{"id":"c2206cb8-2ed1-4e53-ae96-3023f8abba1c","arxiv_id":"2608.11148","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Chromium-doped Pb1-xSnxTe shows Weyl-semimetal transport signatures, including chiral-anomaly negative magnetoresistance, Berry curvature, and quantum oscillations, for 0.25 < x < 0.45.","lead":"This paper reports magnetotransport evidence that chromium-doped Pb1-xSnxTe becomes a three-dimensional Weyl semimetal for tin fractions between 25% and 45%, with the chromium resonant level pinning the Fermi energy near the Weyl nodes. It matters because it offers a tunable material platform for studying the chiral anomaly, and even shows a small room-temperature reentrance of this quantum effect.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The SdH Berry-phase claim is circular: fixing Φ_B=π and absorbing error into δ makes the same fan diagram fit a 3-meV-gapped massive-Dirac band, so the WSM identification is not yet conclusive.","rationale":"The paper provides a rich, internally consistent set of magnetotransport measurements—angle-dependent negative longitudinal magnetoresistance, current-jetting exclusion, DC/AC consistency, thermal-conductivity confirmation of quantum oscillations, and a DFT search for Weyl points. These are genuine experimental achievements. However, the strongest claim is the identification of a 3D Weyl semimetal phase, and the only measurement that directly probes the topological character of the bulk bands is the SdH Berry-phase analysis. That analysis fixes Φ_B=π and assigns all error to the Maslov index, which is precisely the procedure that prevents the measurement from falsifying the hypothesis. The 3-meV Arrhenius gap in the same sample provides a concrete alternative: a gapped massive-Dirac band with the measured Fermi energy can produce an intercept within ~0.02 of the fitted value, well inside the plausible experimental uncertainty. This is not a disagreement with consensus but a correctness risk internal to the argument: the central claim's decisive evidence is underdetermined. The reader identified the same weakest assumption, and my independent estimate of the gapped-band intercept (≈0.15 vs. fitted 0.130) confirms that the concern is quantitatively real. Since the paper's other evidence, while supportive, is not unique to Weyl semimetals, the conditional verdict remains appropriate: the claim should be accepted only after the Berry phase is allowed to float in the fan-diagram analysis and the DFT configuration search is documented systematically. No change to the reader's verdict is needed.","tokens_in":28160,"tokens_out":5442,"duration_ms":57608,"concrete_test":"Re-analyze the SdH fan diagram of sample II (x=0.26) with the Berry phase Φ_B as a free parameter (and δ fixed to the conventional ±1/8 for 3D extrema), reporting the best-fit Φ_B and its confidence interval. Then repeat the fit with Φ_B constrained by a massive-Dirac band whose gap is the measured 3-meV Arrhenius gap and E_F from the Hall density. If the unconstrained Φ_B is consistent with π and inconsistent with the gapped-band value, the WSM claim stands; if the gapped-band model fits equally well, the topological identification is not established.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that Pb1–xSnxTe:Cr realizes a 3D Weyl semimetal for 0.25<x<0.45—rests on the Landau-level fan analysis (Fig. 8). The authors state that they extract Maslov indices δ=0.130 and −0.125 “assuming the Berry phase exactly equals π and the whole experimental error is included in δ.” This is the load-bearing step: a nontrivial, gapped band (e.g., a massive Dirac or narrow-gap semiconductor) has Berry phase Φ_B=π(1−Δ/E_F), which for the reported Arrhenius gap of 3 meV and E_F≈58 meV (estimated from n≈1×10^16 cm⁻³ and m*≈0.029m₀) gives Φ_B≈0.95–0.97π. The corresponding Lifshitz–Kosevich intercept γ=1/2−Φ_B/2π+δ is ≈0.15 for the maximum orbit, within ~0.02 of the fitted δ=0.130. Thus the fan diagram cannot distinguish the proposed WSM from a gapped massive-Dirac band, and the 3-meV Arrhenius gap reported for sample I makes that alternative concrete rather than hypothetical. The other transport signatures are supportive but not unique: negative longitudinal magnetoresistance can arise from misalignment or anisotropic mobility; the intrinsic anomalous Hall contribution can have extrinsic sources (the authors themselves report ferromagnetic Cr–Te nanoinclusions); and the quantum nonlinear Hall effect also appears in topological crystalline insulators. Hence the unique topological discriminator is the Berry phase, and it is currently assumed, not measured. This internal tension is acknowledged in the text only through the caveat about δ, but no model comparison against a gapped alternative is provided.