Axion Insulator State in Hundred-Nanometer-Thick Magnetic Topological Insulator Sandwich Heterostructures

Chao-Xing Liu; Cui-Zu Chang; Deyi Zhuo; Hemian Yi; Ke Wang; K. T. Law; Ling-Jie Zhou; Moses H. W. Chan; Ruobing Mei; Ruoxi Zhang

arxiv: 2306.13016 · v5 · submitted 2023-06-22 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci

Axion Insulator State in Hundred-Nanometer-Thick Magnetic Topological Insulator Sandwich Heterostructures

Deyi Zhuo , Zi-Jie Yan , Zi-Ting Sun , Ling-Jie Zhou , Yi-Fan Zhao , Ruoxi Zhang , Ruobing Mei , Hemian Yi

show 5 more authors

Ke Wang Moses H. W. Chan Chao-Xing Liu K. T. Law Cui-Zu Chang

This is my paper

Pith reviewed 2026-05-24 08:39 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.mtrl-sci

keywords axion insulatortopological insulatormagnetic heterostructuremolecular beam epitaxytransport measurementsmagnetoelectric effectsandwich structure

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The pith

The axion insulator state persists in magnetic topological insulator sandwich heterostructures as thick as 106 nanometers.

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 axion insulator state, previously observed only in samples near the 2D limit at thicknesses around 10 nm, continues to appear in much thicker 3D samples reaching 106 nm. This matters because coupling between top and bottom surface states in thin films can obscure the quantized topological magnetoelectric response that defines the state. The authors use MBE-grown sandwich structures and report that the state emerges once the middle undoped topological insulator layer exceeds roughly 3 nm. The thicker geometry reduces unwanted surface coupling while preserving the bulk symmetry and surface magnetization gap required for the axion insulator.

Core claim

An axion insulator state is realized in hundred-nanometer-thick magnetic topological insulator sandwich heterostructures, with the state emerging when the thickness of the middle undoped topological insulator layer exceeds approximately 3 nm.

What carries the argument

The magnetic topological insulator sandwich heterostructure with a thick middle undoped layer, in which surface states remain gapped by magnetization while the bulk preserves time-reversal or inversion symmetry.

If this is right

The 3D axion insulator supplies a platform for studying the topological magnetoelectric effect without strong top-bottom surface coupling.
The same geometry may host additional emergent phases such as the high-order topological insulator state.
The state appears once the middle layer thickness surpasses about 3 nm, marking a crossover from coupled thin-film to decoupled thick-sample behavior.
Thicker samples reduce fabrication constraints associated with maintaining precise few-nanometer thicknesses.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Similar thickness extensions could be tested in other magnetic topological materials to separate surface and bulk contributions more cleanly.
Device applications of the magnetoelectric effect may become more practical with hundred-nanometer films that are easier to pattern and contact.
Systematic variation of middle-layer thickness around the 3 nm threshold could map the onset of decoupling between surfaces.

Load-bearing premise

The measured transport signatures of high longitudinal resistance and vanishing Hall conductivity uniquely signal the axion insulator state rather than other magnetic or interface effects.

What would settle it

In samples thicker than 100 nm, observation of a finite Hall conductivity or thickness-dependent deviation from the expected resistance plateau that cannot be explained by the axion insulator picture.

read the original abstract

An axion insulator is a three-dimensional (3D) topological insulator (TI), in which the bulk maintains the time-reversal symmetry or inversion symmetry but the surface states are gapped by surface magnetization. The axion insulator state has been observed in molecular beam epitaxy (MBE)-grown magnetically doped TI sandwiches and exfoliated intrinsic magnetic TI MnBi2Te4 flakes with an even number layer. All these samples have a thickness of ~10 nm, near the 2D-to-3D boundary. The coupling between the top and bottom surface states in thin samples may hinder the observation of quantized topological magnetoelectric response. Here, we employ MBE to synthesize magnetic TI sandwich heterostructures and find that the axion insulator state persists in a 3D sample with a thickness of ~106 nm. Our transport results show that the axion insulator state starts to emerge when the thickness of the middle undoped TI layer is greater than ~3 nm. The 3D hundred-nanometer-thick axion insulator provides a promising platform for the exploration of the topological magnetoelectric effect and other emergent magnetic topological states, such as the high-order TI phase.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper reports axion insulator transport signatures in ~106 nm thick MBE-grown sandwiches, extending beyond prior ~10 nm films, but the data do not uniquely exclude non-topological alternatives.

