Pith. sign in

REVIEW 2 major objections 1 minor 50 references

Chiral semimetals can exhibit a quantized Hall conductivity with dephasing while keeping finite longitudinal conductivity.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · grok-4.3

2026-06-29 11:02 UTC pith:IETEZYDH

load-bearing objection The paper floats an interesting extension of QAH into gapless chiral semimetals, but the quantization claim hinges on an unverified step in the Berry curvature integral that standard arguments do not cover. the 2 major comments →

arxiv 2605.27826 v1 pith:IETEZYDH submitted 2026-05-27 cond-mat.mes-hall

Quantum anomalous Hall effect in chiral semimetals

Peng-Yi Liu , Yu-Hao Wan , Qing-Feng Sun This is my paper
classification cond-mat.mes-hall
keywords quantum anomalous Hall effectchiral semimetalsBerry curvaturedephasingHall conductivitylongitudinal conductivityChern insulators
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that the quantum anomalous Hall effect extends to chiral semimetals where bands touch at zero energy. Transport calculations reveal that Hall conductivity quantizes under dephasing, but longitudinal conductivity remains finite and semimetallic unlike Chern insulators. This stems from the quantized Berry curvature integral over occupied states and the semimetallic band structure. The semimetal can transition to a Chern insulator with vanishing longitudinal conductivity and a smaller Hall response length scale. These results expand the scope of QAH to include semimetallic systems with distinct transport features.

Core claim

The quantum anomalous Hall effect persists in chiral semimetals, allowing quantized Hall conductivity in the presence of dephasing while the longitudinal conductivity stays finite and shows semimetallic behavior, due to the quantization of the Berry curvature integral over occupied states.

What carries the argument

The quantized integral of Berry curvature over occupied states that produces the Hall response in a semimetallic band structure with dephasing.

Load-bearing premise

The quantization of the Berry curvature integral over occupied states remains valid and produces a quantized Hall response even though the band structure is semimetallic with touching bands at zero energy.

What would settle it

A transport measurement in a chiral semimetal showing non-quantized Hall conductivity despite dephasing would falsify the claim.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 1 minor

Summary. The manuscript claims that the quantum anomalous Hall effect persists in chiral semimetals, where conduction and valence bands touch at zero energy. Transport calculations with dephasing are said to yield quantized Hall conductivity while longitudinal conductivity remains finite and semimetallic, in contrast to gapped Chern insulators. This behavior is attributed to the quantization of the Berry curvature integral over occupied states together with the semimetallic band structure; the system can be tuned into a Chern insulator phase with vanishing longitudinal conductivity.

Significance. If the central claim holds, the result would extend the QAH effect beyond insulators and metals into a semimetallic regime, identifying distinctive transport signatures (quantized σ_xy with finite σ_xx) that arise from the interplay of topology and gapless band touching. The work would also clarify how dephasing regularizes the touching-point contribution while preserving quantization.

major comments (2)
  1. [Abstract and transport section] The central claim that the Berry curvature integral over all occupied states remains an integer (yielding quantized σ_xy) when bands touch at E=0 is load-bearing. Standard derivations of the Chern number require a gapped spectrum so that the Fermi level lies in a region of vanishing density of states and the occupied manifold forms a closed surface in k-space. The manuscript must explicitly demonstrate how the dephasing term regularizes the singularity at the touching point and why Fermi-surface contributions to the Kubo formula for σ_xy are excluded or cancel, rather than assuming the integral remains quantized by continuity with the gapped case.
  2. [Discussion of phase transition] The transition from the semimetallic QAH phase to the Chern insulator is stated to be accompanied by vanishing longitudinal conductivity. The manuscript should supply the explicit parameter (e.g., gap-opening term or chemical potential) that drives this transition and show the corresponding evolution of both σ_xy and σ_xx, including any length-scale analysis of the Hall response.
minor comments (1)
  1. [Model definition] Notation for the chiral semimetal band structure (e.g., the precise form of the touching bands and the definition of the intrinsic length scale) should be introduced with equations in the main text rather than left implicit.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments identify areas where additional explicit demonstrations and parameter sweeps will improve clarity. We address each point below and will revise the manuscript to incorporate the requested details.

read point-by-point responses

  1. Referee: [Abstract and transport section] The central claim that the Berry curvature integral over all occupied states remains an integer (yielding quantized σ_xy) when bands touch at E=0 is load-bearing. Standard derivations of the Chern number require a gapped spectrum so that the Fermi level lies in a region of vanishing density of states and the occupied manifold forms a closed surface in k-space. The manuscript must explicitly demonstrate how the dephasing term regularizes the singularity at the touching point and why Fermi-surface contributions to the Kubo formula for σ_xy are excluded or cancel, rather than assuming the integral remains quantized by continuity with the gapped case.

