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arxiv: 2604.08907 · v1 · submitted 2026-04-10 · ❄️ cond-mat.mtrl-sci

Higher-order topological insulators in two-dimensional antiferromagnetic and altermagnetic chromium-based group-IV chalcogenides

Ruo-Yu Ning , Yong-Kun Wang , Shifeng Qian , Si Li , Wen-Li Yang This is my paper

Pith reviewed 2026-05-10 17:38 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords higher-order topological insulatorstwo-dimensional materialsantiferromagneticaltermagneticchromium chalcogenidesC3 symmetrycorner states
0
0 comments X p. Extension

The pith

Chromium-based 2D chalcogenide monolayers host higher-order topological insulator phases protected by C3 symmetry.

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

The paper uses first-principles calculations to identify CrCX3 (X = S, Se, Te) and CrSiS3 monolayers as antiferromagnetic with PT symmetry, and certain Janus compounds as altermagnetic. All these systems realize 2D higher-order topological insulator phases where C3 rotational symmetry protects nontrivial topology that appears as zero-dimensional corner states carrying quantized fractional charges. The phases and corner states persist when spin-orbit coupling is added. This establishes a direct link between higher-order topology and magnetic order in two-dimensional materials, offering new platforms for topological and spintronic studies.

Core claim

Based on first-principles calculations combined with theoretical analysis, the CrCX3 (X=S, Se, Te) and CrSiS3 monolayers realize antiferromagnetic ground states with PT symmetry, whereas the Janus compounds Cr2C2S3Se3 and Cr2Si2S3Se3 exhibit altermagnetic ground states. All these monolayer magnetic materials realize 2D HOTI phases in which the nontrivial topology is protected by lattice C3 rotational symmetry and manifests as zero-dimensional corner states carrying quantized fractional charges. Upon inclusion of spin-orbit coupling, these systems remain in the HOTI phase and continue to host robust corner-localized states.

What carries the argument

Lattice C3 rotational symmetry that protects the higher-order topology, producing zero-dimensional corner states with quantized fractional charges in the antiferromagnetic and altermagnetic monolayers.

If this is right

  • The higher-order topology and corner states persist across both antiferromagnetic and altermagnetic magnetic orders.
  • The HOTI phase and its corner states remain stable when spin-orbit coupling is included.
  • An intrinsic connection exists between higher-order topology and magnetic order in these two-dimensional systems.
  • The identified monolayers provide platforms for exploring higher-order topological phases and their relevance to topological and spintronic applications.

Where Pith is reading between the lines

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

  • Local probes such as scanning tunneling spectroscopy could directly image the predicted corner states to test the fractional charge quantization.
  • The altermagnetic members might enable magnetic control of topological corner states without net magnetization, useful for spintronic devices.
  • Similar C3-protected phases could appear in other 2D magnetic chalcogenides if their ground states also respect the required symmetry.
  • Heterostructures incorporating these layers might allow electrostatic tuning of the corner states for potential quantum information applications.

Load-bearing premise

First-principles calculations accurately predict the antiferromagnetic or altermagnetic ground states, preserve C3 symmetry, and correctly determine the higher-order topological character without significant errors from approximations.

What would settle it

Scanning tunneling microscopy or spectroscopy measurements on fabricated monolayers that fail to detect localized states at corners with signatures of fractional charge would disprove the higher-order topological insulator phase.

Figures

Figures reproduced from arXiv: 2604.08907 by Ruo-Yu Ning, Shifeng Qian, Si Li, Wen-Li Yang, Yong-Kun Wang.

Figure 1
Figure 1. Figure 1: FIG. 1. Top and side views of monolayer (a) CrC [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The possible magnetic configurations that we have [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Band structure and PDOS of monolayer (a) CrCS [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Energy spectrum of the triangular-shaped mono [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

Based on first-principles calculations combined with theoretical analysis, we identify a family of monolayer chromium-based group-IV chalcogenides as a new class of two-dimensional (2D) magnetic higher-order topological insulators (HOTIs). Specifically, the CrC$X_3$ ($X=$ S, Se, Te) and CrSiS$_3$ monolayers are found to host conventional antiferromagnetic ground states with $\mathcal{PT}$ symmetry, whereas the Janus compounds Cr$_2$C$_2$S$_3$Se$_3$ and Cr$_2$Si$_2$S$_3$Se$_3$ exhibit altermagnetic ground states. We demonstrate that all these monolayer magnetic materials realize 2D HOTI phases, in which the nontrivial topology is protected by lattice $C_3$ rotational symmetry and manifests as zero-dimensional corner states carrying quantized fractional charges. Moreover, upon inclusion of spin-orbit coupling, these systems remain in the HOTI phase and continue to host robust corner-localized states, confirming the stability of their higher-order topological nature. Our results reveal an intrinsic connection between higher-order topology and magnetic order in 2D antiferromagnetic and altermagnetic systems, identifying chromium-based group-IV chalcogenide monolayers as promising platforms for exploring higher-order topological phases and their potential relevance for future topological and spintronic applications.

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.