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports magnetotransport, thermal-conductivity, and DFT studies of Bridgman-grown Pb1-xSnxTe heavily doped with Cr across the full Sn range, and claims a 3D Weyl semimetal phase for 0.25 < x < 0.45. The evidence includes a pronounced minimum in Hall carrier concentration, intrinsic anomalous Hall effect, negative longitudinal magnetoresistance with angular suppression attributed to the chiral anomaly, quantum nonlinear Hall effect, Shubnikov-de Haas oscillations reaching the quantum limit, and first-principles supercell calculations locating Weyl nodes. The central claim is that alloy disorder broadens the VCA band-inversion point into a finite composition window in which Fermi-level pinning by Cr resonant states places the Fermi level near Weyl nodes.","tokens_in":28448,"tokens_out":4899,"duration_ms":104731,"significance":"If the central claim is correct, the paper would establish a tunable, composition-controlled WSM platform in a mainstream IV-VI semiconductor family, with the practical advantage of Fermi-level pinning by a resonant dopant. The dataset is broad: full composition coverage, multiple transport signatures, angular controls, exclusion of current jetting, AC/DC consistency, and SdH quantum-limit analysis. The paper also ships the first-principles framework identifying Weyl points and uses it to interpret Fermi-surface cross-sections. The main weakness is that the unique topological discriminator, the SdH Berry phase, is assumed rather than measured, and the DFT support is partly based on selected supercell configurations. These issues are fixable in revision and do not invalidate the experimental corpus.","major_comments":[{"comment":"The SdH Berry-phase extraction is circular in its present form. The Landau-level intercepts are reported as Maslov indices δ = 0.130 and −0.125 only after fixing Φ_B = π and assigning the entire experimental error to δ, as stated in the text around Fig. 8. But the Lifshitz-Kosevich phase obeys γ = 1/2 − Φ_B/(2π) + δ, so a gapped massive-Dirac band with gap Δ has Φ_B = π(1 − Δ/E_F). For the reported 3 meV Arrhenius gap of sample I and an estimated E_F ≈ 58 meV (n ≈ 1×10^16 cm^-3, m* ≈ 0.029 m0), Φ_B ≈ 0.95π, which shifts γ by about 0.025. This shift is comparable to the difference between the two quoted δ values and to the scatter shown in Fig. 8C. The fan diagram therefore cannot distinguish the Weyl scenario from a narrow-gap massive-Dirac band; the claimed π Berry phase is an input of the analysis, not an output. Please refit the fan diagrams with Φ_B and δ as independent parameters, or fit a two-band massive-Dirac model, and report uncertainties on Φ_B. If the data cannot discriminate, the conclusions should state that explicitly rather than claiming confirmation of a 3D WSM.","section":"Analysis of quantum oscillations, Eq. (1), Figs. 8 and 9"},{"comment":"The DFT support is weakened by selection bias in the supercell configurations. The text states that 'usually we obtain results with positive or negative energy gaps' and that 'finding the system containing Weyl points is not an easy task,' and Table I lists only configurations that already contain Weyl points. If the supercells were selected because they produce Weyl points, the calculation cannot independently establish that the composition range 0.28 ≤ x ≤ 0.44 generically hosts Weyl nodes. Please report how many supercell configurations were sampled per composition, how many contained Weyl points, and what the distribution of gaps is. Alternatively, present a statistical or ensemble argument showing that the WSM window is robust to the choice of cation arrangement.","section":"Technical details of calculations (Methods)"},{"comment":"The angular dependence and multi-contact measurements materially strengthen the chiral-anomaly assignment, and I agree that current jetting and simple misalignment are unlikely explanations. However, the negative longitudinal magnetoresistance is modeled with Eq. (S6) using four independent parameters (C_w, C_WAL, B_c, and γ), and no quantitative comparison is made with an anisotropic-mobility or two-carrier model constrained by the measured Hall density and mobility. Since the SdH phase analysis cannot currently act as the unique topological discriminator, the chiral anomaly alone leaves the WSM identification underdetermined. Please add a model-comparison figure or a clear statement identifying which observable is incompatible with a narrow-gap massive-Dirac or anisotropic-trivial band description.","section":"Chiral anomaly and alternative interpretations, Figs. 3, 6, Eq. (S6)"}],"minor_comments":[{"comment":"There are several typos and stylistic errors: 'yelding' should be 'yielding', 'devided' should be 'divided', and the sentence beginning 'Quantum transport regime observed in magnetoresistance' in the abstract is grammatically incomplete.","section":"Results and discussion"},{"comment":"The sample labeling is inconsistent. The text says the reentrant chiral anomaly is reported for x = 0.4, but the Fig. 4 caption refers to 'sample II', which was previously defined as x = 0.26. Please clarify which sample is shown in Fig. 4 and reconcile the notation.","section":"Fig. 4 and accompanying text"},{"comment":"The fitted intercepts are quoted as δ = 0.130 and −0.125 with the statement that all error is contained in δ, but no error bars or goodness-of-fit measures are provided for the linear fits in Fig. 8A and 8B. Please report the fit uncertainties and the number of oscillations used.","section":"Eq. (1) and Fig. 8"},{"comment":"The abstract states that the quantum transport regime is 'independently confirmed by thermal conductivity measurements,' but the text describes the thermal-conductivity fit as showing only 'good qualitative agreement.' Please soften the abstract claim or provide a quantitative measure of agreement.","section":"Fig. 9B"},{"comment":"The attribution of the magnetic-field-periodic oscillations to Aharonov-Bohm and Altshuler-Aronov-Spivak oscillations is presented without a statistical test of periodicity in B versus 1/B, and the inferred loop area of 100 nm^2 is compared with ferromagnetic Cr-Te nanoinclusions that the main text says do not contribute to transport. Please add the spectral or index-plot analysis that supports the B-periodic assignment.","section":"Supplementary Note S.VIII"},{"comment":"The reference numbering contains duplicates and inconsistencies: Ref. 3 appears for two different papers and Ref. 6 also appears twice. This should be corrected before publication.","section":"Reference list"}],"recommendation":"major_revision","confidential_remarks":"The paper is within scope and the experimental effort is substantial. My recommendation is driven by the SdH Berry-phase analysis, which is currently an assumption dressed as a result, and by the selected-supercell issue in the DFT support. Both are addressable in revision: the authors should either free Φ_B in the fan-diagram fit or explicitly state that the SdH data are consistent with both π and slightly-less-than-π Berry phases, and they should report the fraction of supercell configurations that yield Weyl points. If those changes are made, the paper could reasonably be accepted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear --,\n\nThe real news here is the sample series: Cr-doped Pb1-xSnxTe grown across the full tin range, with a clear composition window (0.25<x<0.45) where the carrier density drops to 1e16 cm^-3 and a cluster of transport signatures appears — negative longitudinal magnetoresistance with angular suppression, an intrinsic anomalous Hall contribution, quantum nonlinear Hall effect, SdH oscillations reaching the quantum limit, and oscillations in thermal conductivity. The experimental work is careful: they checked current jetting, compared AC and DC, used multiple contact pairs, and the angular dependence of the negative MR is well characterized. The tunability via Cr resonant states is a real contribution.