# Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice

## Abstract

Studies of two-dimensional electron systems in a strong magnetic field revealed the quantum Hall effect1, a topological state of matter featuring a finite Chern number C and chiral edge states2,3. Haldane4 later theorized that Chern insulators with integer quantum Hall effects could appear in lattice models with complex hopping parameters even at zero magnetic field. The ABC-trilayer graphene/hexagonal boron nitride (ABC-TLG/hBN) moiré superlattice provides an attractive platform with which to explore Chern insulators because it features nearly flat moiré minibands with a valley-dependent, electrically tunable Chern number5,6. Here we report the experimental observation of a correlated Chern insulator in an ABC-TLG/hBN moiré superlattice. We show that reversing the direction of the applied vertical electric field switches the moiré minibands of ABC-TLG/hBN between zero and finite Chern numbers, as revealed by large changes in magneto-transport behaviour. For topological hole minibands tuned to have a finite Chern number, we focus on quarter filling, corresponding to one hole per moiré unit cell. The Hall resistance is well quantized at h/2e2 (where h is Planck’s constant and e is the charge on the electron), which implies C = 2, for a magnetic field exceeding 0.4 tesla. The correlated Chern insulator is ferromagnetic, exhibiting substantial magnetic hysteresis and a large anomalous Hall signal at zero magnetic field. Our discovery of a C = 2 Chern insulator at zero magnetic field should open up opportunities for discovering correlated topological states, possibly with topological excitations7, in nearly flat and topologically nontrivial moiré minibands.

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## Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

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## Acknowledgements

We thank Y. Yu and M. Sui for measurement assistance, and acknowledge discussions with M. Zaletel, E. Altman, J. Jung and M. A. Kastner. G.C. and F.W. were supported as part of the Center for Novel Pathways to Quantum Coherence in Materials, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences. A.L.S. was supported by a National Science Foundation Graduate Research Fellowship and a Ford Foundation Predoctoral Fellowship. The work of E.J.F. and D.G.-G. on this project was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under contract number DE-AC02-76SF00515. Low-temperature infrastructure (dilution fridges) and cryostat support were funded in part by the Gordon and Betty Moore Foundation through grant number GBMF3429. Part of the sample fabrication was conducted at the Nano-fabrication Laboratory at Fudan University. Part of the measurement was performed in Oxford Instrument Nanoscience Shanghai Demo Laboratory. Y.Z. acknowledges financial support from National Key Research Program of China (grant numbers 2016YFA0300703, 2018YFA0305600), NSF of China (grant numbers U1732274, 11527805, 11425415 and 11421404), and the Strategic Priority Research Program of Chinese Academy of Sciences (grant number XDB30000000). Z.S. acknowledges support from National Key Research and Development Program of China (grant number 2016YFA0302001) and National Natural Science Foundation of China (grant number 11574204, 11774224), and additional support from a Shanghai talent programme. T.S. was supported by NSF grant DMR-1608505, and partially through a Simons Investigator Award from the Simons Foundation. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan and the CREST (JPMJCR15F3), JST.

## Author information

F.W. and G.C. conceived the project. F.W., Y.Z., D.G.-G. and T.S. supervised the project. G.C. fabricated samples and performed transport characterizations at temperature above 1 K to first identify the C = 2 quantum Hall states. G.C., A.L.S. and E.J.F. performed ultralow temperature transport measurements. G.C., L.J., B.L., H.L. and Z.S. prepared TLG and performed near-field infrared and atomic force microscope measurements. K.W. and T.T. grew hBN single crystals. Y.-H.Z. and T.S. calculated the band structures and Chern numbers. G.C., A.L.S., E.J.F., Y.-H.Z., T.S., D.G.-G., Y.Z. and F.W. analysed the data. G.C., Y.-H.Z., T.S. and F.W. wrote the paper, with input from all authors.

