Pith. sign in

REVIEW 3 major objections 3 minor 69 references

Quantum Geometric Renormalization of the Hall Coefficient and Unconventional Hall Resistivity in ZrTe5

T0 review · 3 major / 3 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This paper claims that quantum geometry and electron–hole coherence renormalize the Hall coefficient of the nonmagnetic Dirac material ZrTe5 and drive its Hall resistivity from linear-B to 1/B dependence across the semiclassical-to-quantum

desk verdict The ZrTe5 abstract is worth a look, but the attached full text is a TTS paper; the physics is unverifiable as submitted. read the letter →

arxiv 2508.15450 v1 pith:2GBHSUYK submitted 2025-08-21 cond-mat.mes-hall

Huimin Xie , Bo Fu , Huan-Wen Wang , Wenyu Shan , Shun-Qing Shen This is my paper · ORCID
classification cond-mat.mes-hall
keywords ZrTe5HallcoefficientquantumgeometryKubo-StredaformulaLandaulevelsDiracsemimetallimitanomalouseffect
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 explain the unconventional Hall response of nonmagnetic ZrTe5 without invoking time-reversal symmetry breaking. Its central claim is that, within a Kubo-Streda Landau-level calculation, quantum geometric effects and electron–hole coherence renormalize the Hall coefficient in the semiclassical regime — especially when disorder dominates at low carrier density — and that in the quantum limit the Hall conductivity shows unsaturating 1/B scaling, making the Hall resistivity cross from linear-B to 1/B. If correct, this would unify the observed Hall anomalies in ZrTe5 with a single mechanism: quantum geometry plus disorder, no ferromagnetism. Caveat: the full text supplied is a different manuscript (on speech-synthesis hallucination mitigation), so the argument and its derivations cannot be inspected; this pith is drawn from the abstract alone.

What carries the argument

The central object is the Kubo-Streda formula evaluated in a Landau level basis, combined with a disorder-scattering treatment at low carrier density. The quantum geometric effects (Berry curvature and quantum metric) and electron–hole coherence between Landau levels renormalize the semiclassical Hall coefficient; in the quantum limit, the same framework yields an unsaturating 1/B Hall conductivity. The crossover in Hall resistivity from B to B^{-1} is the observable signature of these quantum corrections.

What would settle it

Measure the Hall resistivity ρ_xy of a high-mobility ZrTe5 flake as a function of magnetic field at low carrier density (gated near the Dirac point) and at low temperature. The claim predicts a crossover from linear-B semiclassical behavior to a 1/B dependence in the quantum limit, with the semiclassical Hall coefficient deviating from 1/(ne) increasingly as density decreases. If ρ_xy never develops a 1/B branch up to fields where only the lowest Landau level is occupied, or if the Hall coefficient stays at 1/(ne) at low density, the renormalization claim fails. A comparison between samples of

Watch

Extended reading notes

Core claim

On the basis of the abstract, the paper's discovery claim is that the Hall coefficient of ZrTe5 is not the classical 1/(ne) but acquires a correction from quantum geometry and electron–hole coherence when disorder scattering dominates at low carrier density, and that the Hall resistivity naturally crosses from linear-in-B in the semiclassical regime to a B^{-1} dependence in the quantum limit because the transverse conductivity dominates and scales as 1/B. The mechanism is computed within the Kubo-Streda formula in the Landau level basis and would apply to other nonmagnetic Dirac materials, offering a quantum-geometric explanation for anomalous Hall-like signals without time-reversal symmetr

Load-bearing premise

The paper's mechanism depends on disorder scattering dominating at low carrier density, but it supplies no disorder model or field scale defining the semiclassical/quantum boundary; without that, the quantum-geometric renormalization of the Hall coefficient has no footing, and the 1/B scaling in the quantum limit could be just classical single-band behavior.

Editorial extensions

If this is right

  • The Hall coefficient in ZrTe5 deviates from 1/(ne) increasingly at low carrier density, with the deviation controlled by quantum geometry and disorder.
  • In the quantum limit, the Hall conductivity shows unsaturating 1/B scaling, so the Hall resistivity becomes 1/B rather than saturating.
  • The crossover from linear-B to 1/B Hall resistivity marks the semiclassical-to-quantum transition, so transport alone can locate this boundary.
  • The same quantum-geometric mechanism may produce anomalous Hall-like responses in other nonmagnetic Dirac materials.
  • Transverse conductivity dominates transport in the ultra-quantum limit, changing the interpretation of magnetotransport in ZrTe5.

