Pith. sign in

REVIEW 3 major objections 6 minor 65 references

Quantized Topological States and Parity Anomaly in Intrinsic Quantum Anomalous Hall Insulator MnBi2Te4

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read The quantized Hall plateaus in five-layer MnBi2Te4 follow a generalized topological index rooted in the parity anomaly of (2+1)-dimensional Dirac fermions, carried by a single anomalous Landau level.

desk verdict A strong experimental paper with a genuinely new high-field QAH phase diagram, but the parity-anomaly interpretation leans on a level assignment that needs full model disclosure to convince. read the letter →

arxiv 2507.03342 v1 pith:WYFE5GW5 submitted 2025-07-04 cond-mat.mes-hall cond-mat.mtrl-sci

Zhongxun Guo , Jingjing Gao , Zhiwei Huang , Di Yue , Zhaochen Liu , Mingyan Luo , Shuang Wu , Xinyu Chen
show 17 more authors
Guangyi Huang Yujun Deng Mengzhu Shi Yin Xia Zihan Xu Chuanying Xi Guangli Kuang Changlin Zheng Shiwei Wu Hua Jiang X. C. Xie Wenzhong Bao Yuping Sun Xian Hui Chen Jing Wang Wei Ruan Yuanbo Zhang
This is my paper
classification cond-mat.mes-hallcond-mat.mtrl-sci
keywords MnBi2Te4quantumanomalousHalleffectparityanomalyLandauquantizationtopologicalinsulatorhelicaledgetransporthighmagneticfieldspectralasymmetry
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 claims that the quantized topological states observed in five-septuple-layer (5-SL) MnBi2Te4 under magnetic fields up to 45 tesla are not a simple superposition of quantum Hall and quantum anomalous Hall effects, but are governed by a generalized topological index rooted in the parity anomaly of (2+1)-dimensional Dirac fermions. The anomaly manifests as an anomalous Landau level that is hole-derived yet disperses like an electron level, and this level sustains the ν = −1 quantum anomalous Hall state at high fields and produces gate-tunable helical edge transport in the ν = 0 phase. If the claim is right, the paper provides a direct solid-state realization of the parity anomaly and a counting rule—half the imbalance between unoccupied and occupied Landau levels—that should apply to any quantum anomalous Hall insulator in a quantizing magnetic field.

What carries the argument

The central object is the generalized topological index N = (N+ − N−)/2, a Landau-level-resolved expression of the parity anomaly's spectral asymmetry in (2+1) dimensions. The mechanism it captures is an 'inverted' electron-like Landau level descending from a hole sub-band—the first Landau level of the surface band E^h_{s,k}—which, unlike all other hole levels, disperses upward and crosses the Fermi level at the sample boundary, sustaining the chiral edge state behind the ν = −1 plateau and the helical edge channels in the ν = 0 regime. Supporting it is a slab-model band structure of ferromagnetic MnBi2Te4 whose sub-band ordering places three bulk bands (E^e_1, E^h_1, E^h_2) inside the surface band gap of the 5-SL quantum well, so that the lowest observable Landau levels L0, L1, L2 originate from E^h_{1,k}, E^e_{1,k}, and E^e_{2,k} respectively.

What would settle it

A direct spectroscopic probe of the dispersion of the anomalous Landau level—for example, tunneling spectroscopy at the sample edge that resolves a hole-derived level curving upward through the Fermi level—would settle the identification. Alternatively, a transport experiment on the ν = 0 phase that detects the predicted counter-propagating helical edge channels (e.g., via nonlocal resistance) or, conversely, shows purely chiral edge conduction, would confirm or refute the helical-edge scenario.

Watch

Extended reading notes

Core claim

In the presence of Landau quantization, the topology of 5-SL MnBi2Te4 is characterized by the index N = (N+ − N−)/2, where N+ and N− count unoccupied and occupied Landau levels, with the universal relation N− = N+ − 2C0 holding at the QAH gap (here C0 = −1). The paper identifies this index with the spectral asymmetry of the parity anomaly and pinpoints the anomalous Landau level as the first Landau level of the surface hole band E^h_{s,k}, which, unlike ordinary hole levels, disperses upward and crosses the Fermi level at the sample boundary, giving rise to the ν = −1 QAH plateau and, through its crossing with the first hole Landau level, to the helical edge channels that split the ν = 0 phase into three regimes (0−, 0′, 0+). The assignment is anchored by slab-model calculations of a hypothetical ferromagnetic MnBi2Te4 quantum well, which reproduce the observed Landau fan once level broadening and impurity states are included.

