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Fractional quantum anomalous Hall effect in multilayer graphene

Nature volume 626, pages 759–764 (2024)Cite this article

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Abstract

The fractional quantum anomalous Hall effect (FQAHE), the analogue of the fractional quantum Hall effect1 at zero magnetic field, is predicted to exist in topological flat bands under spontaneous time-reversal-symmetry breaking2,3,4,5,6. The demonstration of FQAHE could lead to non-Abelian anyons that form the basis of topological quantum computation7,8,9. So far, FQAHE has been observed only in twisted MoTe2 at a moiré filling factor v > 1/2 (refs. 10,11,12,13). Graphene-based moiré superlattices are believed to host FQAHE with the potential advantage of superior material quality and higher electron mobility. Here we report the observation of integer and fractional QAH effects in a rhombohedral pentalayer graphene–hBN moiré superlattice. At zero magnetic field, we observed plateaus of quantized Hall resistance \({R}_{xy}=\frac{h}{v{{\rm{e}}}^{2}}\) at v = 1, 2/3, 3/5, 4/7, 4/9, 3/7 and 2/5 of the moiré superlattice, respectively, accompanied by clear dips in the longitudinal resistance Rxx. Rxy equals \(\frac{2h}{{{\rm{e}}}^{2}}\) at v = 1/2 and varies linearly with v, similar to the composite Fermi liquid in the half-filled lowest Landau level at high magnetic fields14,15,16. By tuning the gate-displacement field D and v, we observed phase transitions from composite Fermi liquid and FQAH states to other correlated electron states. Our system provides an ideal platform for exploring charge fractionalization and (non-Abelian) anyonic braiding at zero magnetic field7,8,9,17,18,19, especially considering a lateral junction between FQAHE and superconducting regions in the same device20,21,22.

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Fig. 1: Device configuration, topological flat band and phase diagram of the rhombohedral pentalayer graphene–hBN moiré superlattice.
Fig. 2: IQAHE.
Fig. 3: FQAHEs.
Fig. 4: Anomalous Hall effect and phase transitions at half-filling.

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Data availability

The data shown in the main figures are available from https://doi.org/10.7910/DVN/T4QPNP. Other data that support the findings of this study are available from the corresponding authors upon reasonable request.

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Acknowledgements

We acknowledge helpful discussions with X.G. Wen, T. Senthil, P. Lee, F. Wang and R. Ashoori. We thank D. Laroche for assistance with early investigation of a related sample. L.J. acknowledges support from a Sloan Fellowship. Work by T.H., J.Y. and J.S. was supported by NSF grant no. DMR-2225925. The device fabrication of this work was supported by the STC Center for Integrated Quantum Materials, NSF grant no. DMR-1231319 and was carried out at the Harvard Center for Nanoscale Systems and MIT.Nano. Part of the device fabrication was supported by USD(R&E) under contract no. FA8702-15-D-0001. K.W. and T.T. acknowledge support from the JSPS KAKENHI (grant nos. 20H00354, 21H05233 and 23H02052) and World Premier International Research Center Initiative (WPI), MEXT, Japan. A.P.R. was supported by the Air Force Office of Scientific Research (AFOSR) under award no. FA9550-22-1-0432. L.F. was supported by the STC Center for Integrated Quantum Materials (CIQM) under NSF award no. DMR-1231319.

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  1. These authors contributed equally: Zhengguang Lu, Tonghang Han, Yuxuan Yao

Authors and Affiliations

  1. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Zhengguang Lu, Tonghang Han, Yuxuan Yao, Aidan P. Reddy, Jixiang Yang, Junseok Seo, Liang Fu & Long Ju

  2. Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan

    Kenji Watanabe

  3. Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan

    Takashi Taniguchi

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Contributions

L.J. supervised the project. Z.L. and T.H. performed the d.c. magneto-transport measurement. T.H. and Y.Y. fabricated the devices. J.Y., J.S., Z.L. and T.H. helped with installing and testing the dilution refrigerator. A.P.R. and L.F. performed the calculations. K.W. and T.T. grew hBN crystals. All authors discussed the results and wrote the paper.

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Correspondence to Long Ju.

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Extended data figures and tables

Extended Data Fig. 1 Phase diagram and optical micrographs of our devices.

a&b corresponds to the hole-doping and electron-doping sides, respectively. The hole side shows resistive states at filling factors v = −2 and –4, while the electron side shows correlated insulating states at v = 2, 3 and 4 at D < 0—opposite side of D at which we observed IQAHE and FQAHEs. c. Device 1 from which the data in the main text is taken. Scale bar: 3 µm d. Device 2, the data of which is included in Extended Data Fig. 8 & 9. Scale bar:3 µm.

Extended Data Fig. 2 Gate displacement field dependence of Rxx and Rxy at fractional filling factors for Device 1.

Each FQAH state shows quantized Rxy in a range of D, while the center of this range for different states shifts with the filling factor. The D corresponding to the minimum of Rxx also shifts with the filling factor in the same direction.

Extended Data Fig. 3 Temperature dependence of FQAH states.

a–f. Temperature dependence of Rxy. All states still remain quantized at 400 mK. g–l. Temperature dependence of Rxx.

Extended Data Fig. 4 Symmetrization/anti-symmetrization method to obtain Fig. 1b & c.

a,b & d,e. Raw data of R13,24 and R23,14 measured as functions of displacement field and moiré filling factor v at B = ±100 mT. The insets show the measurement pin configurations. c&f. Rxy and Rxx obtained after the symmetrization/anti-symmetrization process.

Extended Data Fig. 5 Symmetrization/anti-symmetrization method to obtain magnetic hysteresis data at v = 3/5.

a, b, d, e, g, h, j & k. Raw data of R13,24, R24,13, R14,23 and R23,14 measured as functions of magnetic field. The insets show the measurement pin configurations. c, f, i&l. Rxy and Rxx obtained after the symmetrization process. m&n. Rxy and Rxx extracted after the symmetrization/anti-symmetrization process using the Onsager reciprocal relation.

Extended Data Fig. 6 Rxy line scans at small magnetic fields.

a. Rxy line scan versus moiré filling factor v at D/ε0 = 0.9 V/nm. Curves with rainbow colors represent multiple scans at B = 0. Black curves show scans at B = ± 100 mT. B. Rxy line scans versus v at B = 10 mT, 50 mT, 100 mT.

Extended Data Fig. 7 Rxx line scans at varying magnetic field.

a & b. Rxx line scans with moiré filling factor v < 1/2 and v > 1/2, respectively. Dips at fractional filling factors shift with magnetic field as indicated by the dashed lines. Curves are equally shifted vertically for clarity.

Extended Data Fig. 8 Data from Device 2.

a & b. Phase diagrams of the device revealed by symmetrized Rxx and anti-symmetrized Rxy at B = ± 0.1 T as functions of charge density ne (filling factor v) and D. The temperature at the mixing chamber of dilution refrigerator is 10 mK. Clear dips of Rxx can be seen at filling factors of the moiré superlattice v = 1, 2/3 and 2/5 (indicated by the dashed lines and arrows), where Rxy shows plateaus of values.

Extended Data Fig. 9 Magnetic hysteresis data from Device 2.

a–c. Magnetic hysteresis measurements at v = 1, 2/3 and 2/5. Clear hysteresis and values of Rxy at \(\frac{{\rm{h}}}{{\rm{v}}{{\rm{e}}}^{2}}\) can been seen.

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Lu, Z., Han, T., Yao, Y. et al. Fractional quantum anomalous Hall effect in multilayer graphene. Nature 626, 759–764 (2024). https://doi.org/10.1038/s41586-023-07010-7

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