The quantum anomalous Hall (QAH) effect—a macroscopic manifestation of chiral band topology at zero magnetic field—has been experimentally realized only by the magnetic doping of topological insulators1,2,3 and the delicate design of moiré heterostructures4,5,6,7,8. However, the seemingly simple bilayer graphene without magnetic doping or moiré engineering has long been predicted to host competing ordered states with QAH effects9,10,11. Here we explore states in bilayer graphene with a conductance of 2 e2 h−1 (where e is the electronic charge and h is Planck’s constant) that not only survive down to anomalously small magnetic fields and up to temperatures of five kelvin but also exhibit magnetic hysteresis. Together, the experimental signatures provide compelling evidence for orbital-magnetism-driven QAH behaviour that is tunable via electric and magnetic fields as well as carrier sign. The observed octet of QAH phases is distinct from previous observations owing to its peculiar ferrimagnetic and ferrielectric order that is characterized by quantized anomalous charge, spin, valley and spin–valley Hall behaviour9.
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R.T.W. and F.R.G. 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). F.Z. and T.X. acknowledge support from the Army Research Office under grant number W911NF-18-1-0416 and by the National Science Foundation under grant numbers DMR-1945351 through the CAREER programme and DMR-1921581 through the DMREF programme.
The authors declare no competing interests.
Peer review information Nature thanks Kayoung Lee, Sergey Slizovskiy and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.
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Extended data figures and tables
a, Rd.c. as a function of Vd.c. during multiple annealing cycles. b, The resistance of quantum Hall plateaus shown as a function of inverse filling factor at B = 2 T and E⊥ = 20 mV nm−1. c, The conductance as a function of density for E⊥ = 0 mV nm−1 and 60 mV nm−1 at B = 0 T.
Extended Data Fig. 2 Representatives of the five competing broken symmetry ground states in bilayer graphene at n = E⊥ = B = 0.
a–e, Bottom panel: layer polarizations of the four spin-valley species. Top-left and top-right panels: bulk (classical) and edge (quantum) pictures of the corresponding spontaneous quantum Hall effect. Note that the edge roughness can produce couplings between counter-propagating edge states (of the same spin but different valleys) and thus gap them. Spin degeneracy is implicit in a and b. See the text for details. T and B refer to the top and bottom graphene layers, respectively.
a–h, Eight different 'ALL' phases that can be classified by the layer polarizations of their two spin species, by which spin species being in which QAH or QVH phases, and by their charge Hall conductivities.
Extended Data Fig. 4 Additional measurements showing the electric and magnetic field dependence of the ν = ±2 state.
a–h, Maps of the conductance as a function of electric field and density for various magnetic fields. The dashed lines in e–h are guides to the eye, and the arrows indicate the range of negative electric field at which the ν = −2 state emerges. i, Conductance as a function of electric and magnetic fields at a fixed filling factor near ν = −2 (at exactly ν = −2.25). The black (white) dots indicating the maximum (minimum) electric field for the ν = −2 to emerge are extracted from the data shown in e–h. The dashed lines are guides to the eye, highlighting the region where the ν = −2 state emerges at negative electric fields.
Derivative of the differential conductance δσ/δn plotted as a function of magnetic field and density for various E⊥. The amount of conductance fluctuations corresponding to the ν = 0, −2 and −4 state are indicated by the number of white, blue and yellow lines in the top of each image.
a, b, Maps of the conductance as a function of E⊥ and n for B = 0.2 T and 0.5 T, respectively. c, Conductance as a function of electric and magnetic field for fixed filling factor of ν = −2. The dashed lines indicate the region where the ν = −2 state at negative electric fields emerges with a conductance of 2 e2 h−1. d, Two-terminal conductance hysteresis measured for ν = −2 and E⊥ = −19 mV nm−1. The hysteresis loop area is shaded for clarity. The forward (reverse) sweep is shown in blue (red), as indicated by the arrows.
Two-terminal conductance hysteresis measured for different magnetic field ranges at ν = −2 and E⊥ = −17 mV nm−1. The hysteresis loop areas are shaded for clarity. The forward (reverse) sweep is shown in blue (red), as indicated by the arrows.
Map of the conductance as a function of density and electric field for various temperatures. The dashed lines in the top left images indicate the position of the linecuts shown in Fig. 4 in the main manuscript.
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Geisenhof, F.R., Winterer, F., Seiler, A.M. et al. Quantum anomalous Hall octet driven by orbital magnetism in bilayer graphene. Nature 598, 53–58 (2021). https://doi.org/10.1038/s41586-021-03849-w
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