Load-bearing premise

The interpretation rests on the slab-model assignment of the observed Landau levels to the calculated sub-band Landau levels of a hypothetical ferromagnetic MnBi2Te4; if that band-structure labeling is wrong, the parity-anomaly reading and its edge-transport picture lose their experimental anchor.

Editorial extensions

If this is right

  • The counting rule N = (N+ − N−)/2 applies to all quantum anomalous Hall insulators in a quantizing magnetic field, so the same imbalance of two extra occupied Landau levels should appear in any |C0| = 1 Chern insulator when the field polarizes the magnetism.
  • The ν = −1 plateau at high field is adiabatically connected to the zero-field QAH state, meaning the zero-field and high-field quantizations share the same topological origin.
  • The ν = 0 phase of 5-SL MnBi2Te4 hosts gate-tunable helical edge transport with three distinct regimes controlled by the Fermi level position, analogous to the edge transport of a quantum spin Hall insulator.
  • Improved crystal growth—slow cooling instead of quenching—suppresses Mn-Bi anti-site defects and raises the zero-field QAH gap to about 30 K, making MnBi2Te4 a practical platform for reaching the extreme quantum limit and for applications in topological electronics.

Reading between the lines

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

  • If the parity-anomaly index is correct, the same anomalous Landau level should appear as a robust feature in other intrinsic magnetic topological insulators with Chern number −1, and its energy spacing relative to ordinary Landau levels could serve as a direct measure of the spectral asymmetry.
  • The fractional state observed between ν = −2 and ν = −3 above 40 T may be a many-body extension of the parity-anomaly picture or an unrelated fractional Chern state; its field threshold suggests interaction effects beyond the single-particle Landau-level description.
  • The slab-model dependence on a hypothetical ferromagnetic 5-SL stack could be tested across thicknesses: if a different layer count shifts the sub-band ordering, the anomalous level's electron-like dispersion should move accordingly, and the ν = 0 helical regime should appear or disappear in concert.
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 / 6 minor

Summary. This manuscript reports transport measurements on high-quality five-septuple-layer (5-SL) MnBi2Te4 devices. The authors observe zero-field quantum anomalous Hall (QAH) effect in Type A devices with quantization precision better than 1 part in 10^4 and a QAH gap up to 29 K. In Type S devices under magnetic fields up to 45 T, they observe quantized Hall plateaus at filling factors ν = +1, -1, -2, -3, -4, -6, -8 and an intervening fractional state. The central claim is that the Landau fan diagram is governed by a generalized topological index N = (N+ - N-)/2 rooted in the parity anomaly of Dirac fermions in 2+1 dimensions, and that an anomalous Landau level—identified as the first Landau level of the surface hole sub-band E^h_{s,k}—explains the ν = -1 QAH state and gives rise to gate-tunable helical edge transport in the ν = 0 phase. The experimental data are extensive and the Landau fan is mapped carefully, but the theoretical interpretation rests on a slab-model calculation whose parameters and level assignments are not fully specified in the main text.

Significance. If the interpretation holds, the observation of a generalized topological index rooted in the parity anomaly and an anomalous Landau level in an intrinsic magnetic topological insulator would be a significant advance, connecting high-field Landau quantization with zero-field topology. The paper provides strong evidence for high-quality samples, reproducible quantized plateaus, and a careful mapping of the Landau fan. The prediction of helical edge transport in the ν = 0 phase is specific and falsifiable, and the observation of three distinct regimes within that phase is a notable experimental finding. However, the load-bearing identification of the experimental Landau levels L0, L1, L2 and the anomalous level with specific sub-bands of a hypothetical ferromagnetic MnBi2Te4 slab is not independently established, and the generalized index is presented more as a reformulation than as a derivation. The experimental contributions themselves are solid, but the theoretical narrative needs stronger support.

