# Odd- and even-denominator fractional quantum Hall states in monolayer WSe2

## Abstract

Monolayer semiconducting transition-metal dichalcogenides (TMDs) represent a unique class of two-dimensional (2D) electron systems. Their atomically thin structure facilitates gate tunability just like graphene does, but unlike graphene, TMDs have the advantage of a sizable band gap and strong spin–orbit coupling. Measurements under large magnetic fields have revealed an unusual Landau level (LL) structure1,2,3, distinct from other 2D electron systems. However, owing to the limited sample quality and poor electrical contact, probing the lowest LLs has been challenging, and observation of electron correlations within the fractionally filled LL regime has not been possible. Here, through bulk electronic compressibility measurements, we investigate the LL structure of monolayer WSe2 in the extreme quantum limit, and observe fractional quantum Hall states in the lowest three LLs. The odd-denominator fractional quantum Hall sequences demonstrate a systematic evolution with the LL orbital index, consistent with generic theoretical expectations. In addition, we observe an even-denominator state in the second LL that is expected to host non-Abelian statistics. Our results suggest that the 2D semiconductors can provide an experimental platform that closely resembles idealized theoretical models in the quantum Hall regime.

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## Data availability

The data that support the plots within this paper and other findings of this study are available at https://doi.org/10.5518/807.

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## Acknowledgements

We thank M. Goerbig, A. Kormanyos and F. Zhang for discussion, and W. Coniglio and B. Pullum for help with experiments. This research is primarily supported by the US Department of Energy (DE-SC0016703). Synthesis of WSe2 (D.R. and B.K.) was supported by the Center for Precision Assembly of Superstratic and Superatomic Solids, a Materials Science and Engineering Research Center (MRSEC), through NSF grant DMR-1420634. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by National Science Foundation Cooperative Agreement no. DMR-1157490 and the state of Florida. Z.P. acknowledges support by EPSRC grant EP/R020612/1. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan and the CREST (JPMJCR15F3), JST.

## Author information

Authors

### Contributions

Q.S. fabricated the device with the help of E.S.; M.V.G. contributed to the development of the measurement set-up. Q.S. performed the measurements and analysed the data. Z.P. performed the numerical calculations. D.A.R. and B.K. grew the WSe2 crystals. K.W. and T.T. grew the hBN crystals. J.H. and C.R.D. advised on the experiments. The manuscript was written with input from all authors.

### Corresponding author

Correspondence to Cory R. Dean.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Nanotechnology thanks Jinfeng Jia and the other, anonymous, reviewers for their contribution to the peer review of this work.

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## Supplementary information

### Supplementary Information

Supplementary discussion, Figs. 1–10 and refs. 1–49.

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Shi, Q., Shih, E., Gustafsson, M.V. et al. Odd- and even-denominator fractional quantum Hall states in monolayer WSe2. Nat. Nanotechnol. 15, 569–573 (2020). https://doi.org/10.1038/s41565-020-0685-6

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