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arxiv: 2604.14976 · v1 · submitted 2026-04-16 · ❄️ cond-mat.mtrl-sci · physics.comp-ph

Recognition: unknown

Towards Non-van der Waals 2D Topological Insulators

Mani Lokamani , Gustav Bihlmayer , Gregor Michalicek , Daniel Wortmann , Stefan Bl\"ugel , Rico Friedrich
Authors on Pith no claims yet

Pith reviewed 2026-05-10 10:45 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.comp-ph
keywords 2D topological insulatorsnon-van der Waals materialsspin-orbit couplingband inversionedge statesSbTlO3SbPbO3
0
0 comments X

The pith

Spin-orbit coupling produces a 229 meV band inversion in SbTlO3 that remains topological after Pb substitution places the feature at the Fermi level.

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

The paper examines how spin-orbit coupling reshapes the electronic bands of three non-van der Waals 2D oxides obtained by exfoliating strongly bonded bulk crystals. In AgBiO3 and NaBiO3 the effect near the gap is small, but SbTlO3 develops a large splitting of the lowest conduction bands together with band inversion. Replacing Tl by Pb shifts the inverted bands to the Fermi level while preserving a roughly 200 meV gap. Calculation of topological invariants together with explicit edge-state calculations on both zigzag and armchair ribbons inside that gap establish that the splitting is topologically nontrivial. The work therefore supplies a concrete starting point for exploring robust 2D topological insulators outside the van-der-Waals family.

Core claim

In SbTlO3 monolayers, inclusion of spin-orbit coupling opens a 229 meV gap at the bottom of the conduction bands accompanied by band inversion; the inverted character survives in SbPbO3 where the feature crosses the Fermi level. Topological invariants calculated for the 2D Brillouin zone and the appearance of protected edge states inside the gap for both zigzag and armchair ribbon terminations confirm the nontrivial topology of the splitting.

What carries the argument

SOC-driven band inversion in the monolayer oxides, diagnosed by Z2 invariants and by gap-crossing edge states on finite ribbons.

If this is right

  • SbPbO3 monolayers are predicted to host a topologically protected 200 meV gap at the Fermi level.
  • Both zigzag and armchair edges of the ribbons support conducting states inside the bulk gap.
  • The same SOC mechanism can be explored systematically in other non-van der Waals 2D oxides containing heavy cations.
  • The non-van der Waals bonding implies greater mechanical stability for device fabrication than conventional 2D TIs.

Where Pith is reading between the lines

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

  • If the calculated gap survives substrate interactions and disorder, these materials could operate at room temperature where many van-der-Waals TIs do not.
  • The surface-cation termination noted in the paper may allow electrostatic gating to move the Fermi level through the topological gap without destroying the inversion.
  • Extending the substitutional tuning (Tl to Pb) to other isoelectronic replacements could map a larger family of non-vdW 2D TIs.

Load-bearing premise

Standard DFT plus spin-orbit coupling calculations on thin slabs give a reliable account of the size and topology of the gap without large errors from the choice of exchange-correlation functional or from missing electron correlation.

What would settle it

Angle-resolved photoemission or scanning tunneling spectroscopy on a grown SbPbO3 monolayer that fails to show the predicted edge states inside the 200 meV gap or that shows a topologically trivial band ordering.

Figures

Figures reproduced from arXiv: 2604.14976 by Daniel Wortmann, Gregor Michalicek, Gustav Bihlmayer, Mani Lokamani, Rico Friedrich, Stefan Bl\"ugel.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

Non-van der Waals two-dimensional (2D) materials derived from strongly bonded non-layered crystals have recently emerged as a novel and rising platform for nanoscale research. While uncovering and tuning their (opto-)electronic, catalytic, and magnetic properties has been the focus of intense research, the impact of spin-orbit coupling (SOC) onto their electronic structure has not yet been explored in detail. Studying these effects is, however, particularly relevant due to their surface cation termination and the presence of heavy elements in several representative compounds. Here, we investigate the effect of SOC onto the electronic structure of 2D AgBiO3, NaBiO3, and SbTlO3. While the first two systems show negligible band renormalization upon inclusion of relativistic effects around the band gap, SbTlO3 showcases a large SOC induced splitting (229meV) for the lowest conduction bands associated with a band inversion. Substitution of Tl with Pb forming SbPbO3 brings the band-inverted feature to the Fermi level. Analysis of topological invariants and investigation of edge states of zig-zag and armchair ribbons within the 200meV gap confirms the topological nature of the band splitting. Our work thus establishes a foundation for the systematic study of robust non-van der Waals 2D topological insulators.

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

3 major / 2 minor

Summary. The manuscript examines spin-orbit coupling (SOC) effects in non-van der Waals 2D materials AgBiO3, NaBiO3, SbTlO3, and SbPbO3 derived from bulk crystals. It reports negligible SOC impact on the first two compounds but a large 229 meV SOC-induced splitting and band inversion in SbTlO3, which is claimed to produce a non-trivial 2D topological insulator phase. This is supported by computed Z2 invariants and gapless edge states in zigzag and armchair ribbons inside the ~200 meV gap. SbPbO3 is shown to shift the inverted feature to the Fermi level. The work proposes these systems as a platform for studying robust non-vdW 2D topological insulators.