Correspondence to David Goldhaber-Gordon or Yuanbo Zhang or Feng Wang.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Fan Zheng and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 Identification of ABC-TLG.

a, Atomic force microscope topography image of an exfoliated TLG on SiO2/Si. b, Near-field infrared image corresponding to a, showing that ABC-TLG has different contrast to ABA-TLG.

### Extended Data Fig. 2 Optical images of device I during fabrication.

a, ABC-TLG is identified by near-field infrared spectroscopy and isolated by atomic force microscope tip. b, ABC-TLG is encapsulated by hBN and etched into Hall bar geometry. c, Final device with metal contacts and top and bottom gates.

### Extended Data Fig. 3 Magneto-transport of the Chern insulator state at T = 1.5 K.

a, b, Colour plots of ρxx and ρyx as a function of carrier density and magnetic field at D = −0.5 V nm−1 and T = 1.5 K. The ν = 2 Chern insulator state is well resolved at 1.5 K, which features a minimum for ρxx, and a quantized ρyx emerges from 1/4 filling. c, d, Horizontal line cuts of a and b, respectively. ρyx shows quantized Hall resistance at finite magnetic field.

### Extended Data Fig. 4 Landau fan at D = 0.

Longitudinal resistivity ρxx (colour scale) as a function of carrier density and magnetic field at displacement field D = 0. Clear Landau levels develop from the charge neutrality point and fully filled points at D = 0, which is direct evidence of the high quality of the encapsulated ABC-TLG device described in the main text. The first resolved quantum Hall state of the charge neutrality point is ν = 6. This Landau fan diagram establishes conclusively that we have ABC trilayer graphene in the hBN encapsulated device; it is completely different from the Landau fan diagram of ABA trilayer graphene (see ref. 14).

### Extended Data Fig. 5 Temperature dependence of the ν = 2 state.

ac, Arrhenius plot of longitudinal resistivity (a), conductivity (b) and the estimated gap at different magnetic field (c). A manual offset of −0.15 on the y axis is applied to each curve in a and b. The gap size in c is extracted from the linear fit of $${\sigma }_{xx}\propto {{\rm{e}}}^{-\varDelta /2{k}_{{\rm{B}}}T}$$ (red line) in b. We note that the Arrhenius plot is only valid for a limited temperature range, suggesting deviation from the thermal activated behaviour at low temperatures. Therefore, the estimated gaps have relatively large uncertainty. However, the qualitative behaviour is robust: insulating behaviour is observed at all magnetic fields, and the quantized Hall insulator at finite magnetic field connects smoothly with the anomalous Hall insulator at zero magnetic field, supporting the identification of the state as a Chern insulator.

### Extended Data Fig. 6 Illustration of the ABC-TLG/hBN system.

The bottom hBN layer is nearly aligned with the graphene layers whereas the one on top is not aligned. A and B refer to the two sublattices in each of the graphene layers.

### Extended Data Fig. 7 Basic characterizations of the second device (device II).

a, Optical image of device II. The device is in a standard Hall bar geometry with top and bottom gates. The scale bar is 3 μm. b, Schematic of the moiré pattern existing between top hBN and ABC-TLG for device II. c, Two-dimensional colour plot of Rxx as a function of Vt and Vb at T = 5 K. The moiré exists between the top hBN and ABC-TLG for device II, opposite to that of device I in the main text. This leads to a non-trivial band at positive displacement fields and a trivial band at negative displacement fields.

### Extended Data Fig. 8 Reproducible Chern insulator data for device II.

a, Ferromagnetic anomalous Hall effect at 1/4 filling at 0.3 K and 1.4 K. b, The evolution of $${\rho }_{yx}^{{\rm{AH}}}$$ and Bc as a function of doping (at D = 0.55 V nm−1) and displacement field (at n = n0) at 1.1 K. c, d, Colour plot of ρxx and ρyx as a function of carrier density and magnetic field. Dashed lines represent the ν = 2 state.

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Chen, G., Sharpe, A.L., Fox, E.J. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020). https://doi.org/10.1038/s41586-020-2049-7

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