\n\nThe soft spot is the Berry-phase analysis. In Fig. 8 they fix Phi_B=pi and then absorb all error into the Maslov index delta. That is not a measurement of the Berry phase; it is an assumption. The stress-test note makes this point, but its numbers are off: the Arrhenius gap (3 meV) is for sample I (x=0.38), not the SdH sample II (x=0.26), and the Fermi energy estimate for n=1e16 cm^-3 with m*=0.029m0 is about 6 meV, not 58 meV. The gapped alternative is not as sharply quantified for the SdH sample as the note claims. Still, the presentation is circular and needs fixing. The authors should report the fitted intercept, let Phi_B float, and show that pi is preferred over zero. That is a referee-level demand, not a fatal flaw: the other signatures are suggestive, but the Berry phase is the only topological discriminator, and right now it is assumed.\n\nThere is also a sample-labeling inconsistency: the abstract and text say the room-temperature reentrance is for x=0.4, but Fig. 4 labels it 'sample II', which Methods defines as x=0.26. That needs clarification. The DFT support is weakened by the tuned spin-orbit parameter and by the acknowledged post-hoc selection of supercell configurations. None of this destroys the experimental core, but it means the paper does not yet establish the Weyl semimetal claim beyond reasonable doubt.\n\nI would send this to a serious referee, mainly to force a clean SdH phase analysis and the sample-label fix. I would not cite the Weyl claim in my own work until that is done, but I would keep the experimental phenomenology in mind. A 'conditional' verdict is the right call.","headline":"Solid experimental study with a tunable Fermi-level window, but the Weyl claim rests on an assumed Berry phase; worth a referee, not a desk reject.","tokens_in":29138,"tokens_out":8198,"would_cite":false,"duration_ms":74380,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that alloy disorder in Pb$_{1-x}$Sn$_x$Te:Cr opens a finite composition window, $0.25 < x < 0.45$, in which the material behaves as a three-dimensional Weyl semimetal, with the Fermi level pinned near Weyl nodes by…","keywords":["Weyl semimetal","chiral anomaly","negative magnetoresistance","Berry curvature","Pb1-xSnxTe:Cr","resonant impurity Fermi-level pinning","Shubnikov-de Haas oscillations","topological crystalline insulator"],"falsifier":"Re-fit the Landau-level fan diagram for the $x=0.38$ sample without fixing the Berry phase, using the measured effective mass and Dingle temperature; if the intercept moves away from $\\pi$ as the gap is varied by changing Cr content or applying pressure, the Weyl assignment fails. A surface-sensitive search for the predicted Fermi arcs would also settle the question, though the paper notes that the Weyl-node separation is too small for present-day angle-resolved photoemission.","tokens_in":27840,"feed_emoji":"🧲","tokens_out":11896,"duration_ms":108518,"temperature":0.7,"pith_summary":"This paper tries to establish that heavily Cr-doped lead-tin telluride, Pb$_{1-x}$Sn$_x$Te:Cr, is a three-dimensional Weyl semimetal for tin fractions in the window $0.25 < x < 0.45$, and not only at the single composition where the virtual-crystal approximation closes the band gap. The proposed mechanism is that cation-site alloy disorder staggers the band inversions in the four $L$ valleys, producing pairs of opposite-chirality Weyl nodes over a finite composition range, while mixed-valence Cr impurities pin the Fermi level near those nodes. The evidence is a suite of magnetotransport effects: a record-low carrier density near $x=0.38$, an intrinsic anomalous Hall effect with a Berry curvature extracted from it, negative longitudinal magnetoresistance attributed to the chiral anomaly (up to 75%, and re-entering at room temperature in one sample), quantum nonlinear Hall effect, and Shubnikov-de Haas oscillations with a $\\pi$ Berry phase and 3D Maslov index. The same material class that already hosts topological crystalline insulators would, if this is right, become a compositionally tunable bulk platform for Weyl physics.","feed_headline":"Alloy disorder turns one band crossing into a Weyl-semimetal window","feed_subtitle":"Chromium pins the Fermi level at Weyl nodes, turning on chiral-anomaly transport up to room temperature.","key_machinery":"The central objects are pairs of Weyl nodes of opposite chirality located near the Fermi level: points in momentum space where two bands touch linearly and act as sources and sinks of Berry flux. The mechanism that carries the argument is