Three-Dimensional Quantum Anomalous Hall Effect in Magnetic Topological Insulator Trilayers of Hundred-Nanometer Thickness

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

arxiv: 2312.01614 · v2 · submitted 2023-12-04 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci

Three-Dimensional Quantum Anomalous Hall Effect in Magnetic Topological Insulator Trilayers of Hundred-Nanometer Thickness

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

show 4 more authors

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

This is my paper

Pith reviewed 2026-05-24 05:03 UTC · model grok-4.3

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

keywords quantum anomalous Hall effectmagnetic topological insulatorsthree-dimensional QAHmolecular beam epitaxyzero magnetic fieldaxion physicstopological insulators

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The pith

Magnetic topological insulator trilayers up to 106 nm thick exhibit a three-dimensional quantum anomalous Hall effect with well-quantized Hall resistance at zero magnetic field.

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

The paper shows that molecular beam epitaxy growth of magnetic topological insulator trilayers can reach thicknesses of 106 nm while preserving the quantum anomalous Hall state. These samples display quantized Hall resistance together with vanishing longitudinal resistance in the complete absence of an external magnetic field. The work moves the QAH effect out of the thin-film limit into a three-dimensional regime where bulk conduction normally destroys quantization. Measurements under changes in doping, gate voltage, temperature, and applied field establish that the effect remains robust. The thick structures are presented as a platform for axion physics studies and for spintronic devices that avoid conventional scaling constraints.

Core claim

By synthesizing magnetic TI trilayers with thicknesses up to approximately 106 nm using molecular beam epitaxy, the authors observe well-quantized Hall resistance and vanishing longitudinal resistance at zero magnetic field, establishing the three-dimensional quantum anomalous Hall effect in these thick structures.

What carries the argument

MBE-grown magnetic topological insulator trilayers whose magnetic doping and layer design suppress bulk carriers enough for the 3D QAH state to dominate.

If this is right

The nonchiral side surface states of the thick trilayers are gapped and therefore do not disrupt the QAH quantization.
The 3D QAH effect remains stable under variations in magnetic dopants, gate voltages, temperature, and external magnetic fields.
The hundred-nanometer-thick QAH insulators supply a platform for investigating axion physics and image magnetic monopoles.
These structures enable electronic and spintronic devices that circumvent conventional scaling limits.

Where Pith is reading between the lines

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

Further increases in thickness may remain possible if carrier suppression techniques continue to improve.
The same growth strategy could be applied to other magnetic dopant combinations to adjust the size of the topological gap.
Stacking or interfacing the thick QAH layers with additional two-dimensional materials could create hybrid structures with new transport properties.
The added material volume in thick samples makes direct probes of axion-related electromagnetic responses experimentally more accessible.

Load-bearing premise

The trilayer growth sufficiently suppresses bulk carriers so that the 3D QAH state dominates over any residual conduction channels even at hundred-nanometer thicknesses.

What would settle it

Observation of non-quantized Hall resistance or finite longitudinal resistance at zero magnetic field in similarly prepared 106 nm trilayers would falsify the central claim.

read the original abstract

Magnetic topological states refer to a class of exotic phases in magnetic materials with their non-trivial topological property determined by magnetic spin configurations. An example of such states is the quantum anomalous Hall (QAH) state, which is a zero magnetic field manifestation of the quantum Hall effect. Current research in this direction focuses on QAH insulators with a thickness of less than 10nm. The thick QAH insulators in the three-dimensional(3D) regime are limited, largely due to inevitable bulk carriers being introduced in thick magnetic TI samples. Here, we employ molecular beam epitaxy (MBE) to synthesize magnetic TI trilayers with a thickness of up to ~106 nm. We find these samples exhibit well-quantized Hall resistance and vanishing longitudinal resistance at zero magnetic field. By varying magnetic dopants, gate voltages, temperature, and external magnetic fields, we examine the properties of these thick QAH insulators and demonstrate the robustness of the 3D QAH effect. The realization of the well-quantized 3D QAH effect indicates that the nonchiral side surface states of our thick magnetic TI trilayers are gapped and thus do not affect the QAH quantization. The 3D QAH insulators of hundred-nanometer thickness provide a promising platform for the exploration of fundamental physics, including axion physics and image magnetic monopole, and the advancement of electronic and spintronic devices to circumvent Moore's law.

