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REVIEW 5 major objections 5 minor 63 references

Disorder-driven Weyl-Kondo Semimetal Phase in WTe$_2$

T0 review · 5 major / 5 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read The paper claims that in disordered bulk WTe2, disorder-driven Kondo screening pins the Fermi level near the Weyl nodes, producing a Weyl-Kondo semimetal phase with spontaneous and nonlinear Hall responses.

desk verdict The transport data are new and worth a look, but the Weyl-Kondo phase claim rests on a Kondo fit whose magnetic evidence is hidden in the SM and a noninteracting model that cannot pin the Fermi level. read the letter →

arxiv 2509.10398 v1 pith:OAL6DV2G submitted 2025-09-12 cond-mat.mes-hall cond-mat.mtrl-sci

Arpan Manna , Sunit Das , Amit Agarwal , Soumik Mukhopadhyay This is my paper
classification cond-mat.mes-hallcond-mat.mtrl-sci
keywords Weyl-KondosemimetalWTe2Kondoeffectdisorder-inducedtopologyspontaneousHallBerrycurvaturedipoletype-IIWeylsecond-harmonic
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

This paper tries to establish that disorder alone can create a Weyl-Kondo semimetal phase in bulk WTe2, a material that starts out nonmagnetic and only weakly correlated. In samples with more disorder, the authors find a low-temperature logarithmic resistivity upturn that fits Kondo scattering, and both the upturn and the magnetoresistance are strongly anisotropic, matching the tilted type-II Weyl band structure. They also observe a spontaneous Hall effect at zero magnetic field and a second-harmonic Hall signal quadratic in current, both stronger in the most disordered sample. Their interpretation is that Kondo interactions pin the Fermi level close to the Weyl nodes, where Berry curvature and Berry curvature dipole are large, making disorder a tuning knob for correlated topology. If correct, WTe2 becomes a platform for Weyl-Kondo fermions outside the usual heavy-fermion compounds.

What carries the argument

The load-bearing machinery is the coupling between disorder-induced Kondo screening and the type-II Weyl band structure. The Hamann resistivity formula with an RKKY effective temperature is used to extract Kondo temperature and spin; the tilted, over-tilted Weyl dispersion provides the anisotropy; the Berry curvature Ω_z enters a fully non-equilibrium Boltzmann distribution g(k) to produce the spontaneous Hall current j_y^sp = -(e^2/ℏ) E_x ∫ Ω_z g(k); and the Berry curvature dipole Λ_zx produces the nonlinear Hall conductivity. Two-band model fits are used to extract carrier densities and to show that the Fermi level in disordered samples sits near the Weyl nodes.

What would settle it

A decisive observation would be magnetic susceptibility, electron spin resonance, or muon spin rotation on the same disordered crystals showing localized moments whose density scales with disorder and which are screened below about 16 K. If no such moments appear, or if the resistivity upturn is unchanged under magnetic fields in a way inconsistent with Kondo spin-flip scattering, the disorder-driven Weyl-Kondo explanation would be ruled out.

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Extended reading notes

Core claim

The central claim is that in bulk WTe2, increasing disorder generates local magnetic moments whose Kondo screening becomes the dominant low-temperature scattering channel. The resistivity upturn is fit with the Hamann Kondo expression using an effective temperature for RKKY interactions, giving TK roughly 16 K for in-plane current and spin S near 1. The screening is anisotropic with respect to current and field directions, reflecting the tilted type-II Weyl dispersion. From simultaneous two-band fits to Hall and longitudinal resistivity, the most disordered sample is charge-decompensated, indicating the Fermi level sits near the Weyl nodes. In that regime the authors observe a spontaneous Ha

Load-bearing premise

The claim rests on the assumption that the low-temperature resistivity upturn in disordered WTe2 comes from Kondo scattering by disorder-induced local magnetic moments; if the upturn instead arises from weak localization or electron-electron interactions, the Weyl-Kondo phase interpretation loses its foundation.

