Abstract
The interplay between spontaneous symmetry breaking and topology can result in exotic quantum states of matter. A celebrated example is the quantum anomalous Hall (QAH) state, which exhibits an integer quantum Hall effect at zero magnetic field owing to intrinsic ferromagnetism1,2,3. In the presence of strong electron–electron interactions, fractional QAH (FQAH) states at zero magnetic field can emerge4,5,6,7,8. These states could host fractional excitations, including non-Abelian anyons—crucial building blocks for topological quantum computation9. Here we report experimental signatures of FQAH states in a twisted molybdenum ditelluride (MoTe2) bilayer. Magnetic circular dichroism measurements reveal robust ferromagnetic states at fractionally hole-filled moiré minibands. Using trion photoluminescence as a sensor10, we obtain a Landau fan diagram showing linear shifts in carrier densities corresponding to filling factor v = −2/3 and v = −3/5 ferromagnetic states with applied magnetic field. These shifts match the Streda formula dispersion of FQAH states with fractionally quantized Hall conductance of \({\sigma }_{xy}=-\,\frac{2}{3}\frac{{e}^{2}}{h}\) and \({\sigma }_{xy}=-\,\frac{3}{5}\frac{{e}^{2}}{h}\), respectively. Moreover, the v = −1 state exhibits a dispersion corresponding to Chern number −1, consistent with the predicted QAH state11,12,13,14. In comparison, several non-ferromagnetic states on the electron-doping side do not disperse, that is, they are trivial correlated insulators. The observed topological states can be electrically driven into topologically trivial states. Our findings provide evidence of the long-sought FQAH states, demonstrating MoTe2 moiré superlattices as a platform for exploring fractional excitations.
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Acknowledgements
We thank X. Wang for discussions. C.W. acknowledges discussions with Y. He and H. Li. This project is mainly supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under the award DE-SC0018171. RMCD measurements are partially supported by Air Force Office of Scientific Research (AFOSR) Multidisciplinary University Research Initiative (MURI) programme, grant number FA9550-19-1-0390. Measurements of electrical control of topological phase transitions are partially supported by AFOSR FA9550-21-1-0177. The device fabrication is partially supported by the Center on Programmable Quantum Materials, an Energy Frontier Research Center funded by DOE BES under award DE-SC0019443. We acknowledge the use of the facilities and instrumentation supported by NSF MRSEC DMR-1719797. E.A. and W.H. acknowledge the support by the National Science Foundation Graduate Research Fellowship Program under grant number DGE-2140004. F.F. and W.Y. acknowledge support from the Research Grants Council of Hong Kong SAR (AoE/P-701/20, HKU SRFS2122-7S05) and Croucher Foundation. C.W. and D.X. acknowledge the support from DoE BES under the award DE-SC0012509. K.W. and T.T. acknowledge support from the JSPS KAKENHI (grant numbers 19H05790, 20H00354 and 21H05233). X.X. acknowledges support from the State of Washington funded Clean Energy Institute and from the Boeing Distinguished Professorship in Physics.
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X.X. conceived of and supervised the experiment. J.C. and E.A. fabricated the devices. T.T. and K.W. provided hBN crystals. E.A. and J.C. performed the magneto-optical measurements with help from W.H. and Y.Z. J.C., E.A. and X.X. analysed the data and interpreted the results, with theoretical input from F.F., L.F., T.C., D.X. and W.Y. L.F. contributed to the idea of trion sensing. C.W., X.Z., X.L., Y.R., T.C. and D.X. performed first-principles and exact diagonalization studies. J.C., E.A., L.F., D.X., W.Y. and X.X. wrote the paper with input from all authors. All authors discussed the results.
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The University of Washington is in the process of applying for patent applications covering dual gate controlled fractional quantum anomalous Hall states which list X.X., E.A. and J.C. as inventors. The other authors declare no competing interests.
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Extended data figures and tables
Extended Data Fig. 1 Doping dependent photoluminescence and mechanism underlying trion sensing of correlated states.
a, Photoluminescence (PL) intensity plot as a function of photon energy and filling factor for hole doping. X0: neutral exciton; X+: positively charged trion. Two prominent trion energy shifts with reduced PL intensity are visible at v = −2/3 and v = −1. b, Zoomed-in plot of PL at µoH = 1T near fractional fillings for hole doping. An additional state at v = −3/5 appears as a trion energy shift with reduced PL intensity. c, PL intensity plot for electron doping. Multiple states including v = 1, 3/4, 4/7, 1/3, and 1/4 can be observed. X− denotes negatively charged trion. d–f, Schematics depicting trion sensing of correlated insulating states. Black lines denote the conduction bands. Green (orange) lines are the moiré valance bands with spin up (down). d, Optically excited exciton formation near charge neutrality. e, Formation of positively charged trions upon finite hole doping, due to binding of excitons and free carriers. f, Reduction of trion population at integer and fractional fillings where correlated insulating states form. The insulating state consumes doped holes and the system is gapped, reducing trion population. g, Longitudinal resistance Rxx as a function of filling factor and temperature at a large electric field which fully polarizes the layer pseudospin. h, Linecuts of data in g at selected filling factors. The observation of a rapid increase in Rxx as temperature decreases demonstrates a correlated insulator at v = −1. i, PL intensity plot at large applied electric field corresponding to g. The data is taken at 1.6 K. The clear observation of a correlated insulating state in electrical transport (g, h), when compared to the PL data in (i), supports that the observed reduction of trion PL corresponds to the formation of an insulating state.
Extended Data Fig. 2 Device image and position independence of correlated states.
a, Optical microscope image of the device. Scale bar, 10 µm. RMCD and PL data in the main text are taken in the homogenous region at spots 1 and 2, respectively. b, Zero magnetic field RMCD versus filling factor and displacement field at spot 1. The electron-doping side is non-ferromagnetic. c,d, Additional RMCD versus v and D plots in spots 2 and 3. Both show an enhancement of the ferromagnetic state at v = −2/3, demonstrating repeatability.
Extended Data Fig. 3 Doping dependent RMCD hysteresis.
a,b, RMCD intensity plot versus filling factor v and magnetic field µ0H swept down (a) and up (b) for spots 1, 2, and 3 as defined in Extended Data Fig. 2. For all spots, µ0HC is enhanced near v = −2/3. However, the v = −3/4 state is not visible for spot 2, showing its spatial dependence.
Extended Data Fig. 4 Temperature-dependent RMCD at v = −1 and −2/3.
a, v = −1. The Curie temperature TC is ~14 K. b, v = −2/3. TC is ~4.5 K.
Extended Data Fig. 5 Optical fan diagram at a ~3.57° twist angle.
As in Fig. 3b, but at a different spot on the same sample with a smaller local twist angle (~3.57°). The fitted Chern numbers are 0.94(7), 0.66(3), and −0.61(4) for the ν = −1, −2/3 and −3/5 states, respectively. A calculation of the ground state as a function of twist angle38 suggests that FQAH is robust in the range of 3.5–3.9° with an optimal twist angle near 3.5°.
Extended Data Fig. 6 Electron doping dependent photoluminescence.
a, PL versus electron doping at selected magnetic fields. b, Fan diagram for the electron doping side, overlaid with extracted carrier densities of the insulating states. No dispersion is observed for any of the correlated insulating states, implying that the lowest moiré conduction band is topologically trivial.
Extended Data Fig. 7 Optical fan diagram at a large electric field around v = −1.
a, As in Fig. 3b, but with a large applied electric field of D/ɛ0 = −250 mV/nm. The dotted white line is a guide to the eye corresponding to v = −1. The extracted carrier density at v = −1 does not disperse for small applied magnetic fields. b, Optical fan diagram at D/ɛ0 = −250 mV/nm in another sample with twist angle θ = 3.9°. Consistent results are obtained. We can resolve a rearrangement of spin orientation from in-plane AFM interactions to fully out-of-plane spin polarized orientation near 2T, as is expected from a previous RMCD study30.
Extended Data Fig. 8 RMCD hysteresis sweeps for selected fillings at T = 3.5 K.
The ferromagnetic states at v = −2/3 and v = −1 retain substantial remnant RMCD signal and sharp spin-flip transitions, signatures of a hard magnet, at an elevated temperature. States at intermediate dopings, however, show behaviour consistent with a soft magnet.
Extended Data Fig. 9 Optical fan diagrams with different PL spectral integration width.
The integration window widths are a, 1 meV b, 5 meV and c, 20 meV. The main features of the fan diagrams are independent of the choice of integration spectral window.
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Cai, J., Anderson, E., Wang, C. et al. Signatures of fractional quantum anomalous Hall states in twisted MoTe2. Nature 622, 63–68 (2023). https://doi.org/10.1038/s41586-023-06289-w
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DOI: https://doi.org/10.1038/s41586-023-06289-w
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