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Ferroelectric and spontaneous quantum Hall states in intrinsic rhombohedral trilayer graphene

Nature Physics volume 20, pages 422–427 (2024)Cite this article

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Abstract

Non-trivial interacting phases can emerge in elementary materials. As a prime example, continuing advances in device quality have facilitated the observation of a variety of spontaneously ordered quantum states in bilayer graphene. Its natural extension, rhombohedral trilayer graphene—in which the layers are stacked in an ABC fashion—is predicted to host stronger electron–electron interactions than bilayer graphene because of its flatter low-energy bands and larger winding number. Theoretically, five spontaneous quantum Hall phases have been proposed to be candidate electronic ground states. Here we observe evidence for four of the five competing ordered states in interaction-maximized, dual-gated, rhombohedral trilayer graphene. In particular, at small magnetic fields, two states with Chern numbers 3 and 6 can be stabilized at elevated and low perpendicular electric fields, respectively, and both exhibit clear magnetic hysteresis. We also show that the quantum Hall ferromagnets of the zero-energy Landau levels are ferroelectrics with spontaneous layer polarizations even at zero electric field, as evidenced by electric hysteresis.

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Fig. 1: Microscopy and transport measurements.
Fig. 2: Electric hysteresis of quantum Hall ferromagnets.
Fig. 3: Anomalous quantum Hall states at low magnetic fields.
Fig. 4: Magnetic hysteresis at a constant electric field E = −20 mV nm−1.

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Data availability

Original data are available in the Göttingen Research Online Data repository (GRO.data) at https://doi.org/10.25625/VXUMPN.

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Acknowledgements

F.W., F.R.G., N. F. and R.T.W. acknowledge funding from the Center for Nanoscience (CeNS) and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy-EXC-2111-390814868 (MCQST). R.T.W. acknowledges partial funding from the DFG SPP 2244 (2DMP). F.Z. acknowledges support from the US National Science Foundation under grant numbers DMR-1945351 through the CAREER programme, DMR-2105139 through the CMP programme and DMR-2324033 through the DMREF programme.

Author information

Authors and Affiliations

  1. Physics of Nanosystems, Department of Physics, Ludwig-Maximilians-Universität München, Munich, Germany

    Felix Winterer, Fabian R. Geisenhof, Noelia Fernandez, Anna M. Seiler & R. Thomas Weitz

  2. 1st Institute of Physics, Faculty of Physics, University of Göttingen, Göttingen, Germany

    Noelia Fernandez, Anna M. Seiler & R. Thomas Weitz

  3. Department of Physics, University of Texas at Dallas, Richardson, TX, USA

    Fan Zhang

Authors
  1. Felix Winterer
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  4. Anna M. Seiler
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Contributions

F.W., F.R.G. and N.F. fabricated the samples. F.W. and N.F. conducted the electrical measurements with the help of A.M.S. and F.R.G. F.Z. developed the theory. All authors discussed and interpreted the data. The paper was written by F.W, F.Z. and R.T.W., with input from all authors.

Corresponding authors

Correspondence to Fan Zhang or R. Thomas Weitz.

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Extended data

Extended Data Fig. 1 Ferroelectric states.

a,b, Map of the resistance difference between forward and backward sweep of the electric field as function of electric field and charge carrier density at B = 3 T in a and B = 8 T in b. The region with vanishing conductance at zero density has been removed due to large resistance variations to enhance visibility.

Extended Data Fig. 2 Quantum Hall states at low magnetic fields.

a-c, fan diagrams of the conductance derivative with respect to the charge carrier density of device A2 (cf. Supporting Table 1) at E = 0 mV nm−1 in a, E = 24 mV nm−1 in b and E = 47 mV nm−1 in c. The filling factors and their corresponding slopes are indicated on the top of each panel. The roman numerals indicate the associated spontaneous quantum Hall states, namely the LAF/CAF state (I), the ALL state (III) and the QAH state (IV). d-f, Fan diagrams of the conductance derivative with respect to the charge carrier density of device B1 (cf. Supporting Table 1) at E = 0 mV nm−1 in d, E = −20 mV nm−1 in e and E = −60 mV nm−1 in f. The filling factors and their corresponding slopes are indicated on the top of each panel.

Extended Data Fig. 3 Device schematics.

a, 3D view of a dual-gated trilayer graphene device with a silicon bottom gate and a gold top gate. b, Cross section of the device shown in a along the graphene axis.

Supplementary information

Supplementary Information

Supplementary Sections 1–6, Figs. 1–5 and Table 1.

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Winterer, F., Geisenhof, F.R., Fernandez, N. et al. Ferroelectric and spontaneous quantum Hall states in intrinsic rhombohedral trilayer graphene. Nat. Phys. 20, 422–427 (2024). https://doi.org/10.1038/s41567-023-02327-6

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