read the letter

The main point is that this group grew magnetic TI sandwich structures up to 106 nm thick and observed transport features they associate with the axion insulator once the middle undoped layer exceeds roughly 3 nm. That thickness is genuinely new relative to the ~10 nm films in the cited earlier work, and it moves the system away from the regime where top and bottom surfaces are strongly coupled. The growth and thickness series look like solid experimental work for mapping how the behavior evolves with the middle layer. They show the high-resistance state emerging in a controlled way, which is useful data even if the interpretation is still open. The soft spot is exactly the one flagged in the stress-test note. The central claim rests on transport (resistance and Hall) being diagnostic of the gapped surfaces plus axion term, yet at 100 nm scale other possibilities such as residual bulk conduction, domain walls, or interface magnetism could produce similar signatures without any topological magnetoelectric response. The abstract does not describe a direct probe of that response or explicit tests that would rule out the alternatives, so the identification stays interpretive. This is for experimentalists working on magnetic topological materials who want thicker platforms for magnetoelectric studies. A reader focused on sample growth and basic transport trends will find usable details. The thickness result is concrete enough that the paper deserves a serious referee, even though the topological assignment will need more scrutiny on alternative mechanisms. I would send it to review rather than desk reject.

Referee Report

1 major / 1 minor

Summary. The manuscript reports MBE growth of magnetic topological insulator sandwich heterostructures and claims that an axion insulator state persists in ~106 nm thick (3D) samples, with the state emerging once the middle undoped TI layer exceeds ~3 nm thickness, as indicated by transport measurements of resistance and Hall response.

Significance. If the transport signatures can be shown to uniquely identify the axion phase, the result would establish that axion insulation survives in the thick-film limit where top-bottom surface coupling is negligible, supplying a platform for magnetoelectric response studies and higher-order topological phases. The controlled variation of the middle-layer thickness via MBE is a clear experimental strength.

major comments (1)

[Abstract] Abstract: the central claim that transport data establish the axion insulator state (rather than bulk conduction, domain-wall conduction, or interface magnetism) is load-bearing, yet the text supplies no explicit exclusion criteria, control samples, or direct magnetoelectric probe to convert the observed high resistance and Hall features into a topological identification, especially once the middle layer is >3 nm and surface coupling is weak.

minor comments (1)

[Abstract] The abstract uses both '~106 nm' and 'hundred-nanometer-thick'; a single consistent phrasing would improve clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback. We address the major comment below.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that transport data establish the axion insulator state (rather than bulk conduction, domain-wall conduction, or interface magnetism) is load-bearing, yet the text supplies no explicit exclusion criteria, control samples, or direct magnetoelectric probe to convert the observed high resistance and Hall features into a topological identification, especially once the middle layer is >3 nm and surface coupling is weak.

Authors: We agree that transport signatures alone require explicit justification to distinguish the axion insulator from alternatives, especially in the decoupled thick-film limit. Our key control is the systematic MBE variation of middle-layer thickness: the high-resistance state with the reported Hall features emerges sharply only above ~3 nm, while thinner middle layers exhibit different transport consistent with surface coupling. This dependence excludes uniform bulk conduction, which would be insensitive to middle-layer thickness. Domain-wall contributions are suppressed by the uniform MBE growth conditions, and interface magnetism is fixed by the doped-layer design. We lack a direct magnetoelectric probe in the present study. We will revise the abstract to note the thickness-dependent identification and add explicit discussion of alternative-exclusion arguments in the main text. revision: yes