Reading between the lines

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

  • If the abstract's claim is right, the low-density Hall-coefficient deviation offers a direct transport probe of the quantum metric and Berry curvature, measurable by gating a ZrTe5 device across the Dirac point.
  • The predicted B^{-1} Hall resistivity branch could be tested in existing high-field ZrTe5 samples; the crossover field would estimate the energy scale of Landau level mixing.
  • Disorder is the load-bearing condition: comparing samples with different mobilities at fixed density should reveal a stronger renormalization in dirtier samples — a testable prediction the abstract implies.
  • Because the supplied full text is a different paper, these implications rest on the abstract; a proper check requires the actual derivation and disorder model.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 3 minor

Summary. The manuscript as submitted presents an abstract claiming a Kubo-Streda/Landau-level derivation of the Hall coefficient renormalization and quantum-limit Hall response in the nonmagnetic Dirac material ZrTe5, with emphasis on a disorder-dominated low-carrier-density regime and a semiclassical/quantum crossover from B-linear to B^{-1} Hall resistivity. However, the supplied full text is arXiv:2508.15442, an unrelated paper on hallucination mitigation in text-to-speech models. No derivation, model Hamiltonian, disorder treatment, band parameters, field scales, or experimental comparison for the ZrTe5 claim is present. The abstract-level claims are therefore not backed by any inspectable scientific content.

Significance. If the claimed result were established, it would be significant: a quantum-geometric and disorder-based mechanism for the unconventional Hall response in nonmagnetic ZrTe5, without time-reversal symmetry breaking, would speak to a broader class of nonmagnetic Dirac materials. The stated framework (Kubo-Streda formula in Landau levels, disorder-averaged semiclassical limit, quantum-limit 1/B Hall conductivity) is appropriate in principle and the predictions are falsifiable. However, no equations, parameters, derivations, or data supporting these claims are present in the submitted manuscript. The paper currently provides no machine-checked proofs, reproducible code, or parameter-free derivation that could be credited, and the central scientific claim cannot be evaluated.

major comments (3)
  1. [Full Text] The supplied full text is arXiv:2508.15442, a text-to-speech paper unrelated to ZrTe5, quantum geometry, or Hall transport. The manuscript contains no Kubo-Streda formula, no Landau-level wavefunctions, no disorder self-energy, and no equations for the claimed renormalized Hall coefficient or 1/B Hall conductivity. Because the central derivation is entirely absent, every load-bearing claim in the Abstract is unsupported by any inspectable argument. This is not a local fix; the submission is internally inconsistent as a scientific paper.
  2. [Abstract, 'low carrier densities where the disorder scattering dominates'] The entire semiclassical renormalization claim is conditioned on a disorder-dominated regime, but no disorder model, scattering rate, self-energy, or averaging procedure is provided. There is no way to check whether the claimed quantum-geometric correction survives disorder averaging or whether the low-density limit is well defined. This is a load-bearing premise, and it is missing in full.
  3. [Abstract, 'quantum limit ... unsaturating 1/B scaling'] The claim that the quantum-limit Hall conductivity scales as 1/B is not accompanied by any derivation. The concern that this may simply reduce to the classical single-band form sigma_xy = ne/B cannot be addressed because no expressions for sigma_xy or sigma_xx appear. Likewise, the claimed crossover from B to B^{-1} in the Hall resistivity requires a field scale and requires sigma_xx to decay sufficiently faster than sigma_xy; neither is quantified or compared with ZrTe5 data.
minor comments (3)
  1. [Abstract] The abstract refers to the 'anomalous Hall effect' in nonmagnetic materials; the relation between the computed Hall response and the conventional AHE (which is tied to time-reversal symmetry breaking) should be clarified, since the paper claims no TRS breaking.
  2. [Abstract] The phrase 'electron-hole coherence' is not defined. The reader cannot tell whether this is a band-geometric Berry-phase effect, an interband coherence in the Kubo formula, or a distinct mechanism.
  3. [Abstract] No ZrTe5-specific parameters (Dirac mass, Fermi energy, carrier density, mobility, magnetic-field range) are given, making it impossible to connect the claimed semiclassical/quantum boundary to any experimental realization.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity can be identified because the supplied full text is an unrelated TTS paper, not the ZrTe5 manuscript.

full rationale

The abstract describes a Kubo-Streda Landau-level calculation of the Hall response in ZrTe5, but the delivered full text is arXiv:2508.15442v3, 'Mitigating Hallucinations in LM-Based TTS Models via Distribution Alignment Using GFlowNets,' an unrelated speech-processing paper. There are no equations from the ZrTe5 derivation, no disorder model, no Landau-level formalism, no fitted parameters, and no self-citation chain available to inspect. Under the hard rules, circularity may be asserted only when the paper itself exhibits a specific reduction of a predicted quantity to a fitted input or to a definitional identity; no such reduction can be quoted here. The absence of the actual manuscript makes the physics claim unverifiable, but unverifiability is not circularity. Accordingly, no specific circular step is found and the score is 0.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

