Imaging two-dimensional generalized Wigner crystals

Hongyuan Li^#^{1

2

3}, Shaowei Li^#^{4

5

6

7}, Emma C Regan^{1

2

3}, Danqing Wang^{1

2}, Wenyu Zhao¹, Salman Kahn^{1

3}, Kentaro Yumigeta⁸, Mark Blei⁸, Takashi Taniguchi⁹, Kenji Watanabe¹⁰, Sefaattin Tongay⁸, Alex Zettl^{1

3

11}, Michael F Crommie^{12

13

14}, Feng Wang^{15

16

17}

Affiliations

¹ Department of Physics, University of California at Berkeley, Berkeley, CA, USA.
² Graduate Group in Applied Science and Technology, University of California at Berkeley, Berkeley, CA, USA.
³ Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
⁴ Department of Physics, University of California at Berkeley, Berkeley, CA, USA. shaoweili@ucsd.edu.
⁵ Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA. shaoweili@ucsd.edu.
⁶ Kavli Energy Nano Sciences Institute at the University of California Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, CA, USA. shaoweili@ucsd.edu.
⁷ Department of Chemistry and Biochemistry, University of California at San Diego, La Jolla, CA, USA. shaoweili@ucsd.edu.
⁸ School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, USA.
⁹ International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan.
¹⁰ Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan.
¹¹ Kavli Energy Nano Sciences Institute at the University of California Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
¹² Department of Physics, University of California at Berkeley, Berkeley, CA, USA. crommie@berkeley.edu.
¹³ Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA. crommie@berkeley.edu.
¹⁴ Kavli Energy Nano Sciences Institute at the University of California Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, CA, USA. crommie@berkeley.edu.
¹⁵ Department of Physics, University of California at Berkeley, Berkeley, CA, USA. fengwang76@berkeley.edu.
¹⁶ Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA. fengwang76@berkeley.edu.
¹⁷ Kavli Energy Nano Sciences Institute at the University of California Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, CA, USA. fengwang76@berkeley.edu.

^# Contributed equally.

PMID: 34588665
DOI: 10.1038/s41586-021-03874-9

Free article

Imaging two-dimensional generalized Wigner crystals

Hongyuan Li et al. Nature. 2021 Sep.

Free article

. 2021 Sep;597(7878):650-654.

doi: 10.1038/s41586-021-03874-9. Epub 2021 Sep 29.

Authors

Affiliations

¹ Department of Physics, University of California at Berkeley, Berkeley, CA, USA.
² Graduate Group in Applied Science and Technology, University of California at Berkeley, Berkeley, CA, USA.
³ Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
⁴ Department of Physics, University of California at Berkeley, Berkeley, CA, USA. shaoweili@ucsd.edu.
⁵ Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA. shaoweili@ucsd.edu.
⁶ Kavli Energy Nano Sciences Institute at the University of California Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, CA, USA. shaoweili@ucsd.edu.
⁷ Department of Chemistry and Biochemistry, University of California at San Diego, La Jolla, CA, USA. shaoweili@ucsd.edu.
⁸ School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, USA.
⁹ International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan.
¹⁰ Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan.
¹¹ Kavli Energy Nano Sciences Institute at the University of California Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
¹² Department of Physics, University of California at Berkeley, Berkeley, CA, USA. crommie@berkeley.edu.
¹³ Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA. crommie@berkeley.edu.
¹⁴ Kavli Energy Nano Sciences Institute at the University of California Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, CA, USA. crommie@berkeley.edu.
¹⁵ Department of Physics, University of California at Berkeley, Berkeley, CA, USA. fengwang76@berkeley.edu.
¹⁶ Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA. fengwang76@berkeley.edu.
¹⁷ Kavli Energy Nano Sciences Institute at the University of California Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, CA, USA. fengwang76@berkeley.edu.

^# Contributed equally.

PMID: 34588665
DOI: 10.1038/s41586-021-03874-9

Abstract

The Wigner crystal¹ has fascinated condensed matter physicists for nearly 90 years^2-14. Signatures of two-dimensional (2D) Wigner crystals were first observed in 2D electron gases under high magnetic field^2-4, and recently reported in transition metal dichalcogenide moiré superlattices^6-9. Direct observation of the 2D Wigner crystal lattice in real space, however, has remained an outstanding challenge. Conventional scanning tunnelling microscopy (STM) has sufficient spatial resolution but induces perturbations that can potentially alter this fragile state. Here we demonstrate real-space imaging of 2D Wigner crystals in WSe₂/WS₂ moiré heterostructures using a specially designed non-invasive STM spectroscopy technique. This employs a graphene sensing layer held close to the WSe₂/WS₂ moiré superlattice. Local STM tunnel current into the graphene layer is modulated by the underlying Wigner crystal electron lattice in the WSe₂/WS₂ heterostructure. Different Wigner crystal lattice configurations at fractional electron fillings of n = 1/3, 1/2 and 2/3, where n is the electron number per site, are directly visualized. The n = 1/3 and n = 2/3 Wigner crystals exhibit triangular and honeycomb lattices, respectively, to minimize nearest-neighbour occupations. The n = 1/2 state spontaneously breaks the original C3 symmetry and forms a stripe phase. Our study lays a solid foundation for understanding Wigner crystal states in WSe₂/WS₂ moiré heterostructures and provides an approach that is generally applicable for imaging novel correlated electron lattices in other systems.

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Comment in

This is what a solid made of electrons looks like.
Castelvecchi D. Castelvecchi D. Nature. 2021 Oct;598(7879):21. doi: 10.1038/d41586-021-02657-6. Nature. 2021. PMID: 34588654 No abstract available.

References

1. Wigner, E. On the interaction of electrons in metals. Phys. Rev. 46, 1002–1011 (1934). - DOI
1. Goldman, V., Santos, M., Shayegan, M. & Cunningham, J. Evidence for two-dimentional quantum Wigner crystal. Phys. Rev. Lett. 65, 2189–2192 (1990). - DOI
1. Jang, J., Hunt, B. M., Pfeiffer, L. N., West, K. W. & Ashoori, R. C. Sharp tunnelling resonance from the vibrations of an electronic Wigner crystal. Nat. Phys. 13, 340–344 (2017). - DOI
1. Zhou, H., Polshyn, H., Taniguchi, T., Watanabe, K. & Young, A. Solids of quantum Hall skyrmions in graphene. Nat. Phys. 16, 154–158 (2020). - DOI
1. Shapir, I. et al. Imaging the electronic Wigner crystal in one dimension. Science 364, 870–875 (2019). - DOI

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Imaging two-dimensional generalized Wigner crystals

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Imaging two-dimensional generalized Wigner crystals

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