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Charge density wave in a band insulator
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  • Published: 09 June 2026

Charge density wave in a band insulator

  • Md Shafayat Hossain  ORCID: orcid.org/0000-0002-3744-58771,2,3,4 na1,
  • Wenhao Liu  ORCID: orcid.org/0000-0001-9757-10775 na1,
  • Yuqi Zhang6,7,8 na1,
  • Qi Zhang2,
  • Chao Lei  ORCID: orcid.org/0000-0002-7249-95399,
  • Nana Shumiya2,
  • Kouta Dagnino  ORCID: orcid.org/0009-0006-6284-879710,
  • Maksim Litskevich  ORCID: orcid.org/0000-0003-3049-65212,
  • Yu-Xiao Jiang  ORCID: orcid.org/0000-0002-7958-31002,
  • Jia-Xin Yin  ORCID: orcid.org/0000-0003-2661-42062,
  • Nikhil Dhale5,
  • Zijia Cheng  ORCID: orcid.org/0000-0002-9473-77532,
  • Byunghoon Kim  ORCID: orcid.org/0000-0001-8949-48332,
  • Yongkai Li6,7,8,
  • Tyler A. Cochran  ORCID: orcid.org/0000-0003-1745-84672,
  • Xian P. Yang  ORCID: orcid.org/0000-0002-5019-374X2,
  • Fan Zhang  ORCID: orcid.org/0000-0003-4623-42005,
  • Yugui Yao  ORCID: orcid.org/0000-0003-3544-37876,7,
  • Zhiwei Wang  ORCID: orcid.org/0000-0003-0182-24716,7,8,
  • Bing Lv  ORCID: orcid.org/0000-0002-9491-51775,
  • Titus Neupert10,
  • Luis Balicas  ORCID: orcid.org/0000-0002-5209-029311 &
  • …
  • M. Zahid Hasan  ORCID: orcid.org/0000-0001-9730-31282 

Nature Communications (2026) Cite this article

We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply.

Subjects

  • Phase transitions and critical phenomena
  • Topological matter

Abstract

Charge-density-wave implies a periodic modulation of the charge density. Typically observed in metallic systems, charge-density-wave arise from Fermi surface instabilities, resulting in the total or partial gapping of the Fermi surface. Here, we present experimental evidence for a charge-density-wave state emerging in a band insulator which has no Fermi surface. The bulk and surface of our material platform, \({\rm{\alpha }}\)-Bi4Br4, is gapped over the entire Brillouin zone. Through topographic and spectroscopic imaging at low temperatures, we unveil an unexpected unidirectional charge modulation in \({\rm{\alpha }}\)-Bi4Br4, breaking the lattice translation symmetry. The charge-density-wave develops at temperatures below 40 K and adds an energy gap atop the existing insulating gap of \({\boldsymbol{\alpha }}\)-Bi4Br4. Furthermore, our transport measurements reveal nonlinear electrical conduction, a phenomenon conventionally associated with the sliding or phason mode of incommensurate charge-density-waves. These unusual observations represent a different type of charge-density-wave.

