# Pairing states of composite fermions in double-layer graphene

## Abstract

Heterostructures of vertically stacked graphene double layers, separated by a thin tunnel barrier, provide a highly tunable system to explore strongly interacting electron states. This is because the interlayer Coulomb interactions can be sensitively tuned simply by varying the barrier thickness. Recent studies of double-layer graphene have shown that, in the quantum Hall effect regime, strong interlayer coupling can induce electron–hole pairing across the two layers, resulting in a superfluid phase of interlayer excitons1,2,3. Here, we report a series of emergent fractional quantum Hall effect (FQHE) states appearing under similar conditions. We find excellent agreement between the sequence of observable FQHE states and the theoretically proposed two-component composite-fermion (CF) model, where the CF quasiparticle construction results from both interlayer and intralayer interactions4,5. Most remarkably, we observe an additional series of incompressible states at fractional filling that do not fit within either the single- or two-component CF models. We interpret these states to result from residual pairing interactions between CFs, representing a new type of correlated ground state that is unique to graphene double-layer structures and not described by the conventional CF model.

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## Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author on reasonable request.

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## Acknowledgements

This work was supported by the National Science Foundation (DMR-1507788) and by the David and Lucille Packard Foundation. Data analysis was partially supported by the US Department of Energy (DE-SC0016703). 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.

## Author information

Authors

### Contributions

J.I.A.L. and C.R.D. designed the experiment. Experimental work and analysis was carried out by J.I.A.L., Q.S. and Y.Z., advised by J.H. and C.R.D. All authors contributed to writing the manuscript.

### Corresponding author

Correspondence to C. R. Dean.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information: Nature Physics thanks G. J. Sreejith, Emanuel Tutuc and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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## Supplementary information

### Supplementary Information

Supplementary Figs. 1–6, Supplementary Refs. 1–3 and additional experimental and theoretical details.

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Li, J.I.A., Shi, Q., Zeng, Y. et al. Pairing states of composite fermions in double-layer graphene. Nat. Phys. 15, 898–903 (2019). https://doi.org/10.1038/s41567-019-0547-z

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