major comments (3)
  1. [Fig. 3c–3e and main text p.6] The identification of L0, L1, L2 as the first Landau levels of E^h_{1,k}, E^e_{1,k}, E^e_{2,k}, and the designation of the first Landau level of E^h_{s,k} as the anomalous level responsible for ν = -1, rest entirely on the slab-model calculation of hypothetical ferromagnetic MnBi2Te4. The Hamiltonian parameters, surface potential, level broadening, and impurity-state inputs are not provided in the main text; they are deferred to Supplementary Fig. S5. Because the DOS simulation in Fig. 3d is a fit that uses these inputs, agreement with the experimental fan diagram does not independently confirm the sub-band assignment. If, for example, surface-potential shifts or disorder reorder the low-lying levels, the anomaly-based interpretation and the helical-edge picture lose their experimental anchor. Please provide the full set of model parameters, a sensitivity analysis of the level ordering to those parameters, and an explicit comparison of the calculated LL spectra (not just the DOS) with the experimentally extracted fan diagram.
  2. [Page 6, generalized topological index N = (N+ - N-)/2] The reformulation of the topological number N as (N+ - N-)/2 and the universal relation N_- = N_+ - 2C_0 are stated without a derivation in the main text. The connection to the parity anomaly via the spectral asymmetry η is mentioned but not made explicit; the reader is left to infer how the spectral asymmetry is computed for the multiple sub-bands in the 5-SL slab and why each Landau level carries Chern number -1. Please provide a self-contained derivation or a precise citation showing how the LL-resolved index follows from the parity anomaly in a system with several occupied and unoccupied sub-bands, and clarify the role of the regularization scheme in a finite slab. As written, the index appears to be assumed rather than demonstrated.
  3. [Page 5, Type S devices and adiabatic continuity] The argument that the high-field ν = -1 state is a QAH state adiabatically connected to the zero-field QAH state relies on continuity, but Type S devices do not show zero-field QAH quantization (as stated on page 5). The authors argue that the high mobility of surface electrons in the FM state enables the observation, yet the absence of zero-field quantization means that the C0 = -1 assignment for the high-field state is inferred, not directly measured. Please discuss whether the high-field ν = -1 state in Type S devices is indeed the same topological state as the zero-field QAH state in Type A devices, and whether the adiabatic connection can be justified given that zero-field quantization is absent.
minor comments (6)
  1. [Abstract and Introduction] The abstract states that the anomaly 'gives rise to gate-tunable helical edge transport,' but the report of helical edge transport in the ν = 0 phase is based on a comparison of transport data with a theoretical model, not a direct measurement of edge-state spin structure. Please temper the wording or provide direct evidence for the helical character.
  2. [Fig. 2c] The fractional state between ν = -2 and ν = -3 is presented as emerging above 40 T, but the available data appear limited to one device. Please state the reproducibility across devices and the sample-to-sample variation in the threshold field.
  3. [Fig. 3d and Supplementary Fig. S5] The caption of Fig. 3d mentions 'impurity states' as an input to the DOS simulation, but the main text does not define what these impurity states are or how they were modeled. Please specify their energy distribution, density, and effect on the simulated fan diagram.
  4. [Page 5, Arrhenius gap extraction] The QAH gap ΔE is extracted from a line fit of ln Rxx versus 1/T. The temperature range and the quality of the fit for each magnetic field are not shown. Please provide representative fits or a statement about the fitting range and uncertainty.
  5. [Page 6, Eq. (1)] The equation N = (N+ - N-)/2 is not numbered, which makes it awkward to reference in the text. Please number equations consistently.
  6. [Page 3, sample preparation] The statement that 'a sharp tip' is used to trim excess MnBi2Te4 would benefit from a reference to the technique, since edge definition is important for interpreting edge transport.

Circularity Check

0 steps flagged · score 2.0 of 10

No substantive circularity: the generalized index, LL assignments, and helical-edge prediction do not reduce to fitted inputs; self-citations are background only.