    Authors: We agree that an explicit demonstration is needed rather than relying on continuity. Our transport calculations employ a Green's-function Kubo formalism with a finite dephasing (imaginary self-energy) that regularizes the band-touching singularity by shifting the poles off the real axis, allowing numerical evaluation of the Berry curvature integral over occupied states. The Fermi-surface contributions at the touching point cancel due to the chiral symmetry and opposite Berry curvature signs from the touching bands. To address the referee's concern directly, we will add an appendix deriving the regularization and cancellation explicitly in the revised manuscript. revision: yes

  2. Referee: [Discussion of phase transition] The transition from the semimetallic QAH phase to the Chern insulator is stated to be accompanied by vanishing longitudinal conductivity. The manuscript should supply the explicit parameter (e.g., gap-opening term or chemical potential) that drives this transition and show the corresponding evolution of both σ_xy and σ_xx, including any length-scale analysis of the Hall response.

    Authors: We agree that the explicit driving parameter and full evolution should be shown. The transition is controlled by a tunable gap-opening mass term added to the Hamiltonian at the band-touching point. We will add a new figure (or panel) plotting both σ_xy and σ_xx versus this mass term, together with a discussion of the intrinsic length scale of the Hall response (extracted from the spatial decay of the current response), which shrinks as the gap opens and longitudinal conductivity vanishes. These additions will be included in the revised version. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained against standard transport formalism

full rationale

The paper presents transport calculations (presumably Landauer-Büttiker or Kubo with dephasing) showing quantized Hall conductivity alongside finite longitudinal conductivity in a chiral semimetal. The central step invokes the Berry curvature integral over occupied states yielding an integer, but this is framed as an output of the band-structure calculation rather than a fitted input or self-definitional assumption. No load-bearing self-citation chain, no renaming of known results, and no ansatz smuggled via prior work is evident from the provided abstract and description. The derivation remains independent of the target result and does not reduce by construction to its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Central claim rests on the assumption that Berry-curvature quantization survives in a gapless semimetal band structure under dephasing; no free parameters or invented entities are visible in the abstract.

axioms (1)
  • domain assumption Berry curvature integral over occupied states remains quantized in a chiral semimetal
    Invoked to explain quantized Hall conductivity despite touching bands.

pith-pipeline@v0.9.1-grok · 5688 in / 1046 out tokens · 35171 ms · 2026-06-29T11:02:31.230353+00:00 · methodology

0 comments
read the original abstract

The quantum anomalous Hall (QAH) effect is conventionally understood to exist only in Chern insulators, while a recent study has shown that ferromagnetic metals can also host the QAH effect. Between insulators and metals, we demonstrate that QAH can persist even in a chiral semimetal, where conduction and valence bands touch at zero energy. Transport calculations demonstrate that the Hall conductivity of such a system can be quantized in the presence of dephasing. Interestingly, its longitudinal conductivity remains finite and exhibits semimetallic behavior, in contrast to Chern insulators. This unusual transport behavior originates from the quantization of the Berry curvature integral over occupied states and the semimetallic band structure. This chiral semimetal can transition into a Chern insulator, accompanied by the vanishing of longitudinal conductivity and a reduction of the intrinsic length scale of the Hall response. Our results extend the concept of QAH and uncover the semimetallic QAH transport signatures.

Figures

Figures reproduced from arXiv: 2605.27826 by Peng-Yi Liu, Qing-Feng Sun, Yu-Hao Wan.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Two-dimensional band structure of the chiral [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Schematic of a six-terminal Hall bar. Six leads [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Berry curvature Ω distribution of the lower [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Band structure of the insulating QAH nanorib [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) the Hall conductivity [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

50 extracted references

  1. [1]

    3(c), which remains quantized as the Fermi energy is varied within−0.5≲E F ≲0.5

    shown in Fig. 3(c), which remains quantized as the Fermi energy is varied within−0.5≲E F ≲0.5. This quantized integral of the Berry curvature provides the microscopic origin of the Hall plateaus observed in the transport calculations of Fig. 2. V. INSULA TING QAH AND SEMIMET AL-INSULA TOR TRANSITION As a contrast to the semimetallic QAH phase discussed ab...

