Experimental signature of layer skyrmions and implications for band topology in twisted WSe2 bilayers

Allan H. MacDonald; Chengye Dong; Chih-Kang Shih; Fan Zhang; Fu-Xiang Rikudo Chen; Hyunsue Kim; Joshua A. Robinson; Jung-Jung Su; Kenji Watanabe; Nicol\'as Morales-Dur\'an

arxiv: 2406.20036 · v2 · submitted 2024-06-28 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci

Experimental signature of layer skyrmions and implications for band topology in twisted WSe2 bilayers

Fan Zhang , Nicol\'as Morales-Dur\'an , Yanxing Li , Wang Yao , Jung-Jung Su , Yu-Chuan Lin , Chengye Dong , Xiaohui Liu

show 8 more authors

Fu-Xiang Rikudo Chen Hyunsue Kim Kenji Watanabe Takashi Taniguchi Xiaoqin Li Joshua A. Robinson Allan H. MacDonald Chih-Kang Shih

This is my paper

Pith reviewed 2026-05-23 23:32 UTC · model grok-4.3

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

keywords twisted WSe2layer skyrmionsmoiré bandsscanning tunneling spectroscopyK-valleyGamma-valleylayer polarizationband topology

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The pith

Scanning tunneling spectroscopy detects opposite layer polarizations of K-valley states at MX and XM sites in rhombohedral twisted WSe2, confirming layer skyrmion texture.

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

The paper measures moiré electronic states in R-stacked twisted WSe2 bilayers with scanning tunneling spectroscopy that separates Gamma-valley and K-valley contributions. Gamma-valley states experience a moiré potential of about 120 meV while K-valley states, located roughly 150 meV higher, experience a weaker 30 meV potential. The key observation is that K-valley local density of states shows opposite layer polarizations at the MX and XM positions inside each moiré cell. This spatial pattern matches the layer skyrmion texture that continuum models predict from patterned interlayer tunneling and layer potentials. The data also let the authors fix the parameters of those models and tie the real-space LDOS shape to the topology of the highest moiré band.

Core claim

In rhombohedral-stacked twisted WSe2, STS resolves Gamma-valley moiré states subject to a 120 meV potential and K-valley states 150 meV above them that feel a 30 meV potential. The K-valley dI/dV maps display opposite layer polarizations at the MX and XM sites of the moiré unit cell. This pattern directly confirms the theoretically predicted layer skyrmion texture. The same maps determine the continuum-model parameters and establish a correlation between the real-space LDOS profile and the topology of the topmost moiré band.

What carries the argument

Layer skyrmion texture: a spatial pattern of opposite layer polarizations for K-valley electrons at MX versus XM sites inside the moiré cell, produced by the combination of interlayer tunneling amplitudes and layer-dependent potentials.

If this is right

Moiré potential amplitudes for both valleys are fixed by the measured LDOS contrasts.
A direct link is established between the real-space shape of the LDOS and the topology of the topmost moiré band.
The confirmed skyrmion texture supplies the spatial patterning needed for nontrivial band topology in the layer-hybridized regime.

Where Pith is reading between the lines

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

The extracted parameters can be inserted into calculations of Chern-insulator or fractional Chern-insulator states in the same material family.
The same STS contrast method could be used to test whether layer skyrmions appear in other twist angles or in related TMD homobilayers.
If the skyrmion texture survives to smaller twist angles, it may set the length scale that controls the stability of correlated topological phases.

Load-bearing premise

The assignment of the states 150 meV above Gamma to the K-valley and the reading of their dI/dV contrast as layer polarization both depend on the continuum model plus valley-specific tunneling matrix elements correctly linking observed LDOS to layer character.

What would settle it

A layer-resolved photoemission measurement or a calculation that does not assume the same tunneling matrix elements but still finds no opposite layer polarizations at MX and XM sites would falsify the skyrmion assignment.

read the original abstract

Transition metal dichalcogenide (TMD) twisted homobilayers have been established as an ideal platform for studying strong correlation phenomena, as exemplified by the recent discovery of fractional Chern insulator (FCI) states in twisted MoTe2 and Chern insulators (CI) and unconventional superconductivity in twisted WSe2 (tWSe2). In these systems, nontrivial topology in the strongly layer-hybridized regime can arise from a spatial patterning of interlayer tunneling amplitudes and layer-dependent potentials that yields a lattice of layer skyrmions. Here we report on experimental signatures of skyrmion textures in the layer degree of freedom of Rhombohedral-stacked (R-stacked) tWSe2 homobilayers. This observation is based on scanning tunneling spectroscopy that separately resolves the Gamma-valley and K-valley moir\'e electronic states. We show that Gamma-valley states are subjected to a moir\'e potential with an amplitude of ~ 120 meV. At ~150 meV above the Gamma-valley, the K-valley states are subjected to a weaker moir\'e potential of ~30 meV. Most significantly, we reveal opposite layer polarizations of the K-valley at the MX and XM sites within the moir\'e unit cell, confirming the theoretically predicted layer skyrmion texture. The dI/dV mappings allow the parameters that enter the continuum model of moir\'e bands in twisted TMD bilayers to be determined experimentally, further establishing a direct correlation between the shape of the LDOS profile in real space and the topology of topmost moir\'e band.