full rationale

The paper's derivation chain is self-contained against its inputs. The observed quantized plateaus and the Landau fan data are independent experimental facts; the generalized index N=(N+−N−)/2 is taken from external theoretical work on the parity anomaly (refs 16-19), and the relation N−=N+−2C0 follows by comparing that external expression with the bookkeeping definition N=C0−ΔN++ΔN−. This is an algebraic consistency relation, not a fitted parameter renamed as a prediction. The identification of L0, L1, L2 and of the 'anomalous' first LL of E^h_s,k comes from a slab-model calculation, and the DOS simulation is presented as a comparison with the experimental fan diagram; although the model parameters are not fully specified in the main text, the paper does not claim the simulation is an independent derivation. The prediction of 0−, 0′, 0+ helical edge transport is a distinct consequence of the calculated LL crossings and is checked against new data. Self-citations (e.g., refs 7 and 50) supply background and fabrication context; the zero-field QAH is remeasured in this work, so these citations are not load-bearing. Model-dependence of the level assignments is a correctness risk, not circularity.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a small number of domain assumptions (Landau-level Chern number counting, adiabatic continuity of the Chern number, applicability of the parity-anomaly regularization) and on a paper-specific slab model that is not fully parameterized. No new particles or forces are introduced; the anomalous Landau level is an established concept applied to a new system. The only explicit fitted quantity is the effective g-factor used to interpret the field-dependent gap.

free parameters (2)
  • Effective g-factor = -2.1
    Extracted from the linear slope of the QAH gap ΔE versus magnetic field in the AFM state (Fig. 1e). Used to interpret Zeeman narrowing, but not central to the generalized index claim.
  • DOS simulation broadening and impurity parameters = not specified
    The simulated DOS fan diagram in Fig. 3d incorporates level broadening and impurity states 'once level broadening and impurity states are taken into account'; exact values are not given, so the match to the experimental fan diagram involves unspecified tuning.
assumptions (4)
  • domain assumption Each Landau level carries Chern number -1, and the spectral asymmetry η equals the imbalance (N+ - N-)/2 under uniform LL degeneracy
    Invoked on page 6 to derive N = (N+ - N-)/2; relies on standard quantum Hall and Dirac-fermion results (refs. 18, 19).
  • domain assumption Adiabatic continuity: the Chern number C0 = -1 of the zero-field QAH state remains valid in finite magnetic fields as long as the gap stays open
    Stated on page 6: 'the QAH gap remains open under finite magnetic fields (Fig. 1e)' and 'the same C0, through adiabatic continuity, continues to describe the QAH phase.'
  • ad hoc to paper The slab calculation for hypothetical FM MnBi2Te4 reproduces the actual 5-SL band structure, including sub-band ordering and LL assignment
    The model in Fig. 3c-e is used to identify L0, L1, L2 and the anomalous LL; parameters are not fully specified, making it a paper-specific modeling assumption.
  • domain assumption The parity anomaly regularization scheme that breaks time-reversal symmetry and preserves gauge symmetry applies to QAH systems like MnBi2Te4
    Cited from ref. 17 on page 6; needed to link the anomalous LL to the parity anomaly.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Quantized Topological States and Parity Anomaly in Intrinsic Quantum Anomalous Hall Insulator MnBi2Te4." pith.science (2026). https://pith.science/paper/WYFE5GW5

@misc{pith2026250703342,
  author       = {Pith},
  title        = {Pith review of: Quantized Topological States and Parity Anomaly in Intrinsic Quantum Anomalous Hall Insulator MnBi2Te4},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WYFE5GW5}},
  note         = {Machine review of arXiv:2507.03342}
}
read the original abstract

When thinned down to just a few atomic layers, the layered magnetic topological insulator MnBi2Te4 offers an exceptional platform for exploring a wide range of topological phenomena. In this work, we overcome longstanding challenges in synthesizing high-purity MnBi2Te4 crystals and report the observation of a myriad of quantized topological states in high-quality five-septuple-layer (5-SL) samples under magnetic fields up to 45 Tesla. We show that the nontrivial topology of 5-SL MnBi2Te4, in the presence of Landau quantization, is governed by a generalized topological index rooted in the parity anomaly of Dirac fermions in (2+1) dimensions. The anomaly manifests as an anomalous Landau level, giving rise to gate-tunable helical edge transport. Our results establish high-quality MnBi2Te4 as a robust platform for exploring emergent topological states and for advancing novel quantum device applications.