  2. [2]

    D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall Conductance in a Two- Dimensional Periodic Potential, Phys. Rev. Lett.49, 405 (1982)

    1982

  3. [3]

    M. V. Berry, Quantal phase factors accompanying adi- abatic changes, Proc. R. Soc. London, Ser. A392, 45 (1984)

    1984

  4. [4]

    Nagaosa, J

    N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, and N. P. Ong, Anomalous Hall effect, Rev. Mod. Phys.82, 1539 (2010)

    2010

  5. [5]

    Hatsugai, Chern number and edge states in the integer quantum Hall effect, Phys

    Y. Hatsugai, Chern number and edge states in the integer quantum Hall effect, Phys. Rev. Lett.71, 3697 (1993)

    1993

  6. [6]

    K. v. Klitzing, G. Dorda, and M. Pepper, New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance, Phys. Rev. Lett.45, 494 (1980)

    1980

  7. [7]

    Chang, J

    C.-Z. Chang, J. Zhang, X. Feng, J. Shen, Z. Zhang, M. Guo, K. Li, Y. Ou, P. Wei, L.-L. Wang, Z.-Q. Ji, Y. Feng, S. Ji, X. Chen, J. Jia, X. Dai, Z. Fang, S.-C. Zhang, K. He, Y. Wang, L. Lu, X.-C. Ma, and Q.-K. Xue, Experi- mental Observation of the Quantum Anomalous Hall Ef- fect in a Magnetic Topological Insulator, Science340, 167-170 (2013)

    2013

  8. [8]

    Y. Deng, Y. Yu, M. Z. Shi, Z. Guo, Z. Xu, J. Wang, X. H. Chen, and Y. Zhang, Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi2Te4, Sci- ence367, 895 (2020)

    2020

  9. [9]

    Y. F. Zhao, R. X. Zhang, R. B. Mei, L. J. Zhou, H. M. Yi, Y. Q. Zhang, J. B. Yu, R. Xiao, K. Wang, N. Samarth, M. H. W. Chan, C. X. Liu, C. Z. Chang, Tuning the Chern number in quantum anomalous Hall insulators, Nature 588, 419 (2020)

    2020

  10. [10]

    G. Chen, A. L. Sharpe, E. J. Fox, Y.-H. Zhang, S. Wang, L. Jiang, B. Lyu, H. Li, K. Watanabe, T. Taniguchi, Z. Shi, T. Senthil, D. Goldhaber-Gordon, Y. Zhang, and F. Wang, Tunable correlated Chern insulator and ferromag- netism in a moir´ e superlattice, Nature579, 56 (2020)

    2020

  11. [11]

    Parity Anomaly

    F. D. M. Haldane, Model for a Quantum Hall Effect with- out Landau Levels: Condensed-Matter Realization of the “Parity Anomaly”, Phys. Rev. Lett.61, 2015 (1988)

    2015

  12. [12]

    Qi, Y.-S

    X.-L. Qi, Y.-S. Wu, and S.-C. Zhang, Topological quan- tization of the spin Hall effect in two-dimensional param- agnetic semiconductors, Phys. Rev. B74, 085308 (2006)

    2006

  13. [13]

    R. Yu, W. Zhang, H.-J. Zhang, S.-C. Zhang, X. Dai, and Z. Fang, Quantized Anomalous Hall Effect in Magnetic Topological Insulators, Science329, 61 (2010)

    2010

  14. [14]

    Zhang, Y

    H. Zhang, Y. Xu, J. Wang, K. Chang, and S.-C. Zhang, Quantum Spin Hall and Quantum Anomalous Hall States Realized in Junction Quantum Wells, Phys. Rev. Lett. 112, 216803 (2014)

    2014

  15. [15]