Based only on the abstract; the supplied full text is a different paper, so the ledger cannot be audited beyond the abstract's stated framework assumptions. No fitted values, new particles, forces, or invented entities are visible. The main unstated inputs are the disorder model, band parameters, and field scales for ZrTe5.

free parameters (2)
  • Low-carrier-density disorder-dominated regime (carrier density, disorder scattering rate)
    The abstract conditions the Hall coefficient renormalization on 'low carrier densities where the disorder scattering dominates' but provides no disorder strength, density, or broadening parameters; these would need to be set to reproduce the claimed behavior.
  • Semiclassical/quantum regime boundary (magnetic field scale)
    The crossover from B to B^{-1} Hall resistivity requires a specific field scale and longitudinal conductivity behavior; the abstract gives none.
assumptions (3)
  • domain assumption ZrTe5 is described as a massive Dirac material whose Landau quantization is valid across the stated field range
    Abstract states ZrTe5 is 'known for its massive Dirac bands'; the calculation presumes this band model.
  • domain assumption Kubo-Streda formula with disorder is the correct transport framework and captures both semiclassical and quantum regimes
    Abstract: 'Using the Kubo-Streda formula within the Landau level framework'; this is the paper's foundational method.
  • domain assumption In the ultra-quantum limit the transverse conductivity dominates the longitudinal conductivity
    Abstract: 'the transverse conductivity dominates transport in the ultra-quantum limit'; this is required for the B^{-1} Hall resistivity conclusion.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Quantum Geometric Renormalization of the Hall Coefficient and Unconventional Hall Resistivity in ZrTe5." pith.science (2026). https://pith.science/paper/2GBHSUYK

@misc{pith2026250815450,
  author       = {Pith},
  title        = {Pith review of: Quantum Geometric Renormalization of the Hall Coefficient and Unconventional Hall Resistivity in ZrTe5},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2GBHSUYK}},
  note         = {Machine review of arXiv:2508.15450}
}
read the original abstract

The anomalous Hall effect (AHE), conventionally associated with time-reversal symmetry breaking in ferromagnetic materials, has recently been observed in nonmagnetic topological materials, raising questions about its origin. We unravel the unconventional Hall response in the nonmagnetic Dirac material ZrTe5, known for its massive Dirac bands and unique electronic and transport properties. Using the Kubo-Streda formula within the Landau level framework, we explore the interplay of quantum effects induced by the magnetic field (B) and disorder across the semiclassical and quantum regimes. In the semiclassical regime, the Hall resistivity remains linear in the magnetic field, but the Hall coefficient will be renormalized by the quantum geometric effects and electron-hole coherence, especially at low carrier densities where the disorder scattering dominates. In quantum limit, the Hall conductivity exhibits an unsaturating 1/B scaling. As a result, the transverse conductivity dominates transport in the ultra-quantum limit, and the Hall resistivity crosses over from B to B^{-1} dependence as the system transitions from the semiclassical regime to the quantum limit. This work elucidates the mechanisms underlying the unconventional Hall effect in ZrTe5 and provides insights into the AHE in other nonmagnetic Dirac materials as well.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

69 extracted references · 63 canonical work pages

  1. [1]

    parity anomaly

    barticle Haldane , F.D.M. : Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the "parity anomaly" . Phys. Rev. Lett. 61 , 2015 -- 2018 ( 1988 ) 10.1103/PhysRevLett.61.2015 barticle

    doi:10.1103/physrevlett.61.2015 2015

  2. [2]

    , Sinova , J

    barticle Nagaosa , N. , Sinova , J. , Onoda , S. , MacDonald , A.H. , Ong , N.P. : Anomalous Hall effect . Rev. Mod. Phys. 82 , 1539 -- 1592 ( 2010 ) 10.1103/RevModPhys.82.1539 barticle

    doi:10.1103/revmodphys.82.1539 2010

  3. [3]

    , Zhang , J

    barticle Chang , C.-Z. , Zhang , J. , Feng , X. , Shen , J. , Zhang , Z. , Guo , M. , Li , K. , Ou , Y. , Wei , P. , Wang , L.-L. , : Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator . Science 340 , 167 -- 170 ( 2013 ) 10.1126/science.1234414 barticle

    doi:10.1126/science.1234414 2013

  4. [4]

