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Real-space imaging of the band topology of transition metal dichalcogenides

Nature Physics (2026)Cite this article

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Abstract

The topological properties of Bloch bands are tied to the structure of their electronic wavefunctions within the unit cell of a crystal. Here we show that scanning tunnelling microscopy and spectroscopy measurements on the prototypical transition metal dichalcogenide semiconductor WSe2 can be used to determine the location of the Wannier centre of the valence band. Using site-specific substitutional doping, we determine the position of the atomic sites within real-space scanning tunnelling microscopy images, and establish that the maximum electronic density of states at the corner of the Brillouin zone lies between the atoms. By contrast, the maximum density of states at the Brillouin zone centre is at the atomic sites. This signifies that WSe2 is a topologically obstructed atomic insulator, which cannot be adiabatically transformed into a trivial atomic limit, constituting direct experimental evidence of this phase of matter.

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Fig. 1: Connecting STM images to the WSe2 atomic lattice.
Fig. 2: Charge density profile from interference of Wannier orbitals in 1H TMDs.
Fig. 3: Bias-dependent imaging of WSe2.
Fig. 4: Atomically centred charge density in NbSe2.

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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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Acknowledgements

J.I. thanks D. Muñoz-Segovia for helpful discussions. J.I. and M.H. give special thanks to J. Balgley for discussions that initiated the project. This work was primarily supported by the NSF MRSEC program at Columbia through the Center for Precision-Assembled Quantum Materials (DMR-2011738). J.I., D.K. and R.Q. acknowledge support by grant NSF PHY-2309135 to the Kavli Institute for Theoretical Physics (KITP). A.N.P. acknowledges support from the Air Force Office of Scientific Research via award number FA9550-21-1-0378. R.Q. and J.I. are further supported by NSF Career award number DMR-2340394. D.K. is supported by the Abrahams postdoctoral fellowship of the Center for Materials Theory, Rutgers University, and the Zuckerman STEM fellowship. D.R. and B.B. were supported by NSF Career award number DMR-2338984. Theoretical calculations (B.H. and D.Y.Q.) were supported by the National Science Foundation Division of Chemistry under award number CHE-2412412. Their calculations used resources of the National Energy Research Scientific Computing (NERSC), a Department of Energy, Office of Science User Facility, operated under contract number DE-AC02-05CH11231, under award numbers BES-ERCAP-0031507 and BES-ERCAP-0027380 and the Texas Advanced Computing Center (TACC) at The University of Texas at Austin.

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Authors and Affiliations

  1. Department of Physics, Columbia University, New York, NY, USA

    Madisen Holbrook, Julian Ingham, Luca Nashabeh, Raquel Queiroz & Abhay N. Pasupathy

  2. Department of Physics and Astronomy, Center for Materials Theory, Rutgers University, Piscataway, NJ, USA

    Daniel Kaplan

  3. Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USA

    Luke N. Holtzman & Katayun Barmak

  4. Department of Chemistry, University of Wisconsin, Madison, WI, USA

    Brenna Bierman

  5. Department of Materials Science, Yale University, New Haven, CT, USA

    Bowen Hou & Diana Y. Qiu

  6. Department of Chemistry, Columbia University, New York, NY, USA

    Nicholas Olsen, Yiliu Li & Xiaoyang Zhu

  7. Department of Mechanical Engineering, Columbia University, New York, NY, USA

    Song Liu & James C. Hone

  8. Department of Materials Science and Engineering, University of Wisconsin, Madison, WI, USA

    Daniel Rhodes

  9. Department of Physics, University of Wisconsin, Madison, WI, USA

    Daniel Rhodes

  10. Condensed Matter Physics and Materials Science Division, Brookhaven National Laboratory, Upton, NY, USA

    Abhay N. Pasupathy

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  1. Madisen Holbrook
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Contributions

J.I. and R.Q. conceived the theoretical premise and M.H. and A.N.P. conceived the experiment. M.H. carried out the STM and STS measurements with L.N. under the supervision of A.N.P. D.K. performed the density functional theory calculations of the band structure and local density of states. J.I. performed the tight-binding calculations of band structure and local density of states. First-principles defect simulations were performed by B.H. under the supervision of D.Y.Q. L.N.H., S.L. and B.B. synthesized the bulk TMD crystals under the supervision of D.R., K.B. and J.C.H. The samples were exfoliated/stacked by N.O. and Y.L. under the supervision of X.Z. M.H. and A.N.P. analysed the STM data. M.H., J.I., D.K., A.N.P. and R.Q. wrote the paper with contributions from all authors.

Corresponding authors

Correspondence to Raquel Queiroz or Abhay N. Pasupathy.

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Extended data

Extended Data Fig. 1 Height dependence of the tunnelling current.

(a) Image to the left shows a flattened current image acquired at -1.9 V near the Γ point, with the raw current shown in grayscale. As the tip is lowered toward the sample (blue profile), the charge density position shifts as the tunnelling becomes dominated by states at K. (b) At -1.4 V, where only K states contribute, the charge density remains unchanged with tip height. Scale bars are 0.5 nm.

Source data

Supplementary information

Supplementary Information (download PDF )

Supplementary Figs. 1–13 and Sections 1–10.

Source data

Source Data Fig. 1 (download XLSX )

Calculated DFT band structure data for monolayer WSe2 for Fig. 1a and statistical source data for Fig. 1d,e.

Source Data Fig. 2 (download XLS )

Calculated DFT band structure data for monolayer NbSe2 (Fig. 4a).

Source Data Extended Data Fig. 1 (download XLSX )

Source data for Extended Data Fig. 1a,b.

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Holbrook, M., Ingham, J., Kaplan, D. et al. Real-space imaging of the band topology of transition metal dichalcogenides. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03197-4

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