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Microscopic signatures of topology in twisted MoTe2

Abstract

In moiré materials with flat electronic bands and suitable quantum geometry, strong correlations can give rise to various topological states of matter. The non-trivial band topology of twisted MoTe2, which is responsible for its fractional quantum anomalous Hall states, is predicted to arise from a skyrmion lattice texture in the layer pseudospin of the electronic wavefunctions. Tracing the layer polarization of wavefunctions within the moiré unit cell can, thus, offer insights into the band topology. Here we measure the out-of-plane component of the layer-pseudospin skyrmion textures of twisted MoTe2 using scanning tunnelling microscopy and spectroscopy. We do this by simultaneously visualizing the moiré lattice structure and the spatial localization of its electronic states. We find that the wavefunctions associated with the topological flat bands exhibit a spatially dependent layer polarization within the moiré unit cell, in agreement with our theoretical modelling. Our work enables future local probe studies of the intertwined correlated and topological states arising in gate-tunable devices.

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Fig. 1: Topographic characterization of tMoTe2.
Fig. 2: Identification of spectroscopic features of tMoTe2.
Fig. 3: Localization of Γ-point states.
Fig. 4: Localization of K-point states and connection to the band topology.

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Source data are provided with this paper. All other data that support the findings of this study are available from the corresponding authors upon request.

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The source code used to perform the calculations described in this paper is available from the corresponding authors upon request.

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Acknowledgements

We thank D. Waters and B. LeRoy for valuable technical discussions. The development of twisted molybdenum ditelluride samples and their STM characterization was primarily supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences (award DE-SC0023062). The theoretical and experimental research on the topological properties of tMoTe2 was supported as part of Programmable Quantum Materials, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences (award DESC0019443). X.X. and M.Y. acknowledge support from the State of Washington-funded Clean Energy Institute. E.T. was supported by the NSF (grant GRFP DGE-2140004). This work made use of shared fabrication facilities provided by NSF MRSEC 2308979. The machine learning and first-principles calculations were partly supported by the discovering AI@UW Initiative and AI-Core of the Molecular Engineering Materials Center at the University of Washington (grant DMR-2308979). This work was facilitated with the advanced computational, storage and networking infrastructure provided by the Hyak supercomputer system and funded by grant DMR-2308979. K.W. and T.T. acknowledge support from the JSPS (KAKENHI grants 21H05233 and 23H02052) and the World Premier International Research Center Initiative, MEXT, Japan.

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Contributions

E.T., K.T.C. and F.M. fabricated the devices and performed the measurements. X.-W.Z. performed the DFT calculations under the supervision of T.C. and D.X. C.H., Y.Z., J.Y. and J.-H.C. grew some of the MoTe2 crystals used in this study. K.W. and T.T. grew the BN crystals. H.P., J.C., E.A. and X.X. participated in valuable discussions on device fabrication and data interpretation. M.Y. supervised the project. E.T., K.T.C., F.M. and M.Y. wrote the paper with input from all authors.

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Correspondence to Ting Cao, Di Xiao or Matthew Yankowitz.

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Nature Physics thanks Yonglong Xie and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Device fabrication and large-area STM topograph.

a, Schematic illustration of the device fabrication process (see Methods for details). b, Optical micrographs of the devices used in this study. Flake boundaries are outlined using the following convention: blue - graphite, cyan - monolayer graphene, pink - tMoTe2. Scale bars are 20 μm. All results in this study were obtained on device D1, except for the following: Fig. 1g, Extended Data Figs. 1c, 3, 6, and Supplementary Information Figs. S2d–f, S5 (device D2); Fig. 1e, Extended Data Fig. 4 (device D3); Supplementary Information Fig. S3a–c (device D4); Extended Data Fig. 7 (device D5). c, STM topograph of a large area of clean monolayer MoTe2 showing two types of atomic defects66, bright and dark, emphasized by the white and black arrows. A graphene-hBN moiré pattern is also visible in this region. (It, Vbias) = (100 pA, -1.6 V), scale bar is 40 nm.

Extended Data Fig. 2 Dependendence of STM topography on tunneling parameters.

STM topographs of the same θ = 2.75 region as shown in Fig. 1f, but with different tunneling setpoint parameters (It, Vbias): a, (50 pA, -1.0 V), b, (110 pA, -0.9 V), and c, (300 pA, -0.8 V). Scale bars are 5 nm.

Extended Data Fig. 3 Localization of Γ-point states for tMoTe2 with θ = 3.52.

a, Averaged constant-height dI/dV spectra at MM, MX, and XM (4x4 pixels, 1.24 nm2). The insets show a sketch of the measurement technique and the STM topograph of the region, with εuni = 1.90%, and εbi = 0.24%, oriented at -21 with respect to the moiré. The tunneling parameters are (It, Vbias) = (140 pA, -2.5 V). b, Line cut of constant-height dI/dV spectra acquired along the dashed path shown in c. c-e, dI/dV maps acquired at different Vbias, as indicated by the arrows in a. All maps are assembled from a grid spectroscopy measurement with initial tunneling setpoint (It, Vbias) = (200 pA, -1.4 V). The scale bar is 5 nm.

Extended Data Fig. 4 Localization of Γ-point states for tMoTe2 with θ = 1.20°.

a, Constant-height dI/dV spectra at various points within the moiré unit cell, acquired at the same region as Fig. 1e. Insets show a sketch of the measurement technique and a representative STM topograph of the region. b, Line cut of constant-height dI/dV spectra acquired along the dashed path shown in the inset of a. c-f, dI/dV maps acquired at different Vbias, as indicated by the arrows in a. All maps are assembled from a grid spectroscopy measurement with initial tunneling setpoint (It, Vbias) = (200 pA, -1.4 V). The scale bar is 16 nm.