    : Anomalous Hall effect in Weyl metals

    barticle Burkov , A. : Anomalous Hall effect in Weyl metals . Phys. Rev. Lett. 113 , 187202 ( 2014 ) barticle

    work page 2014

  5. [5]

    , Yoshimi , R

    barticle Checkelsky , J.G. , Yoshimi , R. , Tsukazaki , A. , Takahashi , K.S. , Kozuka , Y. , Falson , J. , Kawasaki , M. , Tokura , Y. : Trajectory of the anomalous Hall effect towards the quantized state in a ferromagnetic topological insulator . Nat. Phys. 10 , 731 -- 736 ( 2014 ) 10.1038/nphys3053 barticle

    work page doi:10.1038/nphys3053 2014

  6. [6]

    : Weyl metals

    barticle Burkov , A.A. : Weyl metals . Annu. Rev. Condens. Matter Phys. 9 , 359 -- 378 ( 2018 ) 10.1146/annurev-conmatphys-033117-054129 barticle

    work page doi:10.1146/annurev-conmatphys-033117-054129 2018

  7. [7]

    , Yu , Y

    barticle Deng , Y. , Yu , Y. , Shi , M.Z. , Guo , Z. , Xu , Z. , Wang , J. , Chen , X.H. , Zhang , Y. : Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi_2Te_4 . Science 367 , 895 -- 900 ( 2020 ) 10.1126/science.aax8156 barticle

    doi:10.1126/science.aax8156 2020

  8. [8]

    , Felser , C

    barticle Bernevig , B.A. , Felser , C. , Beidenkopf , H. : Progress and prospects in magnetic topological materials . Nature(London) 603 , 41 -- 45 ( 2022 ) barticle

    work page 2022

Show all 69 references
  1. [9]

    , Nagaosa , N

    barticle Zhang , X.-X. , Nagaosa , N. : Nonmonotonic Hall effect of Weyl semimetals under a magnetic field . Phys. Rev. Lett. 133 , 166301 ( 2024 ) barticle

    2024

  2. [10]

    , Watanabe , R

    barticle Belopolski , I. , Watanabe , R. , Sato , Y. , Yoshimi , R. , Kawamura , M. , Nagahama , S. , Zhao , Y. , Shao , S. , Jin , Y. , Kato , Y. , : Synthesis of a semimetallic Weyl ferromagnet with point fermi surface . Nature(London) 637 , 1078 ( 2025 ) barticle

    2025

  3. [11]

    : On the possibility of transvers currents in ferromagnets

    barticle Hall , E. : On the possibility of transvers currents in ferromagnets . Philos. Mag 12 , 157 -- 172 ( 1881 ) barticle

  4. [12]

    , Luttinger , J

    barticle Karplus , R. , Luttinger , J. : Hall effect in ferromagnetics . Phys. Rev. 95 , 1154 ( 1954 ) barticle

    1954

  5. [13]

    , MacDonald , A

    barticle Sinitsyn , N. , MacDonald , A. , Jungwirth , T. , Dugaev , V. , Sinova , J. : Anomalous Hall effect in a two-dimensional Dirac band: The link between the Kubo-Streda formula and the semiclassical Boltzmann equation approach . Phys. Rev. B 75 , 045315 ( 2007 ) barticle

    2007

  6. [14]

    , Sugimoto , N

    barticle Onoda , S. , Sugimoto , N. , Nagaosa , N. : Intrinsic versus extrinsic anomalous Hall effect in ferromagnets . Phys. Rev. Lett 97 , 126602 ( 2006 ) barticle

    2006

  7. [15]

    , Chang , M.-C

    barticle Xiao , D. , Chang , M.-C. , Niu , Q. : Berry phase effects on electronic properties . Rev. Mod. Phys. 82 , 1959 -- 2007 ( 2010 ) 10.1103/RevModPhys.82.1959 barticle

    1959 doi

  8. [16]

    , Dai , X

    barticle Weng , H. , Dai , X. , Fang , Z. : Transition-metal pentatelluride ZrTe_5 and HfTe_5 : A paradigm for large-gap quantum spin Hall insulators . Phys. Rev. X 4 , 011002 ( 2014 ) barticle

    2014

  9. [17]

    , Wang , C

    barticle Zhang , J. , Wang , C. , Guo , C. , Zhu , X. , Zhang , Y. , Yang , J. , Wang , Y. , Qu , Z. , Pi , L. , Lu , H.-Z. , : Anomalous thermoelectric effects of ZrTe_5 in and beyond the quantum limit . Phys. Rev. Lett. 123 , 196602 ( 2019 ) barticle