Editorial extensions

If this is right

  • Disorder can be used as a deliberate tuning parameter to reach a Weyl-Kondo semimetal phase in a weakly correlated, nonmagnetic Weyl semimetal.
  • A spontaneous Hall effect at zero field serves as a transport signature that the Fermi level has been pinned near the Weyl nodes by Kondo screening.
  • The second-harmonic Hall signal, quadratic in current and enhanced at low temperature, provides a measure of Berry curvature dipole strength and Fermi-level position.
  • The magnitude of the resistivity upturn, its anisotropy, and the strength of both Hall effects should track the disorder level across WTe2 samples.
  • The observed charge decompensation is consistent with the Fermi level moving toward the Weyl nodes as disorder and Kondo screening increase.

Reading between the lines

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

  • If the Kondo picture is right, local moments should be directly observable in the same disordered crystals—for example, through a Curie-like magnetic susceptibility or a characteristic heat-capacity anomaly; the paper does not report such magnetic characterization in the main text.
  • The mechanism suggests that controlled defect engineering, such as electron irradiation or ion milling, could tune WTe2 continuously from a clean semimetal to a Weyl-Kondo phase, allowing a systematic map of the spontaneous Hall effect versus Fermi-level position.
  • Other nonmagnetic type-II Weyl semimetals with low carrier density and a low-temperature resistivity upturn may show similar disorder-induced behavior; reanalyzing existing transport data for zero-field Hall anomalies could reveal further candidates.
  • A sharper testable prediction is that the spontaneous Hall signal should be suppressed when the Fermi level is moved away from the Weyl nodes by gating or doping, even in disordered samples.
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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

5 major / 5 minor

Summary. The paper presents transport measurements on three CVT-grown WTe2 crystals with RRR values of about 51, 15, and 6. It interprets a low-temperature resistivity upturn in the disordered samples as anisotropic Kondo screening, using the Hamann expression with an RKKY effective temperature (Eq. 1). It reports a spontaneous zero-field Hall signal extracted as the residual after two-band model fits, and a second-harmonic Hall response with quadratic current scaling. A noninteracting tight-binding type-II Weyl model is then used to argue that charge decompensation is largest near the Weyl nodes and that Berry-curvature nonlinear and spontaneous Hall responses peak there. On this basis the authors claim that disorder-driven Kondo interactions pin the Fermi level near the Weyl nodes, realizing a Weyl-Kondo semimetal phase in WTe2.

Significance. If correct, this would be a significant advance: it would show that a nonmagnetic, weakly correlated semimetal can be tuned by disorder into a correlated topological Weyl-Kondo state, and it would identify transport signatures for such a phase. The paper has useful ingredients: a three-sample disorder series, orientation-dependent transport, Hall-baseline corrections, second-harmonic scaling, and explicit model calculations. However, the load-bearing causal chain is not established: local-moment formation is not directly demonstrated, the spontaneous Hall signal is a model-dependent residual, and the theoretical model does not include Kondo physics. The manuscript therefore cannot currently support the title claim.

