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Mapping charge excitations in generalized Wigner crystals

Nature Nanotechnology (2024)Cite this article

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Abstract

Transition metal dichalcogenide-based moiré superlattices exhibit strong electron–electron correlations, thus giving rise to strongly correlated quantum phenomena such as generalized Wigner crystal states. Evidence of Wigner crystals in transition metal dichalcogenide moire superlattices has been widely reported from various optical spectroscopy and electrical conductivity measurements, while their microscopic nature has been limited to the basic lattice structure. Theoretical studies predict that unusual quasiparticle excitations across the correlated gap between upper and lower Hubbard bands can arise due to long-range Coulomb interactions in generalized Wigner crystal states. However, the microscopic proof of such quasiparticle excitations is challenging because of the low excitation energy of the Wigner crystal. Here we describe a scanning single-electron charging spectroscopy technique with nanometre spatial resolution and single-electron charge resolution that enables us to directly image electron and hole wavefunctions and to determine the thermodynamic gap of generalized Wigner crystal states in twisted WS2 moiré heterostructures. High-resolution scanning single-electron charging spectroscopy combines scanning tunnelling microscopy with a monolayer graphene sensing layer, thus enabling the generation of individual electron and hole quasiparticles in generalized Wigner crystals. We show that electron and hole quasiparticles have complementary wavefunction distributions and that thermodynamic gaps of ∼50 meV exist for the 1/3 and 2/3 generalized Wigner crystal states in twisted WS2.

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Fig. 1: SSEC measurement of a t-WS2 moiré superlattice.
Fig. 2: Scanning tunnelling spectroscopy study of quasiparticle excitations in generalized Wigner crystals.
Fig. 3: Mapping electron and hole excitations of the n = 2/3 generalized Wigner crystal.

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Data availability

The data supporting the findings of this study are included in the main text and in the Supplementary Information files, and are also available at https://github.com/HongyuanLiCMP/Mapping-Charge-Excitations-in-Generalized-Wigner-Crystals.

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Acknowledgements

This work was primarily funded by the US Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under contract number DE-AC02-05-CH11231 (van der Waals heterostructure program KCFW16) (device electrode preparation and STM spectroscopy). Support was also provided by the US Army Research Office under MURI award W911NF-17-1-0312 (device layer transfer) and by National Science Foundation (NSF) award DMR-1807233 (surface preparation). S.T acknowledges support from DOE-SC0020653 (materials synthesis), NSF DMR-1955889 (magnetic measurements), NSF CMMI-1933214, NSF 2206987, NSF ECCS 2052527, DMR 2111812 and CMMI 2129412. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan (grant number JPMXP0112101001), the Japan Society for the Promotion of Science (JSPS) KAKENHI (grant number JP20H00354) and the Core Research for Evolutional Science and Technology (CREST) (JPMJCR15F3), Japan Science and Technology Agency (JST) for bulk hBN crystal growth and analysis.

Author information

Author notes

  1. These authors contributed equally: Hongyuan Li, Ziyu Xiang.

Authors and Affiliations

  1. Department of Physics, University of California at Berkeley, Berkeley, CA, USA

    Hongyuan Li, Ziyu Xiang, Emma Regan, Wenyu Zhao, Alex Zettl, Michael F. Crommie & Feng Wang

  2. Graduate Group in Applied Science and Technology, University of California at Berkeley, Berkeley, CA, USA

    Hongyuan Li, Ziyu Xiang & Emma Regan

  3. Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Hongyuan Li, Ziyu Xiang, Emma Regan, Alex Zettl, Michael F. Crommie & Feng Wang

  4. School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, USA

    Renee Sailus, Rounak Banerjee & Sefaattin Tongay

  5. International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan

    Takashi Taniguchi

  6. Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan

    Kenji Watanabe

  7. Kavli Energy NanoScience Institute at the University of California at Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Alex Zettl, Michael F. Crommie & Feng Wang

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Contributions

H.L., M.F.C. and F.W. conceived the project. H.L. and Z.X. performed the STM measurement. H.L., Z.X., E.R. and W.Z. fabricated the heterostructure device. H.L., Z.X., A.Z., M.F.C. and F.W. discussed the experimental design and analyzed the experimental data. R.S., R.B. and S.T. grew the WS2 crystals. K.W. and T.T. grew the hBN single crystal. All authors discussed the results and wrote the paper.

Corresponding authors

Correspondence to Michael F. Crommie or Feng Wang.

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Nature Nanotechnology thanks the anonymous reviewer(s) for their contribution to the peer review of this work.

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Supplementary Information

Supplementary Figs. 1–12 and Discussion.

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Li, H., Xiang, Z., Regan, E. et al. Mapping charge excitations in generalized Wigner crystals. Nat. Nanotechnol. (2024). https://doi.org/10.1038/s41565-023-01594-x

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