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

Nature Physics (2026)Cite this article 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. 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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.Department of Physics, Columbia University, New York, NY, USAMadisen Holbrook, Julian Ingham, Luca Nashabeh, Raquel Queiroz & Abhay N. PasupathyDepartment of Physics and Astronomy, Center for Materials Theory, Rutgers University, Piscataway, NJ, USADaniel KaplanDepartment of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USALuke N. Holtzman & Katayun BarmakDepartment of Chemistry, University of Wisconsin, Madison, WI, USABrenna BiermanDepartment of Materials Science, Yale University, New Haven, CT, USABowen Hou & Diana Y. QiuDepartment of Chemistry, Columbia University, New York, NY, USANicholas Olsen, Yiliu Li & Xiaoyang ZhuDepartment of Mechanical Engineering, Columbia University, New York, NY, USASong Liu & James C. HoneDepartment of Materials Science and Engineering, University of Wisconsin, Madison, WI, USADaniel RhodesDepartment of Physics, University of Wisconsin, Madison, WI, USADaniel RhodesCondensed Matter Physics and Materials Science Division, Brookhaven National Laboratory, Upton, NY, USAAbhay N. PasupathySearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarJ.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.Correspondence to Raquel Queiroz or Abhay N. Pasupathy.The authors declare no competing interests.Nature Physics thanks Sathwik Bharadwaj and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.(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 dataSupplementary Figs. 1–13 and Sections 1–10.Calculated DFT band structure data for monolayer WSe2 for Fig. 1a and statistical source data for Fig. 1d,e.Calculated DFT band structure data for monolayer NbSe2 (Fig. 4a).Source data for Extended Data Fig. 1a,b.Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.Reprints and permissionsHolbrook, 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/s41567-026-03197-4Download citationReceived: 27 January 2025Accepted: 28 January 2026Published: 31 March 2026Version of record: 31 March 2026DOI: https://doi.org/10.1038/s41567-026-03197-4Anyone you share the following link with will be able to read this content:Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative