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Ferromagnetism and topology of the higher flat band in a fractional Chern insulator

Nature Physics volume 21, pages 549–555 (2025)Cite this article

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Abstract

The recent observation of the fractional quantum anomalous Hall effect in moiré fractional Chern insulators provides an opportunity to investigate zero magnetic field anyons. One approach for potentially realizing non-abelian anyons is to engineer higher flat Chern bands that mimic higher Landau levels. We investigate the interaction, topology and ferromagnetism of the second moiré miniband in twisted MoTe2 bilayers. At half-filling of the second miniband, we observed spontaneous ferromagnetism and an incipient Chern insulator state. The Chern numbers of the top two moiré flat bands exhibited opposite signs for twist angles above 3.1° but had the same sign near 2.6°, consistent with theoretical predictions. In the 2.6° device, increasing the magnetic field induced a topological phase transition due to band-crossing between opposite valleys, resulting in an emergent state with Chern number C = −2. Additionally, an insulating state at half-filling of the second valley-polarized band indicates that a charge-ordered state is favoured over the fractional Chern insulator state. These findings lay a foundation for understanding the higher flat Chern bands, which are crucial for the discovery of non-abelian fractional Chern insulators.

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Fig. 1: Spontaneous ferromagnetism in the second flat Chern band.
Fig. 2: Transport measurements of anomalous Hall effect near ν = −3 for 2.6° tMoTe2.
Fig. 3: Twist-angle-dependent topology of the second Chern band.
Fig. 4: Topological band inversion at high magnetic field for ν = −2.

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Data availability

The datasets generated during and analysed during this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

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Acknowledgements

We thank J. Yu and A. Stern for insightful discussion. This work is mainly supported by DoE BES (Award No. DE-SC0018171). Electrical transport measurements of QAH insulator were partially supported by the AFOSR (Grant No. FA9550-21-1-0177). The investigation of the magnetism and topological phase diagram was partially supported by the AFOSR Multidisciplinary University Research Initiative (Grant No. FA9550- 19-1-0390). Growing the MoTe2 crystals was supported by the Center on Programmable Quantum Materials, an Energy Frontier Research Center funded by DOE BES (Award No. DE-SC0019443). We also acknowledge the use of the facilities and instrumentation supported by the NSF MRSEC (Grant No. DMR-2308979). B.A.B. was supported by a Simons investigator grant (No. 404513) and the Gordon and Betty Moore Foundation’s EPiQS Initiative (Grant No. GBMF11070). E.A. acknowledges support from the National Science Foundation Graduate Research Fellowship Program (Grant No. DGE-2140004). K.W. and T.T. acknowledge support from the JSPS (KAKENHI Grant Nos. 21H05233 and 23H02052) and the World Premier International Research Center Initiative, MEXT, Japan. J.-H.C. and X.X. acknowledge support from the Clean Energy Institute, which is funded by the State of Washington.

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Author notes

  1. These authors contributed equally: Heonjoon Park, Jiaqi Cai, Eric Anderson, Xiao-Wei Zhang.

Authors and Affiliations

  1. Department of Physics, University of Washington, Seattle, WA, USA

    Heonjoon Park, Jiaqi Cai, Eric Anderson, William Holtzmann, Weijie Li, Chaowei Hu, Yuzhou Zhao, David Cobden, Jiun-haw Chu, Di Xiao & Xiaodong Xu

  2. Department of Materials Science and Engineering, University of Washington, Seattle, WA, USA

    Xiao-Wei Zhang, Xiaoyu Liu, Chong Wang, Yuzhou Zhao, Jihui Yang, Ting Cao, Di Xiao & Xiaodong Xu

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

    Takashi Taniguchi

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

    Kenji Watanabe

  5. Department of Physics, Princeton University, Princeton, NJ, USA

    Nicolas Regnault & B. Andrei Bernevig

  6. Laboratoire de Physique de l’Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, France

    Nicolas Regnault

  7. Donostia International Physics Center, Donostia-San Sebastian, Spain

    B. Andrei Bernevig

  8. IKERBASQUE, Basque Foundation for Science, Bilbao, Spain

    B. Andrei Bernevig

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

    Liang Fu

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  1. Heonjoon Park
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Contributions

X.X. conceived and supervised the project. H.P. and E.A. fabricated the samples. H.P. and J.C. performed the transport measurements. E.A. performed the optical measurements with support from W.H. and W.L. J.C., D.C. and X.X. provided support for the dilution fridge measurements. C.H., Y.Z., J.Y. and J.-H.C. synthesized and characterized the bulk MoTe2 crystals. X.-W.Z., T.C. and D.X. performed the large-scale DFT calculations. X.L., C.W., T.C. and D.X. performed the Hartree–Fock calculations. H.P., J.C., E.A., D.C., N.R., B.A.B., L.F., T.C., D.X. and X.X. analysed and interpreted the results. T.T. and K.W. synthesized the hBN crystals. X.X., H.P., J.C., D.X., D.C., B.A.B. and L.F. wrote the paper with input from all authors. All authors discussed the results.