    Z. Qiao, S. A. Yang, W. Feng, W.-K. Tse, J. Ding, Y. Yao2, J. Wang, and Q. Niu, Quantum anomalous Hall ef- fect in graphene from Rashba and exchange effects, Phys. Rev. B82, 161414(R) (2010)

    2010

  16. [16]

    Chang, C.-X

    C.-Z. Chang, C.-X. Liu, and A. H. MacDonald,Collo- quium: Quantum anomalous Hall effect, Rev. Mod. Phys. 95, 011002 (2023)

    2023

  17. [17]

    Tokura, K

    Y. Tokura, K. Yasuda, A. Tsukazaki, Magnetic topolog- ical insulators, Nat. Rev. Phys. 1, 126 (2019)

    2019

  18. [18]

    Wu, Z.-B

    B.-L. Wu, Z.-B. Wang, Z.-Q. Zhang, and H. Jiang, Build- ing programmable integrated circuits through disordered Chern insulators, Phys. Rev. B 104, 195416 (2021)

    2021

  19. [19]

    T., Yi, D

    H. T., Yi, D. Jain, X. Yao, and S. Oh, Enhanced Quan- tum Anomalous Hall Effect with an Active Capping Layer, Nano Lett.23, 5673 (2023)

    2023

  20. [20]

    J. M. D. Coey, Magnetism and Magnetic Materials (Cam- bridge University Press, Cambridge, 2009)

    2009

  21. [21]

    Wan, P.-Y

    Y.-H. Wan, P.-Y. Liu, and Q.-F. Sun, Quantum Anoma- lous Hall Effect in Ferromagnetic Metals, Phys. Rev. Lett.135, 186302 (2025)

    2025

  22. [22]

    X. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates, Phys. Rev. B83, 205101 (2011)

    2011

  23. [23]

    N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys.90, 015001 (2018)

    2018

  24. [24]

    E. Zhai, T. Liang, R. Liu, M. Cai, R. Li, Q. Shao, C. Su, and Y. C. Lin, The rise of semi-metal electronics, Nat. Rev. Electr. Eng.1, 497 (2024)

    2024

  25. [25]

    K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Electric Field Effect in Atomically Thin Carbon Films, Science306, 666 (2004)

    2004

  26. [26]

    K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Two-dimensional gas of massless Dirac fermions in graphene, Nature438, 197 (2005)

    2005

  27. [27]

    A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys.81, 109 (2009)

    2009

  28. [28]

    Wan, P.-Y

    Y.-H. Wan, P.-Y. Liu, and Q.-F. Sun, Classification of Chern numbers based on high-symmetry points, Phys. Rev. B111, L161410 (2025)

    2025

  29. [29]

    Roulleau, F

    P. Roulleau, F. Portier, D. C. Glattli, P. Roche, A. Ca- vanna, G. Faini, U. Gennser, and D. Mailly, Direct mea- surement of the coherence length of edge states in the in- teger quantum Hall regime, Phys. Rev. Lett.100, 126802 (2008)

    2008

  30. [30]

    P. Deng, C. Eckberg, P. Zhang, G. Qiu, E. Emmanouili- 8 dou, G. Yin, S. K. Chong, L. Tai, N. Ni, and K. L. Wang, Probing the mesoscopic size limit of quantum anomalous Hall insulators, Nat. Commun.13, 4246 (2022)

    2022

  31. [31]

    B¨ uttiker, Four-Terminal Phase-Coherent Conduc- tance, Phys

    M. B¨ uttiker, Four-Terminal Phase-Coherent Conduc- tance, Phys. Rev. Lett.57, 1761 (1986)

    1986

  32. [32]

    Liu and Q.-F

    P.-Y. Liu and Q.-F. Sun, Dissipation and dephasing in quantum Hall interferometers, Phys. Rev. B110, 085411 (2024)

    2024

  33. [33]

    Meir and N

    Y. Meir and N. S. Wingreen, Landauer formula for the current through an interacting electron region, Phys. Rev. Lett.68, 2512 (1992)

    1992

  34. [34]

    Datta, Electronic Transport in Mesoscopic Systems (Cambridge University Press, Cambridge, 1995)

    S. Datta, Electronic Transport in Mesoscopic Systems (Cambridge University Press, Cambridge, 1995)

    1995

  35. [35]

