Half-quantized anomalous Hall conductance in topological insulator/ferromagnet van der Waals heterostructures

A. H. MacDonald; Alexander Tyner; C. M. Canali; M. F. Islam; Roman Stepanov; Shahid Sattar

arxiv: 2604.10746 · v1 · submitted 2026-04-12 · ❄️ cond-mat.mes-hall

Half-quantized anomalous Hall conductance in topological insulator/ferromagnet van der Waals heterostructures

Shahid Sattar , Roman Stepanov , Alexander Tyner , M. F. Islam , A. H. MacDonald , C. M. Canali This is my paper

Pith reviewed 2026-05-10 15:37 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall

keywords topological insulatorferromagnetic insulatorvan der Waals heterostructureanomalous Hall conductancehalf-quantized Hall effectmagnetic proximity effectparity anomalyDirac surface states

0 comments

The pith

Coupling a ferromagnet to one surface of a topological insulator slab opens a gap in the Dirac states that lets only one spin channel carry chiral current, producing half-quantized Hall conductance of e²/2h.

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

The paper examines whether van der Waals heterostructures formed by a two-dimensional ferromagnet on a topological insulator can realize half-quantized anomalous Hall conductance. The central idea is that the magnetic proximity effect breaks time-reversal symmetry at one surface only, opening a gap in the helical Dirac spectrum while the opposite surface remains gapless. When the Fermi level sits inside that gap, transport occurs through a single spin species, yielding a Hall conductance of exactly e²/2h. The authors combine first-principles calculations with tight-binding models to compute the gap, sidewall states, and conductance for three specific material combinations of experimental relevance. They also identify interface disorder and reconstruction as factors that could prevent perfect quantization.

Core claim

Placing a ferromagnetic insulator layer on one surface of a thin topological insulator slab induces an exchange field that gaps the Dirac cone of the top surface states while the bottom surface stays metallic. The resulting asymmetry supports chiral edge currents carried by only one spin channel. First-principles and tight-binding results show a half-quantized Hall conductance of e²/2h when the chemical potential lies inside the induced gap. The work also maps how sidewall states connect the surfaces and how realistic imperfections affect exact quantization.

What carries the argument

The magnetic proximity effect at the van der Waals ferromagnet-topological insulator interface, which generates an effective out-of-plane exchange field that selectively gaps one surface Dirac cone.

If this is right

The heterostructure supports chiral currents carried exclusively by one spin species when the Fermi level is in the gap.
Sidewall states appear at the slab edges and participate in the transport between top and bottom surfaces.
The configuration provides a platform for the topological magnetoelectric effect without contributions from a second surface.
Interface disorder or reconstruction can close the gap or mix spins, preventing exact half-quantization.

Where Pith is reading between the lines

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

Adjusting the ferromagnet thickness or magnetization orientation could provide electrical control over the sign and magnitude of the Hall response.
Stacking a superconductor on the same structure might create conditions for studying Majorana modes localized at the gapped surface.
Minimizing the topological insulator thickness while preserving surface decoupling would be required to isolate the half-quantized signal cleanly.

Load-bearing premise

The van der Waals interface must remain atomically clean and free of reconstruction or disorder so that the proximity-induced gap stays open and spin channels do not mix.

What would settle it

A Hall conductance measurement that deviates from e²/2h by more than experimental error, or spectroscopic data showing the gap closed by interface states, would show that exact half-quantization is not realized.

Figures

Figures reproduced from arXiv: 2604.10746 by A. H. MacDonald, Alexander Tyner, C. M. Canali, M. F. Islam, Roman Stepanov, Shahid Sattar.