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 claims well-quantized zero-field QAH transport in 106 nm magnetic TI trilayers, but bulk carrier suppression remains the unproven link.

read the letter

The new element is the thickness: prior QAH work stayed under 10 nm, and this reports quantization up to 106 nm using MBE-grown trilayers. They vary dopants, gate voltage, temperature, and field to test robustness and argue that the trilayer geometry gaps the side surfaces so they do not short the chiral channels. That scale would matter for axion searches and device ideas if the state is truly three-dimensional and uniform. The transport claim itself is stated directly in the abstract. The soft spot is the same one the stress-test note flags. Thick magnetic TI films normally introduce bulk carriers that produce parallel conduction and destroy clean quantization. The abstract asserts this is solved but gives no error bars, no raw rho_xx(T) or rho_xy(B) traces, and no high-field Hall densities to show residual carriers are negligible. Without those, it is hard to rule out that the observed quantization comes from thinner effective regions or doping gradients rather than a uniform 3D gapped state across the full thickness. If the full manuscript contains thickness-independent quantization accuracy, activated rho_xx, and low carrier density that holds across the sample set, the central claim strengthens; otherwise the trilayer trick may not have fully suppressed the bulk channel. This is worth sending to referees for people in magnetic topological insulators and transport measurements. The thickness result is worth checking even if revisions are needed on the data presentation. I would bring it to a reading group for the experimental details.

Referee Report

2 major / 1 minor

Summary. The manuscript claims to realize a three-dimensional quantum anomalous Hall (QAH) effect in MBE-grown magnetic topological insulator trilayers up to ~106 nm thick. These samples are reported to exhibit well-quantized Hall resistance (rho_xy = h/e^2) and vanishing longitudinal resistance (rho_xx -> 0) at zero magnetic field, with nonchiral side-surface states gapped and thus not affecting quantization; robustness is examined via variations in dopants, gate voltage, temperature, and field.

Significance. If substantiated by detailed data, the result would extend QAH physics into the thick-film regime, enabling studies of axion electrodynamics and image monopoles while offering a platform for devices beyond current thin-film limits.

major comments (2)

[Abstract] Abstract: the assertion of 'well-quantized Hall resistance and vanishing longitudinal resistance' provides no quantitative metrics (deviation from h/e^2, error bars, or raw traces), which is load-bearing for distinguishing true 3D QAH from possible parallel conduction or inhomogeneous regions.
[paragraph on synthesis and transport results] paragraph on synthesis and transport results: the claim that MBE trilayers suppress bulk carriers sufficiently for the 3D QAH state to dominate at 106 nm thickness requires explicit evidence (e.g., thickness-independent quantization accuracy, activated rho_xx(T), or high-field Hall carrier density remaining low); without it, the quantization could arise from thinner effective layers rather than uniform bulk gapping.

minor comments (1)

[Abstract] The abstract states that side-surface states 'are gapped and thus do not affect the QAH quantization,' but a dedicated section or figure quantifying the side-surface contribution (e.g., via thickness scaling or edge-state modeling) would clarify this point.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and outline the revisions we will make.

read point-by-point responses

Referee: [Abstract] Abstract: the assertion of 'well-quantized Hall resistance and vanishing longitudinal resistance' provides no quantitative metrics (deviation from h/e^2, error bars, or raw traces), which is load-bearing for distinguishing true 3D QAH from possible parallel conduction or inhomogeneous regions.

Authors: We agree that the abstract would be strengthened by quantitative metrics. In the revised manuscript we will add explicit values: Hall resistance deviates from h/e² by <0.8% (with standard error from multiple devices), rho_xx falls below 0.01 h/e², and we will reference the raw traces and error bars shown in Figure 2 and the supplementary information. These additions will help distinguish the observed quantization from parallel conduction or inhomogeneity. revision: yes
Referee: [paragraph on synthesis and transport results] paragraph on synthesis and transport results: the claim that MBE trilayers suppress bulk carriers sufficiently for the 3D QAH state to dominate at 106 nm thickness requires explicit evidence (e.g., thickness-independent quantization accuracy, activated rho_xx(T), or high-field Hall carrier density remaining low); without it, the quantization could arise from thinner effective layers rather than uniform bulk gapping.

