Local probe of bulk and edge states in a fractional Chern insulator

Zhurun Ji; Heonjoon Park; Mark E Barber; Chaowei Hu; Kenji Watanabe; Takashi Taniguchi; Jiun-Haw Chu; Xiaodong Xu; Zhi-Xun Shen

doi:10.1038/s41586-024-08092-7

Local probe of bulk and edge states in a fractional Chern insulator

Nature. 2024 Nov;635(8039):578-583. doi: 10.1038/s41586-024-08092-7. Epub 2024 Nov 20.

Authors

Zhurun Ji^#^{1

2

3}, Heonjoon Park^#⁴, Mark E Barber^{1

2

3}, Chaowei Hu⁴, Kenji Watanabe^{5

6}, Takashi Taniguchi^{5

6}, Jiun-Haw Chu⁴, Xiaodong Xu^{7

8}, Zhi-Xun Shen^{9

10

11

12}

Affiliations

¹ Department of Physics, Stanford University, Stanford, CA, USA.
² Department of Applied Physics, Stanford University, Stanford, CA, USA.
³ Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA.
⁴ Department of Physics, University of Washington, Seattle, WA, USA.
⁵ Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan.
⁶ Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan.
⁷ Department of Physics, University of Washington, Seattle, WA, USA. xuxd@uw.edu.
⁸ Department of Materials Science and Engineering, University of Washington, Seattle, WA, USA. xuxd@uw.edu.
⁹ Department of Physics, Stanford University, Stanford, CA, USA. zxshen@stanford.edu.
¹⁰ Department of Applied Physics, Stanford University, Stanford, CA, USA. zxshen@stanford.edu.
¹¹ Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA. zxshen@stanford.edu.
¹² Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA, USA. zxshen@stanford.edu.

^# Contributed equally.

PMID: 39567787
DOI: 10.1038/s41586-024-08092-7

Abstract

The fractional quantum Hall effect is a key example of topological quantum many-body phenomena, arising from the interplay between strong electron correlation, topological order and time-reversal symmetry breaking. Recently, a lattice analogue of the fractional quantum Hall effect at zero magnetic field has been observed, confirming the existence of a zero-field fractional Chern insulator (FCI). Despite this, the bulk-edge correspondence-a hallmark of a FCI featuring an insulating bulk with conductive edges-has not been directly observed. In fact, this correspondence has not been visualized in any system for fractional states owing to experimental challenges. Here we report the imaging of FCI edge states in twisted MoTe₂ (t-MoTe₂) using microwave impedance microscopy¹. By tuning the carrier density, we observe the system evolving between metallic and FCI states, the latter of which exhibits insulating bulk and conductive edges, as expected from the bulk-boundary correspondence. Further analysis suggests the composite nature of the FCI edge states. We also observe the evolution of edge states across the topological phase transition as a function of interlayer electric field and reveal exciting prospects of neighbouring domains with different fractional orders. These findings pave the way for research into topologically protected one-dimensional interfaces between various anyonic states at zero magnetic field, such as gapped one-dimensional symmetry-protected phases with non-zero topological entanglement entropy, Halperin-Laughlin interfaces and the creation of non-abelian anyons.