Circularity Check

0 steps flagged

No circularity; experimental observation without derivation or fitting chain

full rationale

This is a purely experimental report on MBE-grown heterostructures and transport measurements. No equations, ansatzes, parameter fits, predictions, or self-citation load-bearing steps appear in the provided text. The central claim rests on interpreting resistance/Hall data as evidence for the axion insulator phase in ~106 nm samples, but this interpretive step is not a mathematical reduction to inputs by construction. The paper is self-contained as a direct observation and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Experimental observation paper. No free parameters or new entities are introduced. The claim rests on the domain assumption that transport data can be unambiguously mapped to the axion insulator phase.

axioms (1)

domain assumption Electrical transport measurements can distinguish the axion insulator state from competing magnetic or interface phases
The abstract converts transport results directly into the claim that the axion state emerges above ~3 nm middle-layer thickness.

pith-pipeline@v0.9.0 · 5800 in / 1198 out tokens · 24695 ms · 2026-05-24T08:39:37.334128+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

the axion insulator state persists in a 3D sample with a thickness of ~106 nm... zero Hall conductance plateau... side surface gap δ
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

axion term θe²E·B/2πh... higher-order TI phase

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

15 extracted references · 15 canonical work pages

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1 Axion Insulator State in Hundred-Nanometer-Thick Magnetic Topological Insulator Sandwich Heterostructures Deyi Zhuo1,4, Zi-Jie Yan1,4, Zi-Ting Sun2,4, Ling-Jie Zhou1, Yi-Fan Zhao1, Ruoxi Zhang1, Ruobing Mei1, Hemian Yi1, Ke Wang3, Moses H. W. Chan1, Chao-Xing Liu1, K. T. Law2, and Cui-Zu Chang1 1 Department of Physics, The Pennsylvania State University,...

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Samarth, N., Chan, M. H. W., Liu, C. X. & Cha ng, C. Z. Tuning the Chern number in quantum anomalous Hall insulators. Nature 588, 419-423 (2020). 22 Zhao, Y .-F., Zhang, R., Zhou, L.-J., Mei, R., Yan, Z.-J., Chan, M. H. W., Liu, C.-X. & Chang, C.-Z. Zero Magnetic Field Plateau Phase Transition in Highe r Chern Number Quantum Anomalous Hall Insulators. Phy...

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X., Chan, M

Liu, C. X., Chan, M. H. W. & Moodera, J. S. High-Precision Realization of Robust Quantum Anomalous Hall State in a Hard Ferromagnetic Topological Insulator. Nat. Mater. 14, 473- 477 (2015). 25 Jiang, J., Xiao, D., Wang, F., Shin, J. H., Andreoli, D., Zhang, J. X., Xiao, R., Zhao, Y . F.,

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Chang, C. Z. Concurrence of quantum anomalous Hall and topological Hall effects in magnetic topological insulator sandwich heterostructures. Nat. Mater. 19, 732-737 (2020). 26 Wu, X., Xiao, D., Chen, C. Z., Sun, J., Zhang, L., Chan, M. H. W., Samarth, N., Xie, X. C.,

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Lin, X. & Chang, C. Z. Scaling behavior of the quantum phase transi tion from a quantum- anomalous-Hall insulator to an axion insulator. Nat. Commun. 11, 4532 (2020). 27 Shahar, D., Tsui, D. C., Shayegan, M., Bhatt, R. N. & Cunningham, J. E. Universal Conductivity at the Quantum Hall Liquid to Insulator Transition. Phys. Rev. Lett. 74, 4511- 4514 (1995). ...

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Murata, K., Tang, J. S., Wang, Y ., He, L., Lee, T. K., Lee, W. L. & Wang, K. L. Scale - Invariant Quantum Anomalous Hall Effect in Magnetic Topological Insulators beyond the Two-Dimensional Limit. Phys. Rev. Lett. 113, 137201 (2014). 29 Checkelsky, J. G., Yoshimi, R., Tsukazaki, A., Takahashi, K. S., Kozuka, Y ., Falson, J.,

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& Tokura, Y

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). 30 Mogi, M., Yoshimi, R., Tsukazaki, A., Yasuda, K., Kozuka, Y ., Takahashi, K. S., Kawasaki, M. & Tokura, Y . Magnetic Modulation Doping in Topologica l Insulators toward Higher - Temperat...