major comments (5)
  1. [Anisotropic Kondo screening, Eq. (1), Fig. 1] The Kondo identification rests on a four-parameter Hamann fit (rho_H, T_K, S, T_W) to a low-temperature resistivity upturn. No magnetic susceptibility or heat-capacity results are shown in the main text (SM S2-S3 are only mentioned), and no competing fits for weak localization or electron-electron interactions are provided. Because local-moment formation is the first step of the claimed disorder-driven Weyl-Kondo chain, this is a load-bearing omission. If the upturn has a nonmagnetic origin, the central claim collapses.
  2. [Spontaneous Hall effect, Fig. 2] The spontaneous Hall signal rho_sp^xy is a residual after subtracting a two-band model fit. This extraction assumes that the two-band model captures all ordinary magnetotransport; any even-in-B background, such as contact admixture at 2 K not captured by the 300-K correction factor, thermoelectric offsets, or a nonlinear magnetoresistance contribution, would masquerade as a zero-field spontaneous Hall signal. No goodness-of-fit or alternative field-range analysis is presented, so the intrinsic nature of the zero-field effect is not established.
  3. [Spontaneous Hall effect and Fig. 4] The reasoning is circular in an important sense. The charge decompensation of S-3 in Fig. 2(f) is taken as evidence that the Fermi level sits near the Weyl nodes, and then the same noninteracting tight-binding model that predicts larger decompensation near the nodes [Fig. 4(b)] is used to argue that the enhanced BCD and spontaneous Hall responses [Fig. 4(c,d)] confirm this pinning. The model does not include Kondo interactions or disorder, so it cannot establish Kondo-induced pinning; a rigid-band shift caused by disorder doping would produce the same qualitative behavior.
  4. [Conclusion and Fig. 4] The claim that 'Kondo interactions pin the Fermi level near the Weyl nodes' is asserted but not derived. The WKSM theory in Refs. [12-18] is for periodic Kondo lattices, whereas the present scenario involves dilute disorder-induced moments in a weakly correlated semimetal. No calculation or experiment discriminates Kondo pinning from a disorder-induced chemical-potential shift. The latter explains the charge imbalance and the Berry-curvature transport without invoking Kondo physics, so the central mechanism is not supported.
  5. [Experimental methods] The paper uses RRR as the sole measure of disorder. In a semimetal, RRR can be controlled by carrier-density changes as well as by defect scattering. Since 'disorder-driven' is the central thesis, the manuscript should provide a microscopic disorder characterization, such as SdH Dingle temperatures, vacancy/dopant densities, or quantitative EDS deviations, to separate doping effects from defect-induced disorder.
minor comments (5)
  1. [Fig. 4 caption] The fourth panel of the caption is labeled 'b)' but should be '(d)'.
  2. [Fig. 2 cross-reference] The text says 'Figure 2(a) clearly shows an anomalous deviation at low magnetic field values,' but the anomaly appears in Fig. 2(b) after the two-band fit. Please correct the cross-reference.
  3. [Section 'BCD induced non-linear Hall effect'] Typo: 'V2omega xy singal' should be 'signal'.
  4. [References] Reference [59] duplicates [28], and [60] duplicates [30]; these should be cited once.
  5. [Reproducibility] No data or code availability statement is included. The model calculations in Fig. 4 would benefit from a reproducibility statement or at least a description of the tight-binding parameters beyond the SM reference.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the transport interpretation is model-dependent but not self-referential; no prediction reduces to an input by construction.

full rationale

The paper's derivation chain is not circular. The Kondo interpretation is a model fit to the resistivity upturn using the Hamann expression (Eq. 1); the extracted TK and S are fit outputs, not quantities that the same fit assumes in a way that forces the conclusion. The charge-decompensation observation in S-3 comes from an independent two-band fit of Hall and magnetoresistance data, while the theoretical model in Fig. 4 is a noninteracting tight-binding calculation that separately predicts larger charge imbalance and BCD peaks near type-II Weyl nodes. The paper compares these model predictions to the experimental observations to infer Fermi-level proximity; no parameter of the model is fitted to the experimental Hall magnitudes, so the enhanced BCD/spontaneous Hall is not forced by construction. The claim that 'Kondo interactions pin the Fermi level near the Weyl nodes' is an interpretive step imported from heavy-fermion WKSM literature rather than derived from a fitted parameter; this is a scientific assumption that may be questioned (e.g., rigid-band doping could also move the Fermi level), but it is not a logical circularity because it is not equivalent to the data used to support it. Self-citations (e.g., refs. 52, 54, 55) are used as methodological examples or supporting context, not as load-bearing justification for the central claim. No equation in the paper reduces to its own input, and no 'prediction' is a renamed fit parameter.

