Quantum Anomalous Hall Effect in $d^{10}$ Oxide Monolayers

Xudong Zhu; Yulei Han; Zeyu Li; Zhenhua Qiao

REVIEW 2 major objections 6 minor 70 references

Quantum Anomalous Hall Effect in $d^{10}$ Oxide Monolayers

T0 review · 2 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Oxygen 2p magnetism yields Chern number 4 in oxide monolayers

desk verdict A clean, internally consistent PBE prediction of O-2p-driven C=4 QAHE in deintercalated oxides; the physics is credible but the 7 meV gap and lack of functional cross-checks leave the central claim fragile. read the letter →

arxiv 2608.11855 v1 pith:XBCOY2ZK submitted 2026-08-12 cond-mat.mes-hall

Zeyu Li , Xudong Zhu , Yulei Han , Zhenhua Qiao This is my paper · ORCID

classification cond-mat.mes-hall

keywords quantumanomalousHalleffectChernnumberoxygen2pferromagnetismoxidemonolayersspin-orbitcouplingDiracpointscationdeintercalationfirst-principlescalculations

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

The paper predicts that monolayer oxides M2DO6 (M = Zn, Cd; D = Se, Te), obtained by removing alkali ions from known layered compounds, are ferromagnetic half-metals whose magnetism comes entirely from oxygen 2p holes, not from transition-metal d electrons. In these monolayers, spin-polarized Dirac points appear at two inequivalent momenta, and C3 rotational symmetry multiplies them into eight crossings per Brillouin zone. Spin-orbit coupling opens a small global gap at each crossing, and the eight massive Dirac points together produce a quantized anomalous Hall conductance of $4e^2/h$, a high-Chern-number quantum anomalous Hall state. The paper also shows that cation deintercalation turns more than twenty closed-shell oxides into O-2p ferromagnets, offering a general route from nonmagnetic oxides to magnetic topological materials.

What carries the argument

The mechanism is a symmetry-constrained filling of an E-type O-$2p$ doublet: in the nonmagnetic parent, the last two valence electrons occupy a twofold-degenerate representation at the Fermi level and, by Hund's rule, align their spins, producing an O-$2p$-driven ferromagnet without cation moments. The topological machinery is the set of eight spin-polarized Dirac points related by $C_3$ symmetry; an effective two-band $k\cdot p$ model expanded around each crossing shows that spin-orbit coupling adds a Dirac mass $d_z$, and each gapped Dirac point contributes a local Chern number $C_{\rm loc}\approx 1/2$. Summing the eight contributions gives the total Chern number $\mathcal{C}=4$.

What would settle it

A hybrid-functional or DFT+U calculation of monolayer Zn2TeO6 would settle the point: if the oxygen 2p ferromagnetic state is not the ground state, or if the spin-orbit gap closes or changes sign under the corrected functional, the predicted C=4 plateau would not survive. Experimentally, measuring the anomalous Hall conductance of an exfoliated monolayer and finding no plateau at $4e^{2}$/h in the gap would falsify the claim.

Watch

Extended reading notes

Core claim

The central claim is that monolayer M2DO6 realizes an intrinsic high-Chern-number quantum anomalous Hall phase with $\mathcal{C}=4$, driven by spontaneous ferromagnetism of half-filled O-$2p$ orbitals rather than partially filled $d$ or $f$ shells. Removing the intercalated alkali cations injects two holes per unit cell into the oxygen framework; because the metal cations keep closed-shell $d^{10}$ configurations, the holes reside on oxygen and spin-polarize into an easy-axis ferromagnetic state with a moment of about $2\,\mu_B$ per unit cell. In the spin-polarized band structure, two inequivalent Dirac crossings appear, at $K/K'$ and along $\Gamma$–$K$, and $C_3$ symmetry generates eight symmetry-related Dirac points. Spin-orbit coupling opens a global gap of about 7 meV in Zn2TeO6; each massive Dirac point carries a local Chern number of approximately 1/2, so the total Chern number is $\mathcal{C}=4$ and the anomalous Hall conductance is quantized at $4e^2/h$, with four chiral edge modes in a ribbon geometry.

Load-bearing premise

The prediction rests on the assumption that the standard density-functional approximation (PBE, without Hubbard U or self-interaction corrections) correctly describes the oxygen 2p holes and the ~7 meV spin-orbit gap; if self-interaction error artificially stabilizes the hole ferromagnetism, the Chern number 4 phase could change or disappear.