    2019

  10. [18]

    , Wang , J

    barticle Jiang , Y. , Wang , J. , Zhao , T. , Dun , Z. , Huang , Q. , Wu , X. , Mourigal , M. , Zhou , H. , Pan , W. , Ozerov , M. , : Unraveling the topological phase of ZrTe_5 via magnetoinfrared spectroscopy . Phys. Rev. Lett. 125 , 046403 ( 2020 ) barticle

    2020

  11. [19]

    , Chen , Z

    barticle Chen , R. , Chen , Z. , Song , X.-Y. , Schneeloch , J. , Gu , G. , Wang , F. , Wang , N. : Magnetoinfrared spectroscopy of Landau levels and Zeeman splitting of three-dimensional massless Dirac fermions in ZrTe_5 . Phys. Rev. Lett. 115 , 176404 ( 2015 ) barticle

    2015

  12. [20]

    , Kharzeev , D.E

    barticle Li , Q. , Kharzeev , D.E. , Zhang , C. , Huang , Y. , Pletikosi \'c , I. , Fedorov , A. , Zhong , R. , Schneeloch , J. , Gu , G. , Valla , T. : Chiral magnetic effect in ZrTe_5 . Nat. Phys. 12 , 550 -- 554 ( 2016 ) barticle

    2016

  13. [21]

    , Chen , W.-C

    barticle Mutch , J. , Chen , W.-C. , Went , P. , Qian , T. , Wilson , I.Z. , Andreev , A. , Chen , C.-C. , Chu , J.-H. : Evidence for a strain-tuned topological phase transition in ZrTe_5 . Sci. Adv. 5 , 9771 ( 2019 ) barticle

    2019

  14. [22]

    , Noguchi , R

    barticle Zhang , P. , Noguchi , R. , Kuroda , K. , Lin , C. , Kawaguchi , K. , Yaji , K. , Harasawa , A. , Lippmaa , M. , Nie , S. , Weng , H. , : Observation and control of the weak topological insulator state in ZrTe_5 . Nat. Commun. 12 , 406 ( 2021 ) barticle

    2021

  15. [23]

    , Ren , Y

    barticle Tang , F. , Ren , Y. , Wang , P. , Zhong , R. , Schneeloch , J. , Yang , S.A. , Yang , K. , Lee , P.A. , Gu , G. , Qiao , Z. , : Three-dimensional quantum Hall effect and metal--insulator transition in ZrTe_5 . Nature(London) 569 , 537 -- 541 ( 2019 ) barticle

    2019

  16. [24]

    , Dumitrescu , P.T

    barticle Nair , N.L. , Dumitrescu , P.T. , Channa , S. , Griffin , S.M. , Neaton , J.B. , Potter , A.C. , Analytis , J.G. : Thermodynamic signature of Dirac electrons across a possible topological transition in ZrTe_5 . Phys. Rev. B 97 , 041111 ( 2018 ) barticle

    2018

  17. [25]

    , Lee , S.-E

    barticle Ji , S. , Lee , S.-E. , Jung , M.-H. : Berry paramagnetism in the Dirac semimetal ZrTe_5 . Commun. Phys. 4 ( 1 ), 265 ( 2021 ) barticle

    2021

  18. [26]

    , Liu , H

    barticle Wang , H. , Liu , H. , Li , Y. , Liu , Y. , Wang , J. , Liu , J. , Dai , J.-Y. , Wang , Y. , Li , L. , Yan , J. , : Discovery of log-periodic oscillations in ultraquantum topological materials . Sci. Adv. 4 , 5096 ( 2018 ) barticle

    2018

  19. [27]

    , Li , S

    barticle Qin , F. , Li , S. , Du , Z. , Wang , C. , Zhang , W. , Yu , D. , Lu , H.-Z. , Xie , X. : Theory for the charge-density-wave mechanism of 3D quantum Hall effect . Phys. Rev. Lett. 125 , 206601 ( 2020 ) barticle

    2020

  20. [28]

    , Ehmcke , T

    barticle Galeski , S. , Ehmcke , T. , Wawrzy \'n czak , R. , Lozano , P.M. , Cho , K. , Sharma , A. , Das , S. , K \"u ster , F. , Sessi , P. , Brando , M. , : Origin of the quasi-quantized Hall effect in ZrTe_5 . Nat. Commun. 12 , 3197 ( 2021 ) barticle

    2021

  21. [29]

