Observation of an obstructed atomic band in a transition metal dichalcogenide

Nature Physics (2026)Cite this article 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.This is a preview of subscription content, access via your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription $32.99 / 30 days cancel any timeSubscribe to this journal Receive 12 print issues and online access $259.00 per yearonly $21.58 per issueBuy this articleUSD 39.95Prices may be subject to local taxes which are calculated during checkoutAll 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.The code required for reproducing the figures is available from the authors upon reasonable request.Marzari, N., Mostofi, A. A., Yates, J. R., Souza, I. & Vanderbilt, D. Maximally localized Wannier functions: theory and applications. Rev. Mod. Phys. 84, 1419 (2012).Article ADS Google Scholar Brouder, C., Panati, G., Calandra, M., Mourougane, C. & Marzari, N. Exponential localization of Wannier functions in insulators. Phys. Rev. Lett. 98, 046402 (2007).Article ADS Google Scholar Soluyanov, A. A. & Vanderbilt, D. Wannier representation of \({{\mathbb{z}}}_{2}\) topological insulators. Phys. Rev. B 83, 035108 (2011).Article ADS Google Scholar Bradlyn, B. et al. Topological quantum chemistry. Nature 547, 298 (2017).Article ADS Google Scholar Elcoro, L. et al. Magnetic topological quantum chemistry. Nat. Commun. 12, 5965 (2021).Article ADS Google Scholar Kruthoff, J., de Boer, J., van Wezel, J., Kane, C. L. & Slager, R.-J. Topological classification of crystalline insulators through band structure combinatorics. Phys. Rev. X 7, 041069 (2017).

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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.These authors contributed equally: Dumitru Călugăru, Yi Jiang, Haojie Guo.Department of Physics, Princeton University, Princeton, NJ, USADumitru Călugăru, Haoyu Hu, Jiabin Yu & B. Andrei BernevigRudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, UKDumitru CălugăruDonostia International Physics Center (DIPC), Donostia-San Sebastián, SpainYi Jiang, Haojie Guo, Sandra Sajan, Yongsong Wang, Haoyu Hu, B. Andrei Bernevig, Fernando de Juan & Miguel M. UgedaDepartment of Physics, University of Florida, Gainesville, FL, USAJiabin YuIKERBASQUE, Basque Foundation for Science, Bilbao, SpainB. Andrei Bernevig, Fernando de Juan & Miguel M. UgedaCentro de Física de Materiales (CSIC-UPV/EHU), San Sebastián, SpainMiguel M. UgedaSearch 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 ScholarD.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.Correspondence to B. Andrei Bernevig, Fernando de Juan or Miguel M. Ugeda.The authors declare no competing interests.Nature Physics thanks Sathwik Bharadwaj, Weida Wu 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) 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.Supplementary Information Sections I–IV, including Figs. 1–12 and Tables 1 and 2.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 permissionsCălugăru, D., Jiang, Y., Guo, H. et al. Observation of an obstructed atomic band in a transition metal dichalcogenide. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03196-5Download citationReceived: 27 January 2025Accepted: 28 January 2026Published: 31 March 2026Version of record: 31 March 2026DOI: https://doi.org/10.1038/s41567-026-03196-5Anyone you share the following link with will be able to read this content:Sorry, a shareable link is not currently available for this article. 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