Editorial extensions

If this is right

Monolayer Zn2TeO6 should show a quantized anomalous Hall plateau of $4e^2/h$ inside its ~7 meV spin-orbit gap, with four chiral edge channels.
Applying ~2.5% tensile strain to Cd2TeO6 aligns the eight Dirac points in energy and turns the monolayer into a $\mathcal{C}=4$ high-Chern-number quantum anomalous Hall insulator.
Cation deintercalation is predicted to activate O-$2p$ ferromagnetism in more than twenty closed-shell oxides, including compounds with $d^0$, $d^{10}$, and main-group cations.
Several other deintercalated monolayers (Cd2SbO6, Cd2BiO6, Mg2SbO6, InO3) are predicted to be Chern insulators with Chern numbers 4, 3, 1, and 1, respectively.

Reading between the lines

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

If O-$2p$ ferromagnetism survives in real samples, the mechanism could widen the search for magnetic topological materials beyond transition-metal compounds, since oxygen-based frameworks are abundant and already synthesized as battery materials.
Because the predicted topological gap is only about 7 meV, confirming the phase experimentally will likely require high-quality exfoliated monolayers and measurement temperatures well below ~80 K; strain or dielectric screening may be needed to stabilize the gap.
A direct testable extension would be to measure the anomalous Hall conductivity as a function of gate voltage in a monolayer device; a plateau at $4e^2/h$ would confirm the half-Chern-number counting, while a different plateau would indicate that the eight Dirac points are not all aligned.
The same deintercalation logic could be applied computationally to other parent compounds with removable cations, such as lithium or potassium analogues, to search for O-$2p$ topological phases with larger gaps.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

The new thing here is real: O-2p hole ferromagnetism as a route to a high-Chern-number QAHE, with a concrete materials family (M2DO6 monolayers) and a plausible deintercalation route. I checked the reasoning from the nonmagnetic band structure to the Hund's-rule occupancy argument to the eight Dirac points and the C=4 result. That chain is internally consistent, and the Berry curvature plus edge-state calculation is the right way to support the Chern number. The k.p fit is used for explanation, not as the source of the topology, so I don't see a circularity problem. The strain tuning and the generalization table are useful extras, and the generalization to more than 20 deintercalatable oxides is at least a testable claim.

The soft spot is exactly where the reader's stress test lands: PBE is the only exchange-correlation functional, and the topologically relevant SOC gap is 7 meV. That is below typical PBE errors for O-2p levels, and PBE's self-interaction error is known to bias hole localization on oxygen. So the O-2p ferromagnetism and the Chern number could both change under hybrid or +U treatment. The authors cite the d0-oxide ferromagnetism literature, which itself is PBE-sensitive, so they know the territory; they just did not do the cross-check. For Cd2SbO6 and InO2 the gaps are larger (11 meV, 20 meV), so at least some members of the family might survive a more accurate functional, but the headline C=4 claim for M2DO6 rests on the 7 meV gap.

Minor points: the claim that M2DO6 monolayers are experimentally accessible is plausible but not demonstrated (exfoliation is mentioned, no exfoliation energy); and one reference list entry (Ref. 4) looks like the wrong venue name. Neither matters much.

Who is this for? People working on oxide magnetism and topological materials prediction. It deserves a serious referee, but the referee should demand PBE+U or hybrid calculations before publication, and ideally a clear statement that the C=4 phase may be functional-dependent. If the authors can show the phase survives even one hybrid calculation for Zn2TeO6, I would treat the prediction as solid. As is, it is a well-argued, interesting but unverified suggestion.

Recommendation: send to peer review, but with the functional question as the make-or-break issue. I would not cite the C=4 claim in my own work until that is settled, though I would cite the deintercalation strategy as a concept.

Referee Report

2 major / 6 minor

Summary. The manuscript proposes that monolayers M2DO6 (M=Zn,Cd; D=Se,Te), derived by deintercalating A cations from honeycomb layered oxides A2M2DO6, realize a quantum anomalous Hall effect driven by O-2p ferromagnetism. Using PBE-based DFT, phonon, and Wannier-interpolation calculations, the authors find a ferromagnetic half-metallic state with two holes in an O-2p E doublet, spin-polarized Dirac points at K/K' and along Γ–K, and, upon spin-orbit coupling, a global gap of about 7 meV with Berry curvature concentrated at the eight gapped Dirac points. Each gapped Dirac point contributes a local Chern number Cloc ≈ 0.5, yielding a quantized anomalous Hall conductance of 4e^2/h. Cd2TeO6 requires about 2.5% tensile strain to align the Dirac points and achieve C=4. The authors generalize the cation-deintercalation strategy to more than 20 oxides, reporting O-2p ferromagnetism and nonzero Chern numbers for several additional slabs including Cd2SbO6 (C=4), Mg2SbO6 (C=1), Cd2BiO6 (C=3), and InO2 (C=1).

