study used to rule out magnetic impurity scattering as the origin of the Cr sample's anomalous Dingle plot and phase."}],"review_version":1}