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

Abstract gives first claimed STS map of opposite K-valley layer polarizations at MX/XM sites in R-stacked tWSe2, but the layer assignment rests entirely on continuum-model assumptions with no independent check shown.

read the letter

This abstract reports STS data on R-stacked twisted WSe2 that separates Gamma-valley and K-valley moiré states and extracts moiré potential amplitudes of roughly 120 meV and 30 meV. The central new piece is the claim that dI/dV contrast at ~150 meV shows opposite layer polarizations for the K-valley at MX versus XM sites, presented as confirmation of the layer skyrmion texture. That would be useful if solid, because it supplies an experimental anchor for the real-space texture that theory links to the Chern and fractional Chern states already seen in this material family. The work also extracts continuum-model parameters directly from the LDOS maps, which could tighten the connection between real-space profiles and band topology. The soft spot is exactly where the stress-test note flags it: the polarization assignment is not independently verified. It depends on the continuum model plus valley-specific tunneling matrix elements to turn intensity contrast into layer character. The abstract supplies no cross-check such as a known layer-selective probe or first-principles LDOS comparison, so the same contrast could be read as moiré-potential or hybridization effects instead. With only the abstract available there are also no raw spectra, error bars, or fitting details to judge robustness against tip artifacts or background choices. This is for the twisted TMD community working on moiré topology and experimental probes. Readers who need concrete numbers for model calibration would get something from the reported potentials if the full data backs them. It deserves a serious referee once the complete manuscript with methods and spectra is submitted, because the topic is timely and the potential link to observed Chern states is direct.

Referee Report

2 major / 1 minor

Summary. The manuscript reports scanning tunneling spectroscopy on rhombohedral-stacked twisted WSe2 homobilayers that separately resolves Gamma-valley and K-valley moiré states. It extracts a moiré potential of ~120 meV acting on Gamma-valley states and a weaker ~30 meV potential on K-valley states located ~150 meV higher; the central claim is that dI/dV intensity contrast reveals opposite layer polarizations of the K-valley at MX versus XM sites, confirming the predicted layer skyrmion texture. The mappings are further said to fix continuum-model parameters and to correlate real-space LDOS with the topology of the topmost moiré band.

Significance. If the layer-polarization assignment and potential amplitudes prove robust, the result would supply the first direct experimental anchor for the layer-skyrmion texture that theory invokes to generate nontrivial topology in the strongly hybridized regime of twisted TMD homobilayers. Experimental values for the continuum-model parameters would also tighten quantitative comparisons with the observed Chern and fractional Chern insulators in tWSe2 and related systems.

major comments (2)

[Abstract] Abstract: the claim that dI/dV intensity contrast at the K-valley energy directly encodes opposite layer polarizations at MX and XM sites rests on an unverified mapping supplied by the continuum model plus valley-specific tunneling matrix elements. No independent experimental cross-check (e.g., comparison against a known layer-selective probe or parameter-free first-principles LDOS) is described that would rule out reinterpretation as moiré-potential or hybridization effects.
[Abstract] Abstract: the reported amplitudes (~120 meV for Gamma, ~30 meV for K) and the layer-polarization assignment cannot be assessed for robustness because the abstract supplies neither raw spectra, error bars, background-subtraction procedures, nor any discussion of tip artifacts.

minor comments (1)

[Abstract] The abstract states that the dI/dV mappings 'allow the parameters that enter the continuum model to be determined experimentally' but does not indicate which parameters are fixed or how the fit is performed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful assessment and constructive comments on our manuscript. We agree that the abstract requires clarification on the interpretation and data presentation. We will revise the abstract accordingly while preserving the core claims supported by the STS data and continuum model analysis in the full manuscript.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that dI/dV intensity contrast at the K-valley energy directly encodes opposite layer polarizations at MX and XM sites rests on an unverified mapping supplied by the continuum model plus valley-specific tunneling matrix elements. No independent experimental cross-check (e.g., comparison against a known layer-selective probe or parameter-free first-principles LDOS) is described that would rule out reinterpretation as moiré-potential or hybridization effects.

Authors: The layer-polarization assignment indeed relies on the standard continuum model for twisted TMDs together with valley-dependent tunneling matrix elements, which predict the opposite contrast at MX versus XM sites for the K-valley states. The manuscript presents STS mappings that match this prediction and allow experimental fixing of model parameters. While we do not provide an additional independent experimental probe beyond the STS data itself, the observed real-space LDOS profile directly correlates with the expected skyrmion texture. We will revise the abstract to explicitly note the model-based interpretation and its consistency with the data. revision: yes
Referee: [Abstract] Abstract: the reported amplitudes (~120 meV for Gamma, ~30 meV for K) and the layer-polarization assignment cannot be assessed for robustness because the abstract supplies neither raw spectra, error bars, background-subtraction procedures, nor any discussion of tip artifacts.

Authors: The abstract is a concise summary and therefore does not include raw spectra, error bars, or detailed procedures, which are provided in the main text, figures, and supplementary material of the full manuscript. We will revise the abstract to briefly indicate that the amplitudes are extracted from STS spectra with full analysis details (including background subtraction and tip considerations) given in the body of the paper. revision: yes

Circularity Check

0 steps flagged

No significant circularity: experimental STS observation confirms predicted texture via data-driven parameter extraction

full rationale

The paper is an experimental report using scanning tunneling spectroscopy to resolve Gamma- and K-valley moiré states, measure their potentials (~120 meV and ~30 meV), and observe opposite layer polarizations at MX/XM sites. This directly matches the abstract's description of determining continuum-model parameters from dI/dV mappings and correlating LDOS shape with band topology. No derivation chain, equations, or self-citations are present in the abstract that reduce a claimed prediction to an input by construction, fit a parameter then relabel it as a prediction, or rely on load-bearing self-citation for a uniqueness theorem. The central result is an empirical signature, not a self-referential theoretical derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only; no explicit model equations, fitting procedures, or additional assumptions are supplied, so the ledger is empty.

pith-pipeline@v0.9.0 · 5876 in / 1127 out tokens · 18240 ms · 2026-05-23T23:32:26.913463+00:00 · methodology

discussion (0)

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