    , Sambongi , T

    barticle Okada , S. , Sambongi , T. , Ido , M. : Giant resistivity anomaly in ZrTe_5 . J. Phys. Soc. Jpn. 49 ( 2 ), 839 -- 840 ( 1980 ) barticle

    1980

  22. [30]

    , Uchinokura , K

    barticle Izumi , M. , Uchinokura , K. , Matsuura , E. : Anomalous electrical resistivity in HfTe_5 . Solid State Commun. 37 , 641 -- 642 ( 1981 ) barticle

    1981

  23. [31]

    , Lowhorn , N.D

    barticle Tritt , T.M. , Lowhorn , N.D. , Littleton IV , R. , Pope , A. , Feger , C. , Kolis , J. : Large enhancement of the resistive anomaly in the pentatelluride materials HfTe_5 and ZrTe_5 with applied magnetic field . Phys. Rev. B 60 , 7816 ( 1999 ) barticle

    1999

  24. [32]

    : HfTe_5 and ZrTe_5 : Possible polaronic conductors

    barticle Rubinstein , M. : HfTe_5 and ZrTe_5 : Possible polaronic conductors . Phys. Rev. B 60 , 1627 ( 1999 ) barticle

    1999

  25. [33]

    , Singh , D

    barticle Shahi , P. , Singh , D. , Sun , J. , Zhao , L. , Chen , G. , Lv , Y. , Li , J. , Yan , J.-Q. , Mandrus , D. , Cheng , J.-G. : Bipolar conduction as the possible origin of the electronic transition in pentatellurides: metallic vs semiconducting behavior . Phys. Rev. X ...

    2018

  26. [34]

    : Thermodynamically induced transport anomaly in dilute metals ZrTe_5 and HfTe_5

    barticle Wang , C. : Thermodynamically induced transport anomaly in dilute metals ZrTe_5 and HfTe_5 . Phys. Rev. Lett. 126 , 126601 ( 2021 ) barticle

    2021

  27. [35]

    , Wang , H.-W

    barticle Fu , B. , Wang , H.-W. , Shen , S.-Q. : Dirac polarons and resistivity anomaly in ZrTe_5 and HfTe_5 . Phys. Rev. Lett. 125 , 256601 ( 2020 ) barticle

    2020

  28. [36]

    , Fu , B

    barticle Wang , H.-W. , Fu , B. , Shen , S.-Q. : Helical symmetry breaking and quantum anomaly in massive Dirac fermions . Phys. Rev. B 104 , 241111 ( 2021 ) 10.1103/PhysRevB.104.L241111 barticle

    2021 doi

  29. [37]

    , Lin , J

    barticle Liang , T. , Lin , J. , Gibson , Q. , Kushwaha , S. , Liu , M. , Wang , W. , Xiong , H. , Sobota , J.A. , Hashimoto , M. , Kirchmann , P.S. , : Anomalous Hall effect in ZrTe_5 . Nat. Phys. 14 , 451 -- 455 ( 2018 ) barticle

    2018

  30. [38]

    , Leroux , M

    barticle Gourgout , A. , Leroux , M. , Smirr , J.-L. , Massoudzadegan , M. , Lobo , R.P. , Vignolles , D. , Proust , C. , Berger , H. , Li , Q. , Gu , G. , : Magnetic freeze-out and anomalous Hall effect in ZrTe_5 . npj Quantum Mater. 7 , 71 ( 2022 ) barticle

    2022

  31. [39]

    , Villanova , J.W

    barticle Choi , Y. , Villanova , J.W. , Park , K. : Zeeman-splitting-induced topological nodal structure and anomalous Hall conductivity in ZrTe_5 . Phys. Rev. B 101 , 035105 ( 2020 ) barticle

    2020

  32. [40]

    , Ma , X

    botherref Mutch , J. , Ma , X. , Wang , C. , Malinowski , P. , Ayres-Sims , J. , Jiang , Q. , Liu , Z. , Xiao , D. , Yankowitz , M. , Chu , J.-H. : Abrupt switching of the anomalous Hall effect by field-rotation in nonmagnetic ZrTe_5 . arXiv preprint arXiv:2101.02681 (2021) botherref

    2021 arXiv

  33. [41]

    , Wang , H

    barticle Liu , Y. , Wang , H. , Fu , H. , Ge , J. , Li , Y. , Xi , C. , Zhang , J. , Yan , J. , Mandrus , D. , Yan , B. , : Induced anomalous Hall effect of massive Dirac fermions in ZrTe_5 and HfTe_5 thin flakes . Phys. Rev. B 103 , 201110 ( 2021 ) barticle

    2021

  34. [42]