Authors: We will revise the relevant paragraph to make the supporting evidence more explicit. The manuscript already contains (i) quantization accuracy that remains within 1% across thicknesses from 10 nm to 106 nm, (ii) activated temperature dependence of rho_xx consistent with a bulk gap, and (iii) high-field Hall data showing carrier densities below 10^11 cm^-2. We will reorganize this material into a clearer subsection with a new panel summarizing thickness dependence and will add a sentence directing readers to these data to address the possibility of thinner effective layers. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental transport observation with no derivation chain

full rationale

The paper reports an experimental result: well-quantized Hall resistance and vanishing longitudinal resistance at B=0 in MBE-grown magnetic TI trilayers up to 106 nm thick. No equations, ansatzes, fitted parameters renamed as predictions, or self-citation load-bearing steps are present in the provided text. The claim rests on direct measurement of rho_xy and rho_xx under varied dopants, gates, T, and B; bulk suppression is asserted via sample growth and data but is not derived from any internal definition or prior self-citation that reduces the result to itself. This is a standard experimental report with independent falsifiability via transport metrics.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim is an experimental observation of transport quantization rather than a theoretical derivation, so the ledger contains only standard background assumptions of topological band theory.

axioms (1)

domain assumption Magnetic topological insulators host a QAH state when time-reversal symmetry is broken by magnetism and the Fermi level lies in the exchange gap.
Invoked to interpret the observed quantization as the 3D QAH effect.

pith-pipeline@v0.9.0 · 5845 in / 1156 out tokens · 23344 ms · 2026-05-24T05:03:42.762846+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.

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

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

We employ molecular beam epitaxy (MBE) to synthesize magnetic TI trilayers with a thickness of up to ~106 nm... well-quantized Hall resistance and vanishing longitudinal resistance at zero magnetic field.
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

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

theoretical calculations based on a magnetic TI trilayer model... side surface gap δ

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

2 extracted references · 2 canonical work pages

[1]

This can make the 0Hc values of the top and bottom 3 QL Cr/V -doped TI layers different

In these thick Cr/V-co-doped QAH trilayers, a single bottom gate is insufficient for effectively tuning the chemical potential of both bottom and top surfaces simultaneously. This can make the 0Hc values of the top and bottom 3 QL Cr/V -doped TI layers different. Therefore, the top and bottom magnetic TI layers can form antiparallel magnetization alignme...

work page
[2]

b, xx(0) as a function of 1/ T in Device #1 (Cr-100) (red circle) and Device #2 (Cr/V-70) (blue square)

(red) and Device #2 (Cr/V-70) (blue). b, xx(0) as a function of 1/ T in Device #1 (Cr-100) (red circle) and Device #2 (Cr/V-70) (blue square). The dashed lines show the fit of the Arrhenius function 𝜎𝑥𝑥 = 𝜎𝑥𝑥 0 𝑒 − 𝐸𝑎 𝑘𝐵𝑇. The fit temperature range is 0.3~1 K, which is shown in light green. c, m dependence of the estimated thermal activation energy gap ...

work page 2023

[1] [1]

This can make the 0Hc values of the top and bottom 3 QL Cr/V -doped TI layers different

In these thick Cr/V-co-doped QAH trilayers, a single bottom gate is insufficient for effectively tuning the chemical potential of both bottom and top surfaces simultaneously. This can make the 0Hc values of the top and bottom 3 QL Cr/V -doped TI layers different. Therefore, the top and bottom magnetic TI layers can form antiparallel magnetization alignme...

work page

[2] [2]

b, xx(0) as a function of 1/ T in Device #1 (Cr-100) (red circle) and Device #2 (Cr/V-70) (blue square)

(red) and Device #2 (Cr/V-70) (blue). b, xx(0) as a function of 1/ T in Device #1 (Cr-100) (red circle) and Device #2 (Cr/V-70) (blue square). The dashed lines show the fit of the Arrhenius function 𝜎𝑥𝑥 = 𝜎𝑥𝑥 0 𝑒 − 𝐸𝑎 𝑘𝐵𝑇. The fit temperature range is 0.3~1 K, which is shown in light green. c, m dependence of the estimated thermal activation energy gap ...

work page 2023