    H. Zhou, H. Li, D.-H. Xu, C.-Z. Chen, Q.-F. Sun, and X. C. Xie, Transport theory of half-quantized Hall con- ductance in a semimagnetic topological insulator, Phys. Rev. Lett.129, 096601 (2022)

    2022

  36. [36]

    M. Mogi, Y. Okamura, M. Kawamura, R. Yoshimi, K. Yasuda, A. Tsukazaki, K. S. Takahashi, T. Mori- moto, N. Nagaosa, M. Kawasaki, Y. Takahashi, and Y. Tokura, Experimental signature of the parity anomaly in a semi-magnetic topological insulator, Nat. Phys.18, 390 (2022)

    2022

  37. [37]

    Fang, A.-M

    J.-Y. Fang, A.-M. Guo, and Q.-F. Sun, Dephasing effect promotes the appearance of quantized Hall plateaus, New J. Phys.25, 033001 (2023)

    2023

  38. [38]

    M. J. McLennan, Y. Lee, and S. Datta, Voltage drop in mesoscopic systems: A numerical study using a quantum kinetic equation, Phys. Rev. B43, 13846 (1991)

    1991

  39. [39]

    Chakravarty and A

    S. Chakravarty and A. Schmid, Weak localization: The quasiclassical theory of electrons in a random potential, Phys. Rep.140, 193 (1986)

    1986

  40. [40]

    Stern, Y

    A. Stern, Y. Aharonov, and Y. Imry, Phase uncertainty and loss of interference: A general picture, Phys. Rev. A 41, 3436 (1990)

    1990

  41. [41]

    Burkard, D

    G. Burkard, D. Loss, and D. P. DiVincenzo, Coupled quantum dots as quantum gates, Phys. Rev. B59, 2070 (1999)

    2070

  42. [42]

    B. A. Bernevig and T. L. Hughes, Topological Insulators and Topological Superconductors (Princeton University Press, Princeton, NJ, 2013)

    2013

  43. [43]

    Wan, P.-Y

    Y.-H. Wan, P.-Y. Liu, and Q.-F. Sun, Interplay of al- termagnetic order and wilson mass in the dirac equa- tion: Helical edge states without time-reversal symmetry, Phys. Rev. B112, 115412 (2025)

    2025

  44. [44]

    Wan, C.-M

    Y.-H. Wan, C.-M. Miao, P.-Y. Liu, and Q.-F. Sun, Helical Fermi arc in altermagnetic Weyl semimetal, Phys. Rev. B112, 235411 (2025)

    2025

  45. [45]

    Liu, Y.-H

    P.-Y. Liu, Y.-H. Wan, and Q.-F. Sun, Emergence of net chirality in a two-dimensional Dirac fermion system with altermagnetic mass, Phys. Rev. B113, L041402 (2026)

    2026

  46. [46]

    Wan and Q.-F

    Y.-H. Wan and Q.-F. Sun, Altermagnetism-induced par- ity anomaly in weak topological insulators, Phys. Rev. B 111, 045407 (2025)

    2025

  47. [47]

    J.-Y. Zou, B. Fu, H.-W. Wang, Z.-A. Hu, and S.-Q. Shen, Half-quantized Hall effect and power law decay of edge- current distribution, Phys. Rev. B105, L201106 (2022)

    2022

  48. [48]

    Marguerite, J

    A. Marguerite, J. Birkbeck, A. Aharon-Steinberg, D. Hal- bertal, K. Bagani, I. Marcus, Y. Myasoedov, A. K. Geim, D. J. Perello, and E. Zeldov, Imaging work and dissipa- tion in the quantum Hall state in graphene, Nature575, 628 (2019)

    2019

  49. [49]

    Fang, N.-X

    J.-Y. Fang, N.-X. Yang, Q. Yan, A.-M. Guo, and Q.-F. Sun, Thermal dissipation in the quantum Hall regime in graphene, Phys. Rev. B104, 115411 (2021)

    2021

  50. [50]

    Kawamura, R

    M. Kawamura, R. Yoshimi, A. Tsukazaki, K. S. Taka- hashi, M. Kawasaki, and Y. Tokura, Current-Driven In- stability of the Quantum Anomalous Hall Effect in Fer- romagnetic Topological Insulators, Phys. Rev. Lett.119, 016803 (2017)

    2017