Significance. If correct, the paper would establish a new route to the QAHE based on oxygen 2p rather than transition-metal d magnetism, and a high-Chern-number phase C=4 with multiple chiral edge modes. The proposed cation deintercalation strategy for activating O-2p ferromagnetism is an attractive design principle for oxide-based magnetic topology. The paper includes explicit first-principles evidence for phonon stability, magnetic ground-state competition, Berry curvature distributions, and edge-state spectra, and the central Chern number is computed by direct integration of the Wannier-interpolated Berry curvature rather than inferred from the fitted k·p model. The main fragility is that all results rest on a single exchange-correlation functional (PBE) with no +U or hybrid cross-check, and the topological gap of about 7 meV is below typical DFT accuracy.

major comments (2)

[Origin of Magnetism; Band Structures and Topological Properties (Figs. 2-3)] The central prediction of C=4 QAHE rests entirely on PBE (Ref. [63]) calculations. The O-2p hole ferromagnetism and the 7 meV spin-orbit gap in Fig. 3(a) are both quantities that PBE is known to treat poorly for oxides; self-interaction error can artificially stabilize hole localization on oxygen. Since the Berry curvature, local Chern numbers, and edge states are all computed on this PBE Hamiltonian, a more accurate functional could close the gap or change its sign and invalidate the C=4 phase. Please provide PBE+U or hybrid-functional (e.g., HSE06) calculations for at least Zn2TeO6 and Cd2TeO6, reporting the magnetic moment per O, the size and sign of the SOC gap, and the Chern number. If such checks cannot be performed, the paper should state this limitation explicitly and moderate the claim.
[Summary; Effect of Strain] The Summary states 'monolayer M2DO6 realizes a high-Chern-number QAHE phase with C=4' without qualification, but the Effect of Strain section states that the other three compounds remain gapless even with spin-orbit coupling and require biaxial strain to align the Dirac points. Only Cd2TeO6 under 2.5% tensile strain is explicitly demonstrated to reach C=4. Please state in the Summary and Abstract which members of the family are intrinsic QAH insulators and which require strain, and give the strained results for Zn2SeO6 and Cd2SeO6 in the main text (or explicitly cite the corresponding supplemental figures).

minor comments (6)

[Abstract; Origin of Magnetism] The phrase 'half-filled O-2p orbital' is imprecise: the two holes occupy the two components of an E doublet at Γ. Please say 'half-filled O-2p doublet' or 'half-filled O-2p manifold'.
[Fig. 1(b) caption] The caption contains the redundant phrase 'high high-symmetry line'; please correct.
[References] Several references appear in the journal 'Coshare Science' (Refs. [4], [8], and [18]), which is not a standard recognized physics venue; please replace them with more conventional sources or verify their existence. Also, Ref. [35] lists the first author as 'Doung' which is likely a typographical error for 'Duong'.
[Effect of Strain] The main text says that the other three compounds require strain to align the Dirac points, but the strain values are only given for Cd2TeO6 (2.5% tensile). Please list the required strain for each compound in the main text or refer explicitly to the relevant supplemental figures.
[k·p model, Eqs. (1)-(3)] The k·p parameters are fitted to the Wannier-interpolated bands, so the local Chern number Cloc ≈ 0.5 is a consistency check rather than an independent derivation. Please emphasize that the C=4 result is obtained from the full Berry curvature integration of the Wannier Hamiltonian (Fig. 3) and not from the fitted model.
[Generalization of O-2p-induced ferromagnetism; Table II] The statement that 'more than 20' oxides exhibit O-2p ferromagnetism is supported only by a reference to Table S2; please add a brief summary in the main text of the screening protocol, the number of materials with and without ferromagnetism, and representative data, so that the generality claim is testable without accessing the supplement.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the C=4 QAHE claim is computed by direct Berry-curvature integration of the DFT/Wannier Hamiltonian, with the fitted k·p model used only as a diagnostic, not as the source of the Chern number.