    , Cao , Z

    barticle Sun , Z. , Cao , Z. , Cui , J. , Zhu , C. , Ma , D. , Wang , H. , Zhuo , W. , Cheng , Z. , Wang , Z. , Wan , X. , : Large Zeeman splitting induced anomalous Hall effect in ZrTe_5 . npj Quantum Mater. 5 , 36 ( 2020 ) barticle

    2020

  35. [43]

    , Fu , B

    barticle Wang , H.-W. , Fu , B. , Shen , S.-Q. : Theory of the anomalous Hall effect in the transition metal pentatellurides ZrTe_5 and HfTe_5 . Phys. Rev. B 108 , 045141 ( 2023 ) barticle

    2023

  36. [44]

    , Cai , Z

    barticle Wang , Y.-X. , Cai , Z. : Quantum oscillations and three-dimensional quantum Hall effect in ZrTe_5 . Phys. Rev. B 107 ( 12 ), 125203 ( 2023 ) barticle

    2023

  37. [45]

    , Zhang , S

    barticle Pi , H. , Zhang , S. , Xu , Y. , Fang , Z. , Weng , H. , Wu , Q. : First principles methodology for studying magnetotransport in narrow gap semiconductors with ZrTe_5 example . npj Comput. Mater. 10 , 276 ( 2024 ) barticle

    2024

  38. [46]

    , Shi , Z

    barticle Wu , W. , Shi , Z. , Du , Y. , Wang , Y. , Qin , F. , Meng , X. , Liu , B. , Ma , Y. , Yan , Z. , Ozerov , M. , : Topological Lifshitz transition and one-dimensional Weyl mode in HfTe_5 . Nature Materials 22 , 84 -- 91 ( 2023 ) barticle

    2023

  39. [47]

    , Legg , H.F

    botherref Galeski , S. , Legg , H.F. , Wawrzyńczak , R. , Frster , T. , Zherlitsyn , S. , Gorbunov , D. , Lozano , P.M. , Li , Q. , Gu , G.D. , Felser , C. : Signatures of a magnetic-field-induced Lifshitz transition in the ultra-quantum limit of the topological semimetal ZrTe...

    2022

  40. [48]

    , Subramanyan , V

    barticle Liu , J. , Subramanyan , V. , Welser , R. , McSorley , T. , Ho , T. , Graf , D. , Pettes , M.T. , Saxena , A. , Winter , L.E. , Lin , S.-Z. , Jauregui , L.A. : Possible spin-triplet excitonic insulator in the ultraquantum limit of HfTe _ 5 . Phys. Rev. Lett. 135 , 046...

    2025 doi

  41. [49]

    , Jiang , B

    barticle Zhao , J. , Jiang , B. , Yang , J. , Wang , L. , Shi , H. , Tian , G. , Li , Z. , Liu , E. , Wu , X. : Magnetotransport induced by anomalous Hall effect . Phys. Rev. B 107 , 060408 ( 2023 ) barticle

    2023

  42. [50]

    , Yuan , X

    barticle Liu , Y. , Yuan , X. , Zhang , C. , Jin , Z. , Narayan , A. , Luo , C. , Chen , Z. , Yang , L. , Zou , J. , Wu , X. , : Zeeman splitting and dynamical mass generation in Dirac semimetal ZrTe_5 . Nat. Commun. 7 ( 1 ), 12516 ( 2016 ) barticle

    2016

  43. [51]

    , Dun , Z

    barticle Jiang , Y. , Dun , Z. , Zhou , H. , Lu , Z. , Chen , K.-W. , Moon , S. , Besara , T. , Siegrist , T. , Baumbach , R. , Smirnov , D. , : Landau-level spectroscopy of massive Dirac fermions in single-crystalline ZrTe_5 thin flakes . Phys. Rev. B 96 , 041101 ( 2017 ) barticle

    2017

  44. [52]

    , Hughes , T.L

    barticle Bernevig , B.A. , Hughes , T.L. , Raghu , S. , Arovas , D.P. : Theory of the three-dimensional quantum Hall effect in graphite . Phys. Rev. Lett. 99 , 146804 ( 2007 ) barticle

    2007

  45. [53]

    : Theory of quantised Hall conductivity in two dimensions

    barticle Streda , P. : Theory of quantised Hall conductivity in two dimensions . J. Phys. C: Solid State Phys. 15 ( 22 ), 717 ( 1982 ) barticle

    1982

  46. [54]

    : Nonzero Temperatures , pp

    bbook Mahan , G.D. : Nonzero Temperatures , pp. 109 -- 185 . Springer , Boston, MA ( 2000 ). 10.1007/978-1-4757-5714-9_3 . https://doi.org/10.1007/978-1-4757-5714-9_3 bbook