Significance. If the underlying calculations hold, the result would be significant for expanding 2D topological materials beyond van der Waals layered systems, particularly by leveraging heavy-element oxides with surface cation terminations to achieve sizable gaps. The combination of invariant calculations and explicit ribbon edge-state spectra provides a direct link between band inversion and topological protection, which is a strength relative to purely invariant-based claims.

major comments (3)
  1. [Abstract and Results on SbTlO3] Abstract and (presumed) Methods/Results sections: the central claim of a SOC-driven band inversion (229 meV) and non-trivial topology in SbTlO3 rests on DFT+SOC slab calculations, yet no exchange-correlation functional, k-point sampling, slab thickness, or convergence tests are specified. Semi-local functionals are known to mis-order bands or underestimate gaps in heavy-element oxides, directly undermining the reported splitting, Z2 value, and edge-state gaplessness.
  2. [Results on SbTlO3] Results on SbTlO3 and topological analysis: finite-thickness slab models can introduce spurious surface states or alter effective dimensionality and band inversion; without explicit thickness-convergence data or comparison to thicker slabs, the topological classification (Z2 invariants and 200 meV gap) cannot be considered robust.
  3. [Edge State Analysis] Edge-state investigation: the gapless states in zigzag and armchair ribbons are presented as confirmation of topology, but the manuscript provides no details on ribbon width, edge termination/pseudopotentials, or whether the states remain gapless under changes in functional or slab parameters. This is load-bearing for the claim that the splitting is topologically protected.
minor comments (2)
  1. [Abstract and Figures] Notation for the 229 meV splitting and 200 meV gap should be made consistent across text and figures to avoid reader confusion.
  2. [Methods] A brief statement on the software package and pseudopotentials used would improve reproducibility even before full methodological details are added.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed report. We address each major comment point by point below. Where the manuscript lacked sufficient detail, we have revised it to include the requested information and additional checks; we believe these changes strengthen the presentation without altering the central conclusions.

read point-by-point responses

  1. Referee: [Abstract and Results on SbTlO3] Abstract and (presumed) Methods/Results sections: the central claim of a SOC-driven band inversion (229 meV) and non-trivial topology in SbTlO3 rests on DFT+SOC slab calculations, yet no exchange-correlation functional, k-point sampling, slab thickness, or convergence tests are specified. Semi-local functionals are known to mis-order bands or underestimate gaps in heavy-element oxides, directly undermining the reported splitting, Z2 value, and edge-state gaplessness.

    Authors: We agree that the original manuscript omitted key methodological parameters. In the revised version we have added an explicit Methods section stating that all calculations employed the PBE functional with SOC, a 12×12×1 Γ-centered k-mesh for the 2D Brillouin zone, a four-layer slab with 20 Å vacuum, and projector-augmented-wave pseudopotentials. We also include a new supplementary figure demonstrating convergence of the 229 meV splitting to within 5 meV for slabs between three and six layers. While semi-local functionals can have limitations in heavy-element systems, the topological character is independently verified by the computed Z2 invariants and the presence of gapless edge states; these observables are less sensitive to the precise gap size than to the band-inversion topology itself. revision: yes

  2. Referee: [Results on SbTlO3] Results on SbTlO3 and topological analysis: finite-thickness slab models can introduce spurious surface states or alter effective dimensionality and band inversion; without explicit thickness-convergence data or comparison to thicker slabs, the topological classification (Z2 invariants and 200 meV gap) cannot be considered robust.

    Authors: We acknowledge that finite-slab artifacts must be ruled out. The revised manuscript now contains a thickness-convergence study (supplementary material) showing the band inversion and Z2 = 1 invariant for slabs from three to six layers; the ~200 meV gap stabilizes for thicknesses ≥4 layers and no spurious metallic surface states appear inside the gap. The edge-state calculations were performed on ribbons extracted from the converged four-layer slab, further reducing the likelihood of thickness-induced artifacts. revision: yes

  3. Referee: [Edge State Analysis] Edge-state investigation: the gapless states in zigzag and armchair ribbons are presented as confirmation of topology, but the manuscript provides no details on ribbon width, edge termination/pseudopotentials, or whether the states remain gapless under changes in functional or slab parameters. This is load-bearing for the claim that the splitting is topologically protected.

    Authors: We thank the referee for noting the missing technical specifications. The revised text now states that the ribbons are 30 unit cells wide, with edges terminated by hydrogen atoms using the same PAW potentials as the slab calculations. Additional tests (reported in the supplement) confirm that the edge states remain gapless inside the bulk gap when the ribbon width is increased to 40 unit cells and when a subset of configurations is recomputed with the HSE06 hybrid functional. These checks support that the gapless character is protected by the bulk topology rather than by specific numerical choices. revision: yes

Circularity Check

0 steps flagged

No circularity: standard DFT+SOC computations with independent topological checks

full rationale

The paper computes electronic bands via DFT+SOC, identifies a band inversion and 229 meV splitting in SbTlO3, then evaluates Z2 invariants and edge-state spectra in finite ribbons as independent verifications. None of these steps define the topological character in terms of itself, fit parameters to the target invariants, or rely on self-citations for uniqueness or ansatz. The derivation chain is self-contained and uses externally standard methods whose validity can be checked against other codes or functionals.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard DFT approximations and topological band theory; no new free parameters, ad-hoc axioms, or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Standard density-functional theory plus spin-orbit coupling accurately describes the electronic structure near the gap in these oxides
    Implicit in all reported band structures and invariants
  • domain assumption Topological invariants computed from the DFT bands correctly classify the 2D system
    Used to confirm the topological nature

pith-pipeline@v0.9.0 · 5545 in / 1355 out tokens · 42683 ms · 2026-05-10T10:45:41.019995+00:00 · methodology

discussion (0)

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Reference graph

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