full rationale

The paper's derivation chain is self-contained against external benchmarks. The central claim that M2DO6 monolayers host a C=4 QAHE is established by (i) DFT (PBE) band structures giving O-2p half-metallic ferromagnetism; (ii) symmetry-identified Dirac crossings; (iii) spin-orbit coupling opening a global gap; and (iv) a direct calculation of Berry curvature and anomalous Hall conductance, yielding a quantized plateau of 4e^2/h (Fig. 3(b)). The two-band k·p model is fitted to the Wannier-projected bands ('The effective models accurately reproduce the low-energy dispersions near the Dirac points'), but this fit is not the source of the Chern number; it is a post-hoc explanation of topology already obtained by integration. The local Chern number C_loc ≈ 0.5 is evaluated from the Berry-curvature integral in Eq. (3), not imposed by the k·p parameters. Self-citations (Refs. 28, 29, 31) are background on high-Chern-number engineering and are not load-bearing. The PBE functional choice and the small 7 meV SOC gap are legitimate correctness risks, but they concern numerical accuracy, not circularity; the paper does not define its target in terms of fitted parameters or import a uniqueness theorem from the authors' prior work.

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

All computational predictions depend on the PBE functional, which is not benchmarked against more accurate methods. The assumed complete deintercalation of alkali cations and the resulting two holes per cell anchor the magnetic and topological results. The monolayer stability is argued from phonons and MD, but experimental realization is not demonstrated. No free parameters are fitted to experimental data, and no new physical entities are postulated.

assumptions (4)

domain assumption PBE/GGA exchange-correlation functional adequately describes O-2p ferromagnetism and band topology.
The paper uses PBE (Ref. [63]) for all electronic structure calculations without benchmarking against +U or hybrid functionals, yet the existence of O-2p holes and the 7 meV gap are central to the claim.
domain assumption Complete removal of A+ cations from layered A2M2DO6 yields the free-standing M2DO6 monolayer with exactly two holes per unit cell.
The electron counting in the Origin of Magnetism section assumes stoichiometric deintercalation; any partial deintercalation or surface effects would change the hole concentration and could destroy the ferromagnetic state.
domain assumption The monolayer is dynamically and thermally stable as computed by phonons and MD, and is experimentally accessible via exfoliation and deintercalation.
The authors assert exfoliation from Na2Zn2TeO6 is possible, and provide phonon/MD evidence, but no experimental synthesis is reported. The entire proposal depends on this realizability.
domain assumption The two-band k.p expansion to linear order in q is sufficient near each crossing point; higher-order terms are negligible.
The effective model around each Dirac point is expanded to O(q^2) and truncated, assuming the local Berry curvature is captured correctly. The authors compare to Wannier bands for a few points, but not exhaustively.

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Cite this review

Pith. "Pith review of Quantum Anomalous Hall Effect in $d^{10}$ Oxide Monolayers." pith.science (2026). https://pith.science/paper/XBCOY2ZK

@misc{pith2026260811855,
  author       = {Pith},
  title        = {Pith review of: Quantum Anomalous Hall Effect in $d^10$ Oxide Monolayers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XBCOY2ZK}},
  note         = {Machine review of arXiv:2608.11855}
}

abstract

Quantum anomalous Hall effect (QAHE) arises from the interplay between magnetic order and spin-orbit coupling, which opens up a topologically nontrivial band gap to host chiral edge states in the absence of magnetic field. So far, magnetic order of QAHE usually originates from partially filled transition-metal $d$ orbitals or correlation-driven moir\'e bands. Here, we propose an experimentally accessible family of two-dimensional oxides, M$_2$DO$_6$ (M = Zn, Cd; D = Se, Te), that can realize QAHE from the half-filled O-$2p$ orbital induced spontaneous ferromagnetism. In M$_2$DO$_6$ monolayers, spin-polarized Dirac points appear at K/K$^{\prime}$ valleys and along $\Gamma$-K/$\Gamma$-K$^{\prime}$ lines. $C_3$ rotational symmetry then generates eight symmetry-related crossings in the first Brillouin zone. Upon gap opening by spin-orbit coupling, each massive Dirac point contributes half Chern number, resulting in a high-Chern-number QAHE phase with $\mathcal{C}=4$. We establish cation deintercalation as a general strategy to activate O-$2p$ ferromagnetism in oxides. Our finding provides a route to realize QAHE from O-$2p$ ferromagnetism and offers design principles applicable to oxygen-based magnetic topology platforms beyond conventional $d$-electron systems.

Figures

Figures reproduced from arXiv: 2608.11855 by the authors.

**Figure 2.** FIG. 2. (a) Nonmagnetic band structure of monolayer [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** FIG. 3. (a) Band structure of monolayer Zn [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: FIG. 4. Wannier90 bands and effective two-band k [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

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