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

65 extracted references · 57 canonical work pages

  1. [1]

    Otrokov, M. M. et al. Unique Thickness -Dependent Properties of the van der Waals Interlayer Antiferromagnet MnBi2Te4 Films. Phys. Rev. Lett. 122, 107202 (2019)

    work page 2019

  2. [2]

    Zhang, D. et al. Topological Axion States in the Magnetic Insulator MnBi2Te4 with the Quantized Magnetoelectric Effect. Phys. Rev. Lett. 122, 206401 (2019)

    work page 2019

  3. [3]

    Gong, Y . et al. Experimental Realization of an Intrinsic Magnetic Topological Insulator. Chin. Phys. Lett. 36, 76801–076801 (2019)

    work page 2019

  4. [4]

    Li, J. et al. Intrinsic magnetic topological insulators in van der Waals layered MnBi 2Te4- family materials. Sci. Adv. 5, eaaw5685 (2019). Page 8 of 13

    work page 2019

  5. [5]

    Aliev, Z. S. et al. Novel ternary layered manganese bismuth tellurides of the MnTe-Bi2Te3 system: Synthesis and crystal structure. J. Alloys Compd. 789, 443–450 (2019)

    work page 2019

  6. [6]

    Otrokov, M. M. et al. Prediction and observation of an antiferromagnetic topological insulator. Nature 576, 416–422 (2019)

    work page 2019

  7. [7]

    Deng, Y . et al. Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi2Te4. Science 367, 895–900 (2020)

    work page 2020

  8. [9]

    Ge, J. et al. High-Chern-number and high-temperature quantum Hall effect without Landau levels. Natl. Sci. Rev. 7, 1280–1287 (2020)

    work page 2020

Show all 65 references
  1. [10]

    Gao, A. et al. Layer Hall effect in a 2D topological axion antiferromagnet. Nature 595, 521–525 (2021)

    2021

  2. [11]

    Gao, A. et al. Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure. Science 381, 181–186 (2023)

    2023

  3. [12]

    Wang, N. et al. Quantum-metric-induced nonlinear transport in a topological antiferromagnet. Nature 621, 487–492 (2023)

    2023

  4. [13]

    Qiu, J.-X. et al. Observation of the axion quasiparticle in 2D MnBi 2Te4. Nature 641, 62– 69 (2025)

    2025

  5. [14]

    Li, S. et al. Progress on the antiferromagnetic topological insulator MnBi 2Te4. Natl. Sci. Rev. 11, nwac296 (2024)

    2024

  6. [15]

    Haldane, F. D. M. Model for a Quantum Hall Effect without Landau Levels: Condensed - Matter Realization of the Parity. Phys. Rev. Lett. 61, 2015 (1988)

    1988

  7. [16]

    Niemi, A. J. & Semenoff, G. W. Axial -Anomaly-Induced Fermion Fractionization and Effective Gauge-Theory Actions in Odd -Dimensional Space-Times. Phys. Rev. Lett. 51, 2077–2080 (1983)

    1983

  8. [17]

    Lapa, M. F. Parity anomaly from the Hamiltonian point of view. Phys. Rev. B 99, 235144 (2019)

    2019

  9. [18]

    & Hankiewicz, E

    Böttcher, J., Tutschku, C. & Hankiewicz, E. M. Fate of quantum anomalous Hall effect in the presence of external magnetic fields and particle -hole asymmetry. Phys. Rev. B 101, 195433 (2020)

    2020

  10. [19]

    Böttcher, J., Tutschku, C., Molenkamp, L. W. & Hankiewicz, E. M. Survival of the Quantum Anomalous Hall Effect in Orbital Magnetic Fields as a Consequence of the Parity Anomaly. Phys. Rev. Lett. 123, 226602 (2019)

    2019

  11. [20]

    The quantized Hall effect

    von Klitzing, K. The quantized Hall effect. Rev. Mod. Phys. 58, 519–531 (1986)

    1986

  12. [21]

    Chang, C.-Z. et al. Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator. Science 340, 167–170 (2013)

    2013

  13. [22]

    Checkelsky, J. G. et al. Trajectory of the anomalous Hall effect towards the quantized state in a ferromagnetic topological insulator. Nat. Phys. 10, 731–736 (2014)

    2014

  14. [23]

    Kou, X. et al. Scale-Invariant Quantum Anomalous Hall Effect in Magnetic Topological Insulators beyond the Two-Dimensional Limit. Phys. Rev. Lett. 113, 137201 (2014)

    2014

  15. [24]

    Chang, C.-Z. et al. High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator. Nat. Mater. 14, 473–477 (2015)