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Liu, C., Shi, J., Han, W., Chan, M. H. W., Samarth, N. & Chang, C. -Z. Observation of Interfacial Antiferromagnetic Coupling between Magnetic Topological Insulator and Antiferromagnetic Insulator. Nano Lett. 19, 2945-2952 (2019). 35 Qi, X. L., Li, R. D., Zang, J. D. & Zhang, S. C. Inducing a Magnetic Monopole with Topological Surface States. Science 323, ...

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[1] [1]

1 Axion Insulator State in Hundred-Nanometer-Thick Magnetic Topological Insulator Sandwich Heterostructures Deyi Zhuo1,4, Zi-Jie Yan1,4, Zi-Ting Sun2,4, Ling-Jie Zhou1, Yi-Fan Zhao1, Ruoxi Zhang1, Ruobing Mei1, Hemian Yi1, Ke Wang3, Moses H. W. Chan1, Chao-Xing Liu1, K. T. Law2, and Cui-Zu Chang1 1 Department of Physics, The Pennsylvania State University,...

work page 2023

[2] [2]

Chan, M. H. W., Samarth, N. & Chang, C. Z. Realization of the Axion Insulator State in Quantum Anomalous Hall Sandwich Heterostructures. Phys. Rev. Lett. 120, 056801 (2018). 6 Mogi, M., Kawamura, M., Tsukazaki, A., Yoshimi, R., Takahashi, K. S., Kawasaki, M. &

work page 2018

[3] [3]

Tailoring Tricolor Structure of Magnetic Topological Insulator for Robust Axion Insulator

Tokura, Y . Tailoring Tricolor Structure of Magnetic Topological Insulator for Robust Axion Insulator. Sci. Adv. 3, eaao1669 (2017). 7 Liu, C., Wang, Y . C., Li, H., Wu, Y ., Li, Y . X., Li, J. H., He, K., Xu, Y ., Zhang, J. S. & Wang, Y . Y . Robust axion insulator and Chern insulator phases in a two -dimensional antiferromagnetic topological insulator. ...

work page 2017

[4] [4]

& Molenkamp, L

Gould, C. & Molenkamp, L. W. Scaling of the Quantum Anomalous Hall Effect as an Indicator of Axion Electrodynamics. Phys. Rev. Lett. 118, 246801 (2017). 9 Fijalkowski, K. M., Liu, N., Hartl, M., Winnerlein, M., Mandal, P., Coschizza, A., Fothergill, A., Grauer, S., Schreyeck, S., Brunner, K., Greiter, M., Thomale, R., Gould, C. & 22

work page 2017

[5] [5]

Molenkamp, L. W. Any axion insulator must be a bulk three -dimensional topologic al insulator. Phys. Rev. B 103, 235111 (2021). 10 Wilczek, F. Two Applications of Axion Electrodynamics. Phys. Rev. Lett. 58, 1799 -1802 (1987). 11 Peccei, R. D. & Quinn, H. R. CPConservation in the Presence of Pseudoparticles. Phys. Rev. Lett. 38, 1440-1443 (1977). 12 Nomura...

work page 2021

[6] [6]

Higher-order topological insulators

Neupert, T. Higher-order topological insulators. Sci. Adv. 4, eaat0346 (2018). 15 Zhang, R. X., Wu, F. C. & Das Sarma, S. Mobius Insulator and Higher -Order Topology in MnBi2nTe3n+1. Phys. Rev. Lett. 124, 136407 (2020). 16 Varnava, N. & Vanderbilt, D. Surfaces of Axion Insulators. Phys. Rev. B 98, 245117 (2018). 17 Zhang, Y ., He, K., Chang, C. Z., Song, ...

work page 2018

[7] [7]

