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Observation of an obstructed atomic band in a transition metal dichalcogenide

Nature Physics volume 22, pages 686–691 (2026) Cite this article

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Abstract

Topologically trivial insulators are classified into two primary categories: unobstructed and obstructed atomic insulators. Although both types can be described by exponentially localized Wannier orbitals, a defining feature of obstructed atomic insulators is that that the centre of charge of at least one of these orbitals is positioned at an empty site within the unit cell, rather than on an occupied atomic site. Despite extensive theoretical predictions, the unambiguous quantitative experimental identification of an obstructed atomic phase has not yet been achieved. Here we present direct evidence of such a phase in 1H-NbSe2. We develop a method to extract the interorbital correlation functions from the local spectral function probed by scanning tunnelling microscopy and using the orbital wavefunctions obtained from ab initio calculations. Applying this technique to real-space spectroscopic images, we determine the interorbital correlation functions for the atomic band of 1H-NbSe2 that crosses the Fermi level. Our results show that this band realizes an optimally compact obstructed atomic phase. This approach is broadly applicable to other material platforms (including related compounds such as 1H-TaSe2 that also feature obstructed atomic bands) and offers a powerful tool for exploring other electronic phases.

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Fig. 1: Crystal structure and electronic band structure of monolayer NbSe2.
The alternative text for this image may have been generated using AI.
Fig. 2: Faithful OA and fictitious UA limits of the quasi-flat band of NbSe2.
The alternative text for this image may have been generated using AI.
Fig. 3: Extracting the orbital correlators from STM.
The alternative text for this image may have been generated using AI.
Fig. 4: Identifying the C3z-symmetric sites using dilute TMD alloys.
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Data availability

All data presented and generated in this study are included in the main text and Supplementary Information. Further simulated or experimental data are available from the authors upon reasonable request.

Code availability

The code required for reproducing the figures is available from the authors upon reasonable request.

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Acknowledgements

We thank Y. Xu for collaboration on a related project45 as well as E. Moroşan, J. Herzog-Arbeitman and R. L. Lee for useful discussions. D.C. acknowledges support from the DOE (Grant no. DE-SC0016239) and the hospitality of the Donostia International Physics Center (DIPC), where this work was carried out. D.C. also gratefully acknowledges the support provided by the Leverhulme Trust and the support from the UKRI Horizon Europe Guarantee (Grant no. EP/Z002419/1 for a European Research Council Consolidator Grant to S. A. Parameswaran). Y.J. and H.H. were supported by the European Research Council under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement no. 101020833) and by the IKUR Strategy under the collaboration agreement between Ikerbasque Foundation and DIPC on behalf of the Department of Education of the Basque Government. B.A.B. was supported by the Gordon and Betty Moore Foundation (Grant no. GBMF8685 towards the Princeton theory programme), the Gordon and Betty Moore Foundation’s EPiQS Initiative (Grant no. GBMF11070), the Office of Naval Research (Grant no. N00014-20-1-2303), the Global Collaborative Network Grant at Princeton University, a Simons Investigator Grant (no. 404513), the BSF Israel US foundation (Grant no. 2018226), the NSF-MERSEC (Grant no. MERSEC DMR 2011750), the Simons Collaboration on New Frontiers in Superconductivity, the Princeton Catalysis Initiative (PCI), and the Schmidt Foundation at Princeton University. J.Y.’s work at Princeton University is supported by the Gordon and Betty Moore Foundation (Grant no. GBMF8685 towards the Princeton theory programme). J.Y.’s work at the University of Florida is supported by startup funds from the University of Florida. M.M.U. acknowledges support from the European Union’s European Research Council Starting grant LINKSPM (Grant no. 758558) and from the Spanish Ministry of Science, Innovation and Universities (Grant no. PID2023-153277NB-I00). H.G. acknowledges funding from the EU NextGenerationEU/PRTR-C17.I1 and from the IKUR Strategy under the collaboration agreement between Ikerbasque Foundation and DIPC on behalf of the Department of Education of the Basque Government. F.d.J. acknowledges support from the Spanish Ministry of Science, Innovation and Universities (Grant no. PID2021-128760NB-I00). S.S. and Y.W. acknowledge enrolment in the doctorate programme Physics of Nanostructures and Advanced Materials from the Advanced Polymers and Materials, Physics, Chemistry and Technology Department of the Universidad del País Vasco.

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Author notes

  1. These authors contributed equally: Dumitru Călugăru, Yi Jiang, Haojie Guo.

Authors and Affiliations

  1. Department of Physics, Princeton University, Princeton, NJ, USA

    Dumitru Călugăru, Haoyu Hu, Jiabin Yu & B. Andrei Bernevig

  2. Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, UK

    Dumitru Călugăru

  3. Donostia International Physics Center (DIPC), Donostia-San Sebastián, Spain

    Yi Jiang, Haojie Guo, Sandra Sajan, Yongsong Wang, Haoyu Hu, B. Andrei Bernevig, Fernando de Juan & Miguel M. Ugeda

  4. Department of Physics, University of Florida, Gainesville, FL, USA

    Jiabin Yu

  5. IKERBASQUE, Basque Foundation for Science, Bilbao, Spain

    B. Andrei Bernevig, Fernando de Juan & Miguel M. Ugeda

  6. Centro de Física de Materiales (CSIC-UPV/EHU), San Sebastián, Spain

    Miguel M. Ugeda

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Contributions

D.C., Y.J., B.A.B. and M.M.U. conceived the study and developed the method for extracting interorbital correlators from STM data. H.G., S.S., Y.W. and M.M.U. synthesized the samples and performed the measurements. Y.J. carried out the ab initio simulations. D.C., Y.J., H.H., F.d.J., J.Y. and B.A.B. performed the theoretical calculations and subsequently analysed the experimental data along with M.M.U. D.C., Y.J., H.G. and Y.W. prepared the initial draft, and D.C. and Y.J. wrote the Supplementary Information, with input from all authors. All authors contributed to the revision and editing of the final paper.

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Correspondence to B. Andrei Bernevig, Fernando de Juan or Miguel M. Ugeda.

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Extended data

Extended Data Fig. 1 Bias-dependent contrast maps in NbSe2.

(a) shows a large-bias-range differential conductance (\(\frac{dI}{dV}\)) curve for monolayer NbSe2 consistent with previously reported results32,35. The edges of the quasi-flat OA band are delimited by the V1 and C1 peaks, while the band edges of the lower valence bands of NbSe2 are labeled by V2 and V3. The inset shows a zoom-in \(\frac{dI}{dV}\) curve with higher resolution acquired near the V1 region. The spatially-resolved constant-height conductance maps at two bias voltages are illustrated in (b). (c) plots the spatially-averaged conductance at the three C3z-symmetric sites (colored dots) for various bias voltages acquired in two different experiments. The error bars quantify the spreads of the relative conductance values and are computed as explained in the Methods. The conductance is compared with the ab initio spectral function \({\mathcal{A}}(\bf{r},\omega )\) computed at the same C3z-symmetric positions for two different tip heights (z/Å = 4.4, 5.3). The conductance (spectral function) is normalized to one at the 1a site. Stabilization parameters set: (a) Vs = − 2 V, It = 0.8 nA, Vac = 3.5 mV. (b) Vs = − 2 V, It = 2 nA.

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Supplementary Information Sections I–IV, including Figs. 1–12 and Tables 1 and 2.

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Călugăru, D., Jiang, Y., Guo, H. et al. Observation of an obstructed atomic band in a transition metal dichalcogenide. Nat. Phys. 22, 686–691 (2026). https://doi.org/10.1038/s41567-026-03196-5

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