    2015

  16. [25]

    Mogi, M. et al. Magnetic modulation doping in topological insulators toward higher - temperature quantum anomalous Hall effect. Appl. Phys. Lett. 107, 182401 (2015). Page 9 of 13

    2015

  17. [26]

    Götz, M. et al. Precision measurement of the quantized anomalous Hall resistance at zero magnetic field. Appl. Phys. Lett. 112, 072102 (2018)

    2018

  18. [27]

    Fox, E. J. et al. Part-per-million quantization and current -induced breakdown of the quantum anomalous Hall effect. Phys. Rev. B 98, 075145 (2018)

    2018

  19. [28]

    Okazaki, Y . et al. Precise resistance measurement of quantum anomalous Hall effect in magnetic heterostructure film of topological insulator. Appl. Phys. Lett. 116, 143101 (2020)

    2020

  20. [29]

    Okazaki, Y . et al . Quantum anomalous Hall effect with a permanent magnet defines a quantum resistance standard. Nat. Phys. 18, 25-29 (2022)

    2022

  21. [30]

    Rodenbach, L. K. et al. Realization of the quantum ampere using the quantum anomalous Hall and Josephson effects. arXiv.2308.00200 (2023)

    2023 arXiv

  22. [31]

    Patel, D. K. et al. A zero external magnetic field quantum standard of resistance at the 10−9 level. Nat. Electron. 7, 1111–1116 (2024)

    2024

  23. [32]

    & Tsukazaki, A

    Tokura, Y ., Yasuda, K. & Tsukazaki, A. Magnetic topological insulators. Nat. Rev. Phys. 1, 126–143 (2019)

    2019

  24. [33]

    Liu, C.-X., Zhang, S. -C. & Qi, X. -L. The Quantum Anomalous Hall Effect: Theory and Experiment. Annu. Rev. Condens. Matter Phys. 7, 301–321 (2016)

    2016

  25. [34]

    -Z., Liu, C

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

    2023

  26. [35]

    B., Qi, X.-L., Maciejko, J

    Chung, S. B., Qi, X.-L., Maciejko, J. & Zhang, S.-C. Conductance and noise signatures of Majorana backscattering. Phys. Rev. B 83, 100512 (2011)

    2011

  27. [36]

    R., Nilsson, J

    Akhmerov, A. R., Nilsson, J. & Beenakker, C. W. J. Electrically Detected Interferometry of Majorana Fermions in a Topological Insulator. Phys. Rev. Lett. 102, 216404 (2009)

    2009

  28. [37]

    & Kane, C

    Fu, L. & Kane, C. L. Probing Neutral Majorana Fermion Edge Modes with Charge Transport. Phys. Rev. Lett. 102, 216403 (2009)

    2009

  29. [38]

    & Zhang, S

    Wang, J., Zhou, Q., Lian, B. & Zhang, S. -C. Chiral topological superconductor and half - integer conductance plateau from quantum anomalous Hall plateau transition. Phys. Rev. B 92, 064520 (2015)

    2015

  30. [39]

    & Zhang, S.-C

    Lian, B., Sun, X.-Q., Vaezi, A., Qi, X.-L. & Zhang, S.-C. Topological quantum computation based on chiral Majorana fermions. Proc. Natl. Acad. Sci. 115, 10938–10942 (2018)

    2018

  31. [40]

    Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science 367, 900–903 (2020)

    2020

  32. [41]

    Li, T. et al. Quantum anomalous Hall effect from intertwined moiré bands. Nature 600, 641–646 (2021)

    2021

  33. [42]

    Park, H. et al. Observation of fractionally quantized anomalous Hall effect. Nature 622, 74–79 (2023)

    2023

  34. [43]

    Xu, F. et al. Observation of Integer and Fractional Quantum Anomalous Hall Effects in Twisted Bilayer MoTe2. Phys. Rev. X 13, 031037 (2023)

    2023

  35. [44]

    Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020)

    2020

  36. [45]

    Han, T. et al. Large quantum anomalous Hall effect in spin -orbit proximitized rhombohedral graphene. Science 384, 647–651 (2024)

    2024

  37. [46]

    Lu, Z. et al. Fractional quantum anomalous Hall effect in multilayer graphene. Nature 626, 759–764 (2024)

    2024

  38. [47]

    Lian, Z. et al. Antiferromagnetic quantum anomalous Hall effect under spin flips and flops. Page 10 of 13 Nature 641, 70–75 (2025)

    2025

  39. [48]

    Li, Y . et al. Reentrant quantum anomalous Hall effect in molecular beam epitaxy -grown MnBi2Te4 thin films. arXiv:2401.11450 (2024)

    2024 arXiv

  40. [49]

    Wang, Y . et al. Towards the Quantized Anomalous Hall effect in AlOx-capped MnBi2Te4. Nat. Commun. 16, 1727 (2025)

    2025

  41. [50]

    Deng, Y . et al. Gate-tunable room -temperature ferromagnetism in two -dimensional Fe3GeTe2. Nature 563, 94–99 (2018)

    2018

  42. [51]

    Hou, F. et al. Te-Vacancy-Induced Surface Collapse and Reconstruction in Antiferromagnetic Topological Insulator MnBi2Te4. ACS Nano 14, 11262–11272 (2020)

    2020

  43. [52]

    Liu, C. et al. Magnetic-field-induced robust zero Hall plateau state in MnBi 2Te4 Chern insulator. Nat. Commun. 12, 4647 (2021)

    2021

  44. [53]

    Yang, S. et al. Odd-Even Layer -Number Effect and Layer -Dependent Magnetic Phase Diagrams in MnBi2Te4. Phys. Rev. X 11, 011003 (2021)

    2021

  45. [54]

    Ovchinnikov, D. et al. Intertwined Topological and Magnetic Orders in Atomically Thin Chern Insulator MnBi2Te4. Nano Lett. 21, 2544–2550 (2021)

    2021

  46. [55]

    Lei, C. et al. Metamagnetism of few-layer topological antiferromagnets. Phys. Rev. Mater. 5, 064201 (2021)

    2021

  47. [56]

    Ying, Z. et al. Experimental evidence for dissipationless transport of the chiral edge state of the high -field Chern insulator in MnBi 2Te4 nanodevices. Phys. Rev. B 105, 085412 (2022)

    2022

  48. [57]

    Liu, C. et al. Robust axion insulator and Chern insulator phases in a two -dimensional antiferromagnetic topological insulator. Nat. Mater. 19, 522–527 (2020)

    2020

  49. [58]

    Cai, J. et al. Electric control of a canted-antiferromagnetic Chern insulator. Nat. Commun. 13, 1668 (2022)

    2022

  50. [59]

    Lai, Y ., Ke, L., Yan, J., McDonald, R. D. & McQueeney, R. J. Defect-driven ferrimagnetism and hidden magnetization in MnBi2Te4. Phys. Rev. B 103, 184429 (2021)

    2021

  51. [60]

    Garnica, M. et al. Native point defects and their implications for the Dirac point gap at MnBi2Te4(0001). npj Quantum Mater. 7, 1–9 (2022)

    2022

  52. [61]

    Chong, S. K. et al. Anomalous Landau quantization in intrinsic magnetic topological insulators. Nat. Commun. 14, 4805 (2023)

    2023

  53. [62]

    Kane, C. L. & Mele, E. J. Quantum Spin Hall Effect in Graphene. Phys. Rev. Lett. 95, 226801 (2005)

    2005

  54. [63]

    A., Hughes, T

    Bernevig, B. A., Hughes, T. L. & Zhang, S.-C. Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells. Science 314, 1757–1761 (2006)

    2006

  55. [64]

    Bernevig, B. A. & Zhang, S. -C. Quantum Spin Hall Effect. Phys. Rev. Lett. 96, 106802 (2006)

    2006

  56. [65]

    & Zhang, S.-C

    Maciejko, J., Qi, X.-L. & Zhang, S.-C. Magnetoconductance of the quantum spin Hall state. Phys. Rev. B 82, 155310 (2010)

    2010

  57. [66]

    & Richter, K

    Essert, S. & Richter, K. Magnetotransport in disordered two -dimensional topological insulators: signatures of charge puddles. 2D Mater. 2, 024005 (2015). Acknowledgements We thank Philip Kim, Xiaofeng Jin, Yizheng Wu, Dung-Hai Lee, Taige Wang, Zhiqiang Gao, Raquel Queiroz and...

    2015

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.