C., He, K., Ma, X

Zhang, S. C., He, K., Ma, X. C., Xue, Q. K. & Wang, Y . Y . O bservation of the Zero Hall Plateau in a Quantum Anomalous Hall Insulator. Phys. Rev. Lett. 115, 126801 (2015). 21 Zhao, Y . F., Zhang, R., Mei, R., Zhou, L. J., Yi, H., Zhang, Y . Q., Yu, J., Xiao, R., Wang, K.,

work page 2015

[8] [8]

Samarth, N., Chan, M. H. W., Liu, C. X. & Cha ng, C. Z. Tuning the Chern number in quantum anomalous Hall insulators. Nature 588, 419-423 (2020). 22 Zhao, Y .-F., Zhang, R., Zhou, L.-J., Mei, R., Yan, Z.-J., Chan, M. H. W., Liu, C.-X. & Chang, C.-Z. Zero Magnetic Field Plateau Phase Transition in Highe r Chern Number Quantum Anomalous Hall Insulators. Phy...

work page 2020

[9] [9]

L., Ji, Z

Wei, P., Wang, L. L., Ji, Z. Q., Feng, Y ., Ji, S. H., Chen, X., Jia, J. F., Dai, X., Fang, Z., Zhang, S. C., He, K., Wang, Y . Y ., Lu, L., Ma, X. C. & Xue, Q. K. Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator. Science 340, 167-170 (2013). 24 Chang, C. Z., Zhao, W. W., Kim, D. Y ., Zhang, H. J., Assaf, B...

work page 2013

[10] [10]

X., Chan, M

Liu, C. X., Chan, M. H. W. & Moodera, J. S. High-Precision Realization of Robust Quantum Anomalous Hall State in a Hard Ferromagnetic Topological Insulator. Nat. Mater. 14, 473- 477 (2015). 25 Jiang, J., Xiao, D., Wang, F., Shin, J. H., Andreoli, D., Zhang, J. X., Xiao, R., Zhao, Y . F.,

work page 2015

[11] [11]

Chang, C. Z. Concurrence of quantum anomalous Hall and topological Hall effects in magnetic topological insulator sandwich heterostructures. Nat. Mater. 19, 732-737 (2020). 26 Wu, X., Xiao, D., Chen, C. Z., Sun, J., Zhang, L., Chan, M. H. W., Samarth, N., Xie, X. C.,

work page 2020

[12] [12]

& Chang, C

Lin, X. & Chang, C. Z. Scaling behavior of the quantum phase transi tion from a quantum- anomalous-Hall insulator to an axion insulator. Nat. Commun. 11, 4532 (2020). 27 Shahar, D., Tsui, D. C., Shayegan, M., Bhatt, R. N. & Cunningham, J. E. Universal Conductivity at the Quantum Hall Liquid to Insulator Transition. Phys. Rev. Lett. 74, 4511- 4514 (1995). ...

work page 2020

[13] [13]

S., Wang, Y ., He, L., Lee, T

Murata, K., Tang, J. S., Wang, Y ., He, L., Lee, T. K., Lee, W. L. & Wang, K. L. Scale - Invariant Quantum Anomalous Hall Effect in Magnetic Topological Insulators beyond the Two-Dimensional Limit. Phys. Rev. Lett. 113, 137201 (2014). 29 Checkelsky, J. G., Yoshimi, R., Tsukazaki, A., Takahashi, K. S., Kozuka, Y ., Falson, J.,

work page 2014

[14] [14]

& Tokura, Y

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). 30 Mogi, M., Yoshimi, R., Tsukazaki, A., Yasuda, K., Kozuka, Y ., Takahashi, K. S., Kawasaki, M. & Tokura, Y . Magnetic Modulation Doping in Topologica l Insulators toward Higher - Temperat...

work page 2014

[15] [15]

Liu, C., Shi, J., Han, W., Chan, M. H. W., Samarth, N. & Chang, C. -Z. Observation of Interfacial Antiferromagnetic Coupling between Magnetic Topological Insulator and Antiferromagnetic Insulator. Nano Lett. 19, 2945-2952 (2019). 35 Qi, X. L., Li, R. D., Zang, J. D. & Zhang, S. C. Inducing a Magnetic Monopole with Topological Surface States. Science 323, ...

work page 2019