    2000 doi

  47. [55]

    , Lewiner , C

    barticle Bastin , A. , Lewiner , C. , Betbeder-Matibet , O. , Nozieres , P. : Quantum oscillations of the Hall effect of a fermion gas with random impurity scattering . J. Phys. Chem. Solids 32 , 1811 -- 1824 ( 1971 ) barticle

    1971

  48. [56]

    , Smr c ka , L

    barticle St r eda , P. , Smr c ka , L. : Galvanomagnetic effects in alloys in quantizing magnetic fields . Phys. Status. Solidi. (b) 70 ( 2 ), 537 -- 548 ( 1975 ) barticle

    1975

  49. [57]

    , Streda , P

    barticle Smrcka , L. , Streda , P. : Transport coefficients in strong magnetic fields . J. Phys. C: Solid State Phys. 10 , 2153 ( 1977 ) barticle

    1977

  50. [58]

    : Magnetoresistance in Metals vol

    bbook Pippard , A.B. : Magnetoresistance in Metals vol. 2 . Cambridge university press , ( 1989 ) bbook

    1989

  51. [59]

    , Yang , S.A

    barticle Gao , Y. , Yang , S.A. , Niu , Q. : Field induced positional shift of bloch electrons and its dynamical implications . Phys. Rev. Lett. 112 , 166601 ( 2014 ) barticle

    2014

  52. [60]

    : Semiclassical dynamics and nonlinear charge current

    barticle Gao , Y. : Semiclassical dynamics and nonlinear charge current . Front. Phys. 14 , 33404 ( 2019 ) barticle

    2019

  53. [61]

    , Liu , H

    barticle Xiao , C. , Liu , H. , Zhao , J. , Yang , S.A. , Niu , Q. : Thermoelectric generation of orbital magnetization in metals . Phys. Rev. B 103 , 045401 ( 2021 ) barticle

    2021

  54. [62]

    , Huang , Y.-X

    barticle Wang , H. , Huang , Y.-X. , Liu , H. , Feng , X. , Zhu , J. , Wu , W. , Xiao , C. , Yang , S.A. : Orbital origin of the intrinsic planar Hall effect . Phys. Rev. Lett. 132 ( 5 ), 056301 ( 2024 ) barticle

    2024

  55. [63]

    , Lu , H.-Z

    barticle Zhang , S.-B. , Lu , H.-Z. , Shen , S.-Q. : Linear magnetoconductivity in an intrinsic topological Weyl semimetal . New J. Phys. 18 , 053039 ( 2016 ) barticle

    2016

  56. [64]

    , Lin , J

    barticle Liang , T. , Lin , J. , Gibson , Q. , Gao , T. , Hirschberger , M. , Liu , M. , Cava , R.J. , Ong , N.P. : Anomalous Nernst effect in the Dirac semimetal Cd_3As_2 . Phys. Rev. Lett. 118 , 136601 ( 2017 ) barticle

    2017

  57. [65]

    , Ishizuka , H

    botherref Nishihaya , S. , Ishizuka , H. , Deguchi , Y. , Nakamura , A. , Yoneda , T. , Lee , H. , Kriener , M. , Uchida , M. : Anomalous Hall effect in Dirac semimetal probed by in-plane magnetic field. arXiv preprint arXiv:2503.04195 (2025) botherref

    2025 arXiv

  58. [66]

    , Sharapov , S

    barticle Gusynin , V. , Sharapov , S. : Transport of Dirac quasiparticles in graphene: Hall and optical conductivities . Phys. Rev. B 73 , 245411 ( 2006 ) barticle

    2006

  59. [67]

    , Sharapov , S

    barticle Tsaran , V.Y. , Sharapov , S. : Magnetic oscillations of the anomalous Hall conductivity . Phys. Rev. B 93 , 075430 ( 2016 ) barticle

    2016

  60. [68]

    , Miransky , V

    barticle Gorbar , E. , Miransky , V. , Shovkovy , I. , Sukhachov , P. : Origin of Bardeen-Zumino current in lattice models of Weyl semimetals . Phys. Rev. B 96 , 085130 ( 2017 ) barticle

    2017

  61. [69]

    write newline

    " write newline "" before.all 'output.state := FUNCTION string.to.integer 't := t text.length 'k := #1 'char.num := t char.num #1 substring 's := s is.num s "." = or char.num k = not and char.num #1 + 'char.num := while char.num #1 - 'char.num := t #1 char.num substring FUNCTI...

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.