Extended Data Fig. 5 Additional (dI/dV)/I0 maps of K-point states in the θ = 2.75 sample.

Reduced-height (dI/dV)/I0 maps in the same region as Fig. 4a, shown for additional values of Vbias with the same color scale across all maps. Scale bars are 5 nm. See Supplementary Video 2 for an animation of the full evolution with Vbias, and Supplementary Information section Reduced Height Spectroscopy for a discussion about the remnant signal at Vbias = -0.55 V.

Extended Data Fig. 6 Localization of K-point states for tMoTe2 with θ = 3.48.

a, Averaged reduced-height (dI/dV)/I0 spectra at MM, MX, and XM (3x3 pixels, 0.71 nm2). Insets show a sketch of the measurement technique and a representative STM topograph of the region, with εuni = 0.74%, and εbi = 0.00%, oriented at 2 with respect to the moiré. The tunneling parameters are (It, Vbias) = (50 pA, -2.0 V). b-g, dI/dV maps acquired at different values of Vbias, as specified in each panel, with the same color scale across all maps. All maps are assembled from a grid spectroscopy measurement with initial tunneling setpoint (It, Vbias) = (10 pA, -1.2 V). The tip was moved towards the sample by Δz = 0.36 nm before the bias sweep. The scale bars are all 3 nm. See Supplementary Video 3 for animation of the full evolution with Vbias.

Extended Data Fig. 7 Localization of K-point states for tMoTe2 with θ = 0.84.

a, Averaged reduced-height dI/dV spectra at MM (2x2 pixels, 2.71 nm2), MX, and XM (4x4 pixels, 10.85 nm2). Insets show a sketch of the measurement technique and a representative STM topograph of the region, where ε = 0.38%. b, Decay constant as a function of Vbias in this region, measured at MX. Error bars are defined as the standard deviation of the fit for k (see Methods for details of fitting). c-f, dI/dV maps acquired at different values of Vbias, as specified in each panel and by the arrows in a. All maps are assembled from a grid spectroscopy measurement with initial tunneling setpoint (It, Vbias) = (90 pA, -1.1 V). The tip was moved towards the sample by Δz = 0.3 nm before the bias sweep. The scale bars are all 20 nm. The precise localization of the flat bands at small twist angle appears ambiguous, based on the almost simultaneous rise of dI/dV at around Vbias = -0.72 V at MX, XM, and MM, as well as the lack of a distinct spectral peak (in contrast with the MX case in Fig. 4b). Although we are unable to unambiguously determine the layer pseudospin skyrmion texture at this twist angle, our measurements are most consistent with the north pole being at MX given the that we see the largest values of dI/dV there.

Extended Data Fig. 8 Predicted effects of displacement field on the K-point states.

a-b, Calculated bandstructure for tMoTe2 with θ = 2.88 with a, D = 0 mV/nm, and b, D = 300 mV/nm. c-d, Calculated LDOS at different high symmetry points within the moiré unit cell. The top (bottom) layer is shown as the solid (dashed) curve. For D = 0, the curves from the top and bottom layer are perfectly C2y symmetric (note that the curves from the bottom layer are offset by 0.02% for visual clarity). For D ≠ 0, C2y symmetry is broken and there is an energy splitting between the LDOS of different stacking sites in the two layers. e, Calculated spatially resolved LDOS at E = -10 meV for both the top and bottom MoTe2 layers with D = 300 mV/nm. The top layer shows localization on MX, while the bottom shows localization on XM, similar to in Fig. 4d. However, in this calculation the overall value of the LDOS across the moiré is notably larger on the top layer as a consequence of the displacement field. f, Calculated spatially resolved LDOS at E = -170 meV and D = 300 mV/nm, corresponding to states arising from the Γ point. Because of their interlayer hybridization, these states depend only very weakly on D, and this calculation is nearly indistinguishable from the D = 0 case shown in Fig. 4f.

Extended Data Fig. 9 Calculated LDOS excluding the in-plane lattice relaxations.

a, Height of top layer in θ = 2.88 tMoTe2 predicted by an atomic relaxation DFT calculation excluding in-plane lattice relaxations (but retaining the out-of-plane relaxations). The height profile is identical to that shown in Fig. 1c. b, Calculated band structure with in-plane lattice relaxations excluded. The first moiré valence band has a valley Chern number of 0, in contrast to its value of 1 when in-plane relaxations are included. c, Corresponding calculations of LDOS at MM, MX, and XM in the top MoTe2 layer as a function of energy near the valence band edge. d, Layer-resolved LDOS at -10 meV, showing localization on the XM sites in the top layer and the MX sites in the bottom layer. This result is in contrast to the calculated LDOS including in-plane lattice relaxations shown in Fig. 4, in which the LDOS is localized on MX in the top layer near the band edge.

Supplementary information

Supplementary Information

Supplementary Discussion and Figs. 1–7.

Supplementary Video 1

Evolution of constant-height dI/dV maps with Vbias in the same region as Fig. 4a. Scale bar, 5 nm.

Supplementary Video 2

Evolution of reduced-height dI/dV maps with Vbias in the same region as Fig. 4a. Scale bar, 5 nm.

Supplementary Video 3

Evolution of reduced-height dI/dV maps with Vbias in the same region as Extended Data Fig. 6b–g. Scale bar, 3 nm.

Source data

Source Data Fig. 2

Raw data for Fig. 2a,c–e.

Source Data Fig. 4

Raw data for Fig. 4b,c.

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Thompson, E., Chu, K.T., Mesple, F. et al. Microscopic signatures of topology in twisted MoTe2. Nat. Phys. 21, 1224–1230 (2025). https://doi.org/10.1038/s41567-025-02877-x

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