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

The central claim rests on a chain of assumptions: the existence of local moments, the uniqueness of the Kondo mechanism, the validity of a noninteracting model with a fully nonequilibrium distribution, and the authenticity of the two-band-subtracted zero-field signal. No new physical entities are introduced, but the interpretational chain is not independently established.

free parameters (5)
  • Kondo temperature T_K = 16±2 K (I||a), 9±2 K (I||c)
    Fitted to the resistivity upturn using Eq. (1) with T_eff; used to identify the Kondo regime.
  • Effective spin S = 1.16±0.20 (I||a), 0.89±0.25 (I||c)
    Fitted spin quantum number in the Hamann expression; used to infer local moments with S≈1.
  • RKKY temperature T_W = 0.74±0.19 K (I||a), ≈0 K (I||c)
    Introduced ad hoc to improve the Kondo fit at low T; represents an RKKY energy scale.
  • Hamann scaling constant ρ_H = not specified in text
    Overall scale in Eq. (1); a fit constant.
  • Two-band carrier densities and mobilities = values shown in Fig. 2(d-f), not tabulated
    Extracted by simultaneous two-band fits to ρ_xx and ρ_xy; used to infer charge imbalance and Fermi-level position.
assumptions (5)
  • domain assumption Local magnetic moments exist in disordered WTe2 and are associated with W4+ ions in a distorted Te2- environment.
    Invoked to explain the resistivity upturn via Kondo scattering (Fig. 1). No direct magnetic data shown in the main text.
  • domain assumption The low-T resistivity upturn has no other significant contribution (e.g., weak localization, electron-electron interactions).
    The fit to Eq. (1) assumes Kondo is the sole mechanism; alternatives are not evaluated.
  • domain assumption The fully nonequilibrium Boltzmann distribution g(k)=exp(k_x/k_E)... is valid for the transport regimes studied.
    Adopted from ref [36] to derive the spontaneous Hall current (Eq. 2); its validity for WTe2 is not established.
  • domain assumption A noninteracting tight-binding model of a type-II Weyl semimetal captures the essential physics of disordered WTe2, including the Fermi-level pinning by Kondo interactions.
    The model (Sec. S7) has no disorder or Kondo interaction, yet is used to argue the observed SHE and BCD enhancement are due to proximity to Weyl nodes.
  • domain assumption The residual ρ_xy after two-band model subtraction is a genuine current-induced spontaneous Hall signal, not a misalignment artifact.
    The correction uses a room-temperature misalignment factor; the two-band model is fitted at high field and extrapolated to zero field.

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Pith. "Pith review of Disorder-driven Weyl-Kondo Semimetal Phase in WTe$_2$." pith.science (2026). https://pith.science/paper/OAL6DV2G

@misc{pith2026250910398,
  author       = {Pith},
  title        = {Pith review of: Disorder-driven Weyl-Kondo Semimetal Phase in WTe$_2$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OAL6DV2G}},
  note         = {Machine review of arXiv:2509.10398}
}
abstract

In this Letter, we report the observation of disorder-driven anisotropic Kondo screening and spontaneous Hall effect in bulk WTe${_2}$, a nonmagnetic type-II Weyl semimetal. We show that Kondo scattering emerges more prominently in disordered samples and produces magnetoresistance that is strongly anisotropic with respect to both current and magnetic field orientation, reflecting the underlying type-II Weyl dispersion. Strikingly, we find a spontaneous Hall effect in zero magnetic field, whose magnitude is enhanced with disorder, together with a large second-harmonic Hall signal exhibiting quadratic current scaling. Our analysis indicates that disorder-driven Kondo interactions pin the Fermi level near the Weyl nodes. This enhances the Berry curvature-driven nonequilibrium transport, accounting for both the second-order and spontaneous Hall responses. These findings establish disordered WTe${_2}$ as a platform hosting Weyl-Kondo fermions and highlight disorder as an effective control knob for inducing correlated topological phases in weakly correlated Weyl semimetals.

Figures

Figures reproduced from arXiv: 2509.10398 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: (a) shows the band structure of such a system with two pairs of Weyl nodes. In [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

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Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.