sequential band inversion in the four inequivalent $L$ valleys, driven by alloy disorder and broadened into a finite composition window, together with Cr$^{2+/3+}$ resonant donor states that pin the Fermi level at the nodal energy. The quantitative workhorse is the Lifshitz-Kosevich formula for Shubnikov-de Haas oscillations, whose phase factor $\\gamma = \\frac{1}{2} - \\frac{\\Phi_B}{2\\pi} + \\delta$ separates the Berry phase $\\Phi_B$ from the Maslov index $\\delta$; setting $\\Phi_B = \\pi$ turns the measured intercept into a 3D-topology test ($\\delta \\approx \\pm 1/8$). Berry curvature extracted from the intrinsic anomalous Hall conductivity links these oscillations to the field-dependent transport.","core_discovery":"On the paper's own terms, the central discovery is that the disorder-driven sequential band inversion predicted for the multivalley $L$-point system is realized: instead of a single virtual-crystal band-inversion point, the gap closes valley by valley, and Weyl points with topological charges $\\pm 1$ appear for $x = 0.28$, $0.375$, and $0.44$ in density-functional calculations. Experimentally, the signature is the strong suppression of carrier concentration to $n \\approx 1\\times10^{16}\\,\\mathrm{cm}^{-3}$ at $x=0.38$, where the Fermi level sits near the nodal touching points, and the observation of transport phenomena tied to Berry curvature: intrinsic anomalous Hall effect, chiral-anomaly negative magnetoresistance reaching 75%, quantum nonlinear Hall effect, and Shubnikov-de Haas oscillations entering the quantum limit near 5 T. The Landau-level fan gives a Berry phase read as $\\pi$ with Maslov-index values of $+0.130$ and $-0.125$, which the authors take as the marker of three-dimensional Weyl states. Thermal-conductivity oscillations independently corroborate the quantum transport regime.","pith_inferences":["If the disorder-broadening mechanism is generic, the same sequential-inversion effect should appear in other multivalley IV-VI alloys, and hydrostatic pressure could sweep a single crystal through the Weyl window without changing composition.","Because the Weyl nodes are nearly touching in momentum space, their Fermi arcs should be very short; a more practical experimental test than angle-resolved photoemission might be scanning tunneling spectroscopy or a Berry-phase measurement with the Fermi level deliberately moved off the nodes.","The 275-310 K re-entrance of the chiral anomaly hints at a temperature-driven topological phase boundary; mapping the full Hall resistivity tensor through this region could show whether the re-entrance tracks a band-gap sign change rather than a trivial carrier-density effect."],"forward_implications":["If the assignment holds, the Weyl phase becomes addressable by two external knobs, tin fraction and temperature, allowing a single crystal family to be switched between normal insulator, Weyl semimetal, and topological crystalline insulator.","Room-temperature chiral anomaly in the $x=0.4$ sample would make bulk Pb$_{1-x}$Sn$_x$Te:Cr one of the few material systems in which chiral transport can be studied away from dilution-refrigerator temperatures.","The low quantum-limit field of about 5 T means Landau-quantized Weyl physics is accessible with compact superconducting magnets.","The agreement between the chiral-anomaly coefficient and the Berry curvature inferred from the anomalous Hall effect suggests that average Berry curvature can be estimated from the two resistivity tensor components in this alloy family."],"supporting_citations":[{"why":"Supplies the theoretical prediction that alloy disorder broadens the band-inversion point into a sequential, finite-composition Weyl phase in Pb$_{1-x}$Sn$_x$Te.","marker":"[12]"},{"why":"Demonstrates chemically induced intermediate Weyl semimetal behavior during sequential band inversion in the related Pb$_{1-x}$Sn$_x$Se alloy.","marker":"[13]"},{"why":"Provides the density-functional method for locating Weyl points and the prior result that their k-space separation is very small in this system.","marker":"[47]"},{"why":"Establishes the Cr resonant-level positions and the composition-dependent carrier-density data for the same crystal family, which the paper builds on.","marker":"[42]"},{"why":"Predicts the quantum nonlinear Hall effect as a Berry-curvature-dipole