Referee Report

2 major / 1 minor

Summary. The manuscript identifies a family of monolayer chromium-based group-IV chalcogenides (CrCX3 with X=S,Se,Te; CrSiS3; and Janus Cr2C2S3Se3, Cr2Si2S3Se3) as 2D magnetic higher-order topological insulators. First-principles calculations combined with symmetry analysis show conventional antiferromagnetic ground states with PT symmetry for the first group and altermagnetic order for the Janus compounds. All are claimed to realize HOTI phases protected by C3 rotational symmetry, manifesting as zero-dimensional corner states with quantized fractional charges; these features remain stable upon inclusion of spin-orbit coupling.

Significance. If the calculations hold, the work establishes an intrinsic link between antiferromagnetic/altermagnetic order and higher-order topology in 2D materials, identifying specific chromium chalcogenide monolayers as platforms for exploring magnetic HOTIs and potential spintronic applications. The systematic treatment of multiple compounds and emphasis on C3-protected corner states with fractional charge provide concrete, testable predictions. The combination of DFT with theoretical analysis is a clear strength when methods are fully documented.

major comments (2)
  1. [Computational Methods] Computational Methods section: The central claims rest on first-principles identification of AFM/altermagnetic ground states and the higher-order topological character. No details are given on the exchange-correlation functional, Hubbard U value for Cr 3d states, energy convergence criteria, or k-point sampling. This is load-bearing because the relative magnetic energies and band inversions determining both the ground state and topology are known to be sensitive to these choices; explicit tests (e.g., varying U or hybrid functionals) are required to substantiate the results.
  2. [Topological properties] Topological properties and corner-state sections: The persistence of the HOTI phase and quantized corner charges with and without SOC is asserted on the basis of C3 symmetry protection. The manuscript does not specify the computational protocol for the higher-order invariant (e.g., nested Wilson loops, quadrupole moment, or finite-size corner-charge calculation) nor demonstrate that SOC does not break the protecting symmetry or alter the invariant. This directly affects the stability claim.
minor comments (1)
  1. [Abstract] Abstract: The phrase 'quantized fractional charges' would be clearer if the specific fraction (e.g., e/2) were stated, consistent with standard HOTI literature.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of our work and for the constructive comments, which have helped us improve the manuscript. We have revised the paper to address the concerns on computational details and the characterization of topological properties.

read point-by-point responses

  1. Referee: [Computational Methods] Computational Methods section: The central claims rest on first-principles identification of AFM/altermagnetic ground states and the higher-order topological character. No details are given on the exchange-correlation functional, Hubbard U value for Cr 3d states, energy convergence criteria, or k-point sampling. This is load-bearing because the relative magnetic energies and band inversions determining both the ground state and topology are known to be sensitive to these choices; explicit tests (e.g., varying U or hybrid functionals) are required to substantiate the results.

    Authors: We agree that these methodological details are necessary for reproducibility and to confirm robustness. In the revised manuscript we have added a dedicated Computational Methods section that specifies the exchange-correlation functional, the Hubbard U value applied to Cr 3d states, energy and force convergence thresholds, k-point sampling, and the results of explicit sensitivity tests (varying U and comparing with hybrid functionals) that verify the stability of the magnetic ground states and the band inversions underlying the topology. revision: yes

  2. Referee: [Topological properties] Topological properties and corner-state sections: The persistence of the HOTI phase and quantized corner charges with and without SOC is asserted on the basis of C3 symmetry protection. The manuscript does not specify the computational protocol for the higher-order invariant (e.g., nested Wilson loops, quadrupole moment, or finite-size corner-charge calculation) nor demonstrate that SOC does not break the protecting symmetry or alter the invariant. This directly affects the stability claim.

    Authors: We thank the referee for highlighting this omission. The revised manuscript now explicitly describes the computational protocol: the higher-order invariant is obtained via the nested Wilson-loop method, cross-checked with direct corner-charge calculations on finite-size flakes. We further demonstrate that C3 symmetry remains intact under SOC (SOC does not break the underlying lattice symmetry) and that the invariant stays nontrivial, with the corner states and their fractional charge quantization persisting in the presence of SOC. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper identifies the HOTI phases via first-principles DFT calculations of magnetic ground states (AFM with PT symmetry or altermagnetic) followed by symmetry-based analysis of C3 protection and explicit computation of zero-dimensional corner states with quantized fractional charges, both with and without SOC. These outputs are produced by the computational pipeline and do not reduce by construction to any fitted parameter, self-defined quantity, or load-bearing self-citation chain. No equations or steps in the abstract or described workflow equate the claimed topology to its own inputs; the result remains an independent verification against external DFT benchmarks and symmetry indicators.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard DFT-based electronic structure methods and symmetry arguments; no new entities are postulated.

free parameters (1)
  • DFT exchange-correlation functional and related parameters
    Choice of functional and convergence settings in first-principles calculations can influence predicted magnetic order and band topology.
axioms (2)
  • domain assumption The monolayers possess C3 rotational symmetry that protects the higher-order topology.
    Invoked to explain the existence and robustness of corner states.
  • domain assumption First-principles calculations reliably determine magnetic ground states and topological invariants in these systems.
    Basis for identifying the HOTI phase in both antiferromagnetic and altermagnetic cases.

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Reference graph

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