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Acknowledgements

We acknowledge illuminating discussions with C. Yoon. M.Z.H. group acknowledges primary support from the US Department of Energy (DOE), Office of Science, National Quantum Information Science Research Centers, Quantum Science Center (at ORNL) and Princeton University; STM Instrumentation support from the Gordon and Betty Moore Foundation (GBMF9461) and the theory work; and support from the US DOE under the Basic Energy Sciences programme (grant number DOE/BES DE-FG-02-05ER46200) for the theory and sample characterization work including ARPES. M.S.H. acknowledges support from Samueli Foundation, and the UCLA Council on Research. L.B. is supported by the United States Department of Energy under the Basic Energy Sciences programme through grant no. DE-SC0002613. The National High Magnetic Field Laboratory acknowledges support from the United States National Science Foundation cooperative agreement grant no. DMR-1644779 and the state of Florida. The crystal growth at the University of Texas at Dallas acknowledges the support by the US Air Force Office of Scientific Research (AFOSR) (FA9550-19-1-0037), National Science Foundation (NSF) (DMREF-2324033 and 2516364) and Office of Naval Research (ONR) (N00014-23-1-2020). T.N. acknowledges support from the Swiss National Science Foundation through a Consolidator Grant (iTQC, TMCG-2_213805). Crystal growth at Beijing Institute of Technology is supported by the National Science Foundation of China (NSFC) (Grant No: 92065109), the National Key R&D Program of China (Grant Nos: 2020YFA0308800, 2022YFA1403400), the Beijing National Laboratory for Condensed Matter Physics (Grant No. 2023BNLCMPKF007), the Zhenjiang Science&Technology Program (Grant No. JC2024003), Y.G.Y. is supported by the National Science Foundation of China (NSFC) (Grant Nos: 12321004, 12234003). Z.W. thanks the Analysis & Testing Center at BIT for assistance in facility support. FZ acknowledges support from the Welch Foundation under Grant No. AT-2264-20250403.

Author information

Author notes
  1. These authors contributed equally: Md Shafayat Hossain, Wenhao Liu, Yuqi Zhang.

Authors and Affiliations

  1. Department of Materials Science and Engineering, University of California, Los Angeles, CA, USA

    Md Shafayat Hossain

  2. Laboratory for Topological Quantum Matter and Advanced Spectroscopy, Department of Physics, Princeton University, Princeton, NJ, USA

    Md Shafayat Hossain, Qi Zhang, Nana Shumiya, Maksim Litskevich, Yu-Xiao Jiang, Jia-Xin Yin, Zijia Cheng, Byunghoon Kim, Tyler A. Cochran, Xian P. Yang & M. Zahid Hasan

  3. California NanoSystems Institute, University of California, Los Angeles, Los Angeles, USA

    Md Shafayat Hossain

  4. Center for Quantum Science and Engineering, University of California, Los Angeles, Los Angeles, USA

    Md Shafayat Hossain

  5. Department of Physics, University of Texas at Dallas, Richardson, TX, USA

    Wenhao Liu, Nikhil Dhale, Fan Zhang & Bing Lv

  6. Centre for Quantum Physics, Key Laboratory of Advanced Optoelectronic, Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing, China

    Yuqi Zhang, Yongkai Li, Yugui Yao & Zhiwei Wang

  7. Beijing Key Lab of Nanophotonics and Ultrafine Optoelectronic Systems, Beijing Institute of Technology, Beijing, China

    Yuqi Zhang, Yongkai Li, Yugui Yao & Zhiwei Wang

  8. Material Science Center, Yangtze Delta Region Academy of Beijing Institute of Technology, Jiaxing, China

    Yuqi Zhang, Yongkai Li & Zhiwei Wang

  9. Department of Physics, The University of Texas at Austin, Austin, TX, USA

    Chao Lei

  10. Department of Physics, University of Zurich, Winterthurerstrasse, Zurich, Switzerland

    Kouta Dagnino & Titus Neupert

  11. Department of Physics and Astronomy, Baylor University, Waco, TX, USA

    Luis Balicas

Authors
  1. Md Shafayat Hossain
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  2. Wenhao Liu
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  9. Yu-Xiao Jiang
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  10. Jia-Xin Yin
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  14. Yongkai Li
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  18. Yugui Yao
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  20. Bing Lv
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  21. Titus Neupert
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  23. M. Zahid Hasan
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Corresponding authors

Correspondence to Md Shafayat Hossain, Zhiwei Wang, Bing Lv or M. Zahid Hasan.

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The authors declare no competing interests.

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Cite this article

Hossain, M.S., Liu, W., Zhang, Y. et al. Charge density wave in a band insulator. Nat Commun (2026). https://doi.org/10.1038/s41467-026-71570-1

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  • Received: 07 May 2024

  • Accepted: 23 March 2026

  • Published: 09 June 2026

  • DOI: https://doi.org/10.1038/s41467-026-71570-1

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