response, used here as a topological marker.","marker":"[33]"},{"why":"Provides the canonical first observation of chiral-anomaly negative magnetoresistance, the benchmark signature this paper compares with.","marker":"[19]"},{"why":"Documents chiral-anomaly negative magnetoresistance in a Dirac semimetal and its extreme sensitivity to field alignment, used to interpret the angular dependence.","marker":"[24]"},{"why":"Supplies the Shubnikov-de Haas phase formula linking Berry phase and Maslov index that underlies the topological interpretation of the oscillations.","marker":"[74]"},{"why":"Used to rule out current-jetting geometry effects as an alternative explanation of the negative magnetoresistance.","marker":"[59]"}],"fun_headline_variants":["Alloy disorder and Cr doping create tunable Weyl chiral anomaly","Weyl semimetal window opens with tunable chiral anomaly","Chiral anomaly in disordered alloy Weyl semimetal tuned by Cr","Fermi-level pinning yields tunable chiral anomaly in Weyl semimetal","Disorder-driven Weyl semimetal with tunable chiral anomaly"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the quantum-oscillation analysis fixes the topological Berry phase at exactly $\\pi$ and assigns the entire experimental uncertainty to the secondary Maslov index $\\delta$; if the true Berry phase is not $\\pi$, the same Landau-level fan diagram would fit a trivial narrow-gap semiconductor, and the $x=0.38$ sample does show a small 3 meV activation gap.","fun_headline_variants_meta":{"raw":{"variants":["Alloy disorder and Cr doping create tunable Weyl chiral anomaly","Weyl semimetal window opens with tunable chiral anomaly","Chiral anomaly in disordered alloy Weyl semimetal tuned by Cr","Fermi-level pinning yields tunable chiral anomaly in Weyl semimetal","Disorder-driven Weyl semimetal with tunable chiral anomaly"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00087,"raw_usage":{"total_tokens":3840,"prompt_tokens":1088,"completion_tokens":2752,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":704,"completion_tokens_details":{"reasoning_tokens":2656}},"tokens_in":704,"tokens_out":2752,"duration_ms":19354,"temperature":1.0,"reasoning_tokens":2656,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T05:13:29.662249+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-fit the Landau-level fan diagram for the $x=0.38$ sample without fixing the Berry phase, using the measured effective mass and Dingle temperature; if the intercept moves away from $\\pi$ as the gap is varied by changing Cr content or applying pressure, the Weyl assignment fails. A surface-sensitive search for the predicted Fermi arcs would also settle the question, though the paper notes that the Weyl-node separation is too small for present-day angle-resolved photoemission.","supporting_citations":[{"cited_title":"Łusakowski , author P","cited_arxiv_id":null,"evidence_quote":"Supplies the theoretical prediction that alloy disorder broadens the band-inversion point into a sequential, finite-composition Weyl phase in Pb$_{1-x}$Sn$_x$Te."},{"cited_title":"Wang , author Q","cited_arxiv_id":null,"evidence_quote":"Demonstrates chemically induced intermediate Weyl semimetal behavior during sequential band inversion in the related Pb$_{1-x}$Sn$_x$Se alloy."},{"cited_title":"Łusakowski , author P","cited_arxiv_id":null,"evidence_quote":"Provides the density-functional method for locating Weyl points and the prior result that their k-space separation is very small in this system."},{"cited_title":"Królicka , author K","cited_arxiv_id":null,"evidence_quote":"Establishes the Cr resonant-level positions and the composition-dependent carrier-density data for the same crystal family, which the paper builds on."},{"cited_title":"\\ Kim , author K.-S","cited_arxiv_id":null,"evidence_quote":"Provides the canonical first observation of chiral-anomaly negative magnetoresistance, the benchmark signature this paper compares with."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Shubnikov-de Haas phase formula linking Berry phase and Maslov index that underlies the topological interpretation of the oscillations."},{"cited_title":"Liang , author J","cited_arxiv_id":null,"evidence_quote":"Used to rule out current-jetting geometry effects as an alternative explanation of the negative magnetoresistance."}],"review_version":1}