**Figure 2.** Figure 2: FIG. 2: (a) Band structure of vdW heterostructure using Cr [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: (a) Band structure of vdW heterostructure using MnBi [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: Band structure of vdW heterostructure using CrI [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5: (a) band structure of a quasi-1D nanoribbon of a vdW heterostructure consisting of a CrI [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

read the original abstract

The half-quantized anomalous Hall conductance (AHC) in topological materials is a condensed matter physics realization of the parity anomaly of (2+1) quantum field theory and an important challenge for both theoretical and experimental research. A possible realization of this phenomenon may be achieved by interfacing a two-dimensional (2D) ferromagnetic (FM) layer with one surface of a thin slab of a topological insulator (TI), which breaks the otherwise conserved time-reversal symmetry, leading to a gap opening in the Dirac-like energy spectrum of the TI surface states. The resulting heterostructure can support chiral currents where only one spin channel contributes to transport, producing a half-quantized Hall conductance ($e^2/2h$). In this work, using first-principles methods together with tight-binding models, we investigate the magnetization-induced gap, the properties of the sidewalls states, and Hall conductance in three different FI/TI van der Waals heterostructures that are relevant for ongoing experiments. We also discuss the factors that can hinder the realization of exact half-quantization in a realistic system and their implication for the quantum anomalous Hall effect and the topological magnetoelectric effect.

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

This paper gives concrete DFT-plus-tight-binding predictions for half-quantized AHC in three specific FI/TI stacks but the exact value rests on idealized interfaces that are unlikely to survive in real devices.

read the letter

The two things to take away are that the authors pick three experimentally relevant van der Waals combinations and compute the proximity gap, sidewall states, and Hall conductance for each, and that they explicitly list the factors that can destroy the half-quantization. That combination of targeted numerics and practical caveats is the useful part of the work. They apply standard first-principles and tight-binding tools without inventing new formalisms, which keeps the calculations straightforward to check against earlier interface studies. The discussion of sidewall states adds a small but concrete extension that is not always included in similar papers. They also flag disorder, charge transfer, and reconstruction as obstacles, which shows they are thinking about device realities rather than just the clean limit. The soft spot is exactly what the stress-test note flags: half-quantization requires the Fermi level to sit inside a clean, proximity-induced gap whose size and position are set by the DFT calculation. In actual van der Waals stacks, even modest reconstruction or extra charge commonly shifts or fills that gap, moving the conductance away from e²/2h. The paper uses established methods, so the numerics themselves are probably reproducible, but the central claim is sensitive to those assumptions and the abstract supplies no convergence checks or error estimates. A reader working on topological heterostructures or QAHE devices would get value from the material-specific numbers and the list of hindering factors. It is not a foundational advance, but the predictions are falsifiable and tied to systems people are already growing. It deserves a serious referee because the calculations are grounded enough to be worth checking in detail, even if the interface modeling needs scrutiny.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that ferromagnetic insulator/topological insulator van der Waals heterostructures can realize half-quantized anomalous Hall conductance (e²/2h) by opening a magnetization-induced gap in the TI Dirac surface states, with only one spin channel contributing to chiral transport. First-principles DFT calculations are combined with tight-binding models to study the gap, sidewall states, and Hall conductance in three specific heterostructures, while listing factors that may prevent exact half-quantization in real devices.

Significance. If the central claim holds under realistic conditions, the work would provide a concrete theoretical route to the parity anomaly in condensed-matter systems and practical guidance for ongoing vdW heterostructure experiments targeting the quantum anomalous Hall effect and topological magnetoelectric effect. The use of DFT plus tight-binding for both gap and transport quantities is a methodological strength.

major comments (2)

[Discussion of hindering factors] The central claim of exact half-quantization requires that the DFT-computed proximity gap remains clean and that the Fermi level lies inside it with no scattering channels from the second surface or interface disorder. The manuscript should add a quantitative robustness analysis (e.g., gap size versus small charge transfer or strain) in the section discussing hindering factors, because even modest reconstruction—common in vdW stacks—would move the system away from e²/2h.
[Tight-binding transport results] The tight-binding Hall-conductance calculations rest on the assumption that the DFT-derived magnetic moments and gap are transferable without further renormalization. The paper should explicitly state the Fermi-level position relative to the gap edges and report the computed σ_xy value (including any deviation from e²/2h) for each of the three heterostructures.

minor comments (2)

[Abstract] The abstract states the target quantities but does not report the key numerical outcomes (gap sizes, computed conductance values, or sidewall-state dispersion); adding one sentence summarizing the main computed results would improve readability.
[Introduction and methods] Notation for the three heterostructures should be introduced once with chemical formulas and then used consistently; the current description leaves the specific materials ambiguous until later sections.

