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Fractional quantization in insulators from Hall to Chern

Nature Physics volume 21, pages 1702–1713 (2025)Cite this article

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Abstract

The discovery of the integer and fractional quantum Hall effects naturally prompted the question of whether these effects can be realized without a magnetic field. Answering this is fundamentally important and requires a synthesis of the concepts of band topology, quantum geometry and electronic correlations. Here we summarize the basic concepts of both fractional Chern and fractional topological insulators and illustrate them with the theoretical lattice models that support the flat Chern bands in which the states were first predicted. We then examine their experimental realizations in twisted bilayer transition metal dichalcogenides and moiré rhombohedral few-layer graphene. We also discuss the future challenges and opportunities in this research field.

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Fig. 1: Schematic illustrations of quantized Hall effects.
Fig. 2: Electronic properties of moiré TMDs.
Fig. 3: FCI, FQAH and evidence for FQSH in moiré MoTe2.
Fig. 4: FQAH and FCIs in moiré rhombohedral graphene.
Fig. 5: Theory for FCIs in moiré rhombohedral graphene.

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Acknowledgements

B.A.B. was supported by the Gordon and Betty Moore Foundation through grant no. GBMF8685 towards the Princeton theory programme, the EPiQS Initiative of the Gordon and Betty Moore Foundation (grant no. GBMF11070), Simons Investigator grant no. 404513, the Materials Research Science and Engineering Centers of the National Science Foundation (grant no. MRSEC DMR-2011750), the Simons Collaboration on New Frontiers in Superconductivity (grant no. SFI-MPS-NFS-00006741-01), the Princeton collaborative network, the Schmidt Foundation at the Princeton University, the Princeton Catalysis Initiative and the Department of Energy, Office of Science, Basic Energy Sciences, under award no. DE-SC0019481. L.F. was supported by a Simons Investigator Award from the Simons Foundation. L.J. was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under grant no. DE-SC0025325, the Nano & Material Technology Development Program through the National Research Foundation of Korea funded by the Ministry of Science and ICT (RS-2024-004447252) and the MIT Portugal Program. A.H.M. was supported by the Simons Targeted Grant in Mathematics and Physical Sciences on Moiré Materials Magic. K.F.M. and J.S. were supported by the US Department of Energy, Office of Science, Basic Energy Sciences, under award no. DE-SC0019481.

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Authors and Affiliations

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

    B. A. Bernevig

  2. Donostia International Physics Center, Donostia-San Sebastian, Spain

    B. A. Bernevig

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

    B. A. Bernevig

  4. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    L. Fu & L. Ju

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

    A. H. MacDonald

  6. Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany

    K. F. Mak & J. Shan

  7. School of Applied and Engineering Physics and Department of Physics, Cornell University, Ithaca, NY, USA

    K. F. Mak & J. Shan

  8. Kavli Institute at Cornell for Nanoscale Science, Ithaca, NY, USA

    K. F. Mak & J. Shan

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  1. B. A. Bernevig
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  2. L. Fu
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  3. L. Ju
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  4. A. H. MacDonald
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  5. K. F. Mak
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Correspondence to B. A. Bernevig, L. Fu, L. Ju, A. H. MacDonald, K. F. Mak or J. Shan.

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Bernevig, B.A., Fu, L., Ju, L. et al. Fractional quantization in insulators from Hall to Chern. Nat. Phys. 21, 1702–1713 (2025). https://doi.org/10.1038/s41567-025-03072-8

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