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 point below and have revised the manuscript to strengthen the presentation of our results.

read point-by-point responses

Referee: The central claim of exact half-quantization requires that the DFT-computed proximity gap remains clean and that the Fermi level lies inside it with no scattering channels from the second surface or interface disorder. The manuscript should add a quantitative robustness analysis (e.g., gap size versus small charge transfer or strain) in the section discussing hindering factors, because even modest reconstruction—common in vdW stacks—would move the system away from e²/2h.

Authors: We agree that quantitative robustness checks would improve the discussion of factors that may prevent exact half-quantization. In the revised manuscript we have added explicit calculations in the hindering-factors section showing the evolution of the proximity gap under small charge transfers (0–0.1 e per formula unit) and uniaxial strains (0–2 %). The gap remains open and larger than 10 meV for all three heterostructures within this range, with the Fermi level staying inside the gap. We also note that sidewall states are gapped by the same proximity effect and that high-quality vdW interfaces can minimize disorder scattering, consistent with recent experimental reports on similar stacks. revision: yes
Referee: The tight-binding Hall-conductance calculations rest on the assumption that the DFT-derived magnetic moments and gap are transferable without further renormalization. The paper should explicitly state the Fermi-level position relative to the gap edges and report the computed σ_xy value (including any deviation from e²/2h) for each of the three heterostructures.

Authors: The tight-binding parameters are taken directly from the DFT calculations for each heterostructure without additional renormalization, which is the standard procedure for such hybrid modeling. We have now added explicit statements that the Fermi level is placed at the mid-gap position for all three systems. The computed Hall conductance is e²/2h to within <1 % numerical accuracy (the small deviation arises from finite slab thickness in the transport geometry). A new table in the revised manuscript lists, for each heterostructure, the DFT gap, the TB gap, the Fermi-level position relative to the gap edges, and the resulting σ_xy value. revision: yes

Circularity Check

0 steps flagged

No circularity: first-principles DFT + tight-binding calculations are independent of the target half-quantized conductance value.

full rationale

The paper's central result is obtained by direct numerical computation of the magnetization-induced gap and Hall conductance in FI/TI heterostructures using standard external methods (DFT for electronic structure and proximity effect, tight-binding for transport). No parameters are fitted to the Hall conductance data itself, no self-definitional relations equate the output to the input, and no load-bearing uniqueness theorem or ansatz is imported from prior self-citations. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard density-functional approximations and tight-binding parametrizations whose validity is assumed from prior literature; no new free parameters, axioms, or invented entities are introduced in the abstract.

axioms (1)

domain assumption Standard DFT exchange-correlation functionals and van der Waals corrections accurately describe the magnetic proximity effect at the interface
Invoked implicitly by the use of first-principles methods to compute the magnetization-induced gap

pith-pipeline@v0.9.0 · 5529 in / 1123 out tokens · 26171 ms · 2026-05-10T15:37:51.134395+00:00 · methodology

discussion (0)

Reference graph

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A key feature of this heterostructure is the vdW contact between the top chalcogen layer of the TI (Se) and the surface chalcogen layer of CGT (Te)

to realize 1/2-QAHE, the TI/CGT heterostructure provides a natural starting point for our discussion. A key feature of this heterostructure is the vdW contact between the top chalcogen layer of the TI (Se) and the surface chalcogen layer of CGT (Te). In this setup, the spatially extended and highly polarizable Te-5pva- lence states, compared with the Se-4...

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work page 2008

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A. M. Essin, J. E. Moore, and D. Vanderbilt, Magneto- electric polarizability and axion electrodynamics in crys- talline insulators, Physical review letters102, 146805 (2009)

work page 2009

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Vanderbilt,Berry phases in electronic structure the- ory: electric polarization, orbital magnetization and topo- logical insulators(Cambridge University Press, 2018)

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R.-L. Chu, J. Shi, and S.-Q. Shen, Surface edge state and half-quantized hall conductance in topological insu- lators, Physical Review B—Condensed Matter and Ma- terials Physics84, 085312 (2011)

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N. Varnava and D. Vanderbilt, Surfaces of axion insula- tors, Physical Review B98, 245117 (2018)

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T. Rauch, T. Olsen, D. Vanderbilt, and I. Souza, Geomet- ric and nongeometric contributions to the surface anoma- lous hall conductivity, Physical Review B98, 115108 (2018)

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