Corresponding authors

Correspondence to Di Xiao or Xiaodong Xu.

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Nature Physics thanks Su-Yang Xu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Reproducibility of ferromagnetism at ν = -3 in devices with different twist angles.

a-f, Reflective magnetic circular dichroism (RMCD) signal as a function of carrier density (n, bottom axis) or filling factor (ν, top axis) and displacement field (D/ε0). Twist angles are indicated on top of each panel. All data were taken at zero magnetic field at a temperature of 1.6 K. Magnetic fluctuations are visible at ν = -1 and -3, which can be stabilized with a small out of plane field as seen in Fig. 1b in the main text.

Extended Data Fig. 2 Device images and contact resistance characterization.

a, Schematic of device structure. The top (Vtg) and bottom gates (Vbg) form a dual-gate geometry to independently control carrier density and electric field, while contact gates (Vcg) lower the contact resistance. b, Schematic of the contact region of Pt and transition metal dichalcogenide (TMD) interface. The hole travels sequentially from the Pt to the metallized TMD to the intrinsic TMD Hall bar region. c, Simplified energy level diagram of the three regions. The metallized TMD region forms defect-like localized bands as it is heavily strained by the contacts with a height of ~8 nm. A Schottky barrier forms between the metallized TMD and the intrinsic TMD, that can be overcome by heavily hole-doping the metallized TMD region with a large negative voltage on the contact gate. d, Optical image (top) of the 2.6° twisted MoTe2 device and the AFM image (bottom) taken after transfer of the twisted MoTe2 bilayer. The scale bars are 10 μm and 2 μm, respectively. e, Same for the 3.8° twisted MoTe2 device. f, Characterization of R2T for different contacts within the 3.8° device, measured at the gate limit voltages of Vtg = -8.4 V, Vbg = -8 V, Vcg = -3.1 V at T = 4 K under an AC excitation of 0.1 mV. g, R2T as a function of carrier density (n) at D/ε0 = 0 and T = 4 K. The contact resistance starts to increase at very low doping levels. Inset, contact scheme for measuring R2T.

Extended Data Fig. 3 Additional RMCD measurements of the 2.6° tMoTe2.

a, RMCD signal as a function of filling factor (ν) and electric field (D/ε0) near ν = -3, measured at zero magnetic field. A clear ferromagnetic ‘wing-like’ feature is visible. b, Magnetic field dependence of RMCD at selected filling factors, represented by the green dots in a. The electric field was fixed at zero (D/ε0 = 0). c, Magnetic field dependence of RMCD at selected electric fields, marked by the black dots in a, at a fixed filling factor of ν ≈ -3.7. The data in a-c are taken at 1.6 K. d-i, RMCD maps as a function of ν and D/ε0 at different temperatures (T), measured at a small field of 50 mT. The ferromagnetic signal at ν = -3 disappears first around 6 K while the ν = -1 signal persists up to approximately 9-10 K. j, k, Magnetic field dependence of RMCD at D/ε0 = 0 for ν = -1 (j) and ν = -3 (k) at different temperatures from 2 K to 9 K (j) and 2 K to 6 K(k).

Extended Data Fig. 4 Hartree-Fock bands and real-space wavefunction calculations.

a, Non-interacting single particle band structure for tMoTe2 with a twist angle of 2.45°. b, Hartree-Fock band structure with spin-split bands for a small interaction strength of ε = 60. The Fock energy is inhomogeneous across momentum space, resulting in momentum dependent gaps across the Brillouin zone. It is noteworthy that the first moiré Chern band is fully gapped out, but the second Chern band remains gapless, consistent with transport measurements of a weak metallic state at ν = -3. c, Real-space hole density of the first (ρ1) and second (ρ2) Chern bands calculated for 2.45° twisted MoTe2. Both ρ1 and ρ2 form a honeycomb lattice at the MX and XM sites, leading to ferromagnetism via direct exchange. d, e, Wavefunction distribution across the moiré unit cell for the first Chern band at the γ point (d) and κ/κ′ point (e). Both form a honeycomb lattice, consistent with the hole density distribution in c. f, g, Wavefunction distribution for the second Chern band at the γ point (f) and κ/κ′ point (g). The wavefunctions are normalized with respect to their maximum value within the moiré unit cell. In contrast to the κ/κ′ point, which remains a honeycomb lattice, the γ point forms a triangular lattice which has decreased mean-field Fock energy. As a result, the gap between the two spin-split Chern bands in (b) is less for the γ point compared to the κ/κ′ point. h, i, j, Wannier orbitals for each valley (spin) localized at the MX, XM and MM site, respectively.

Extended Data Fig. 5 Temperature dependence of Rxx and gap extraction.

a-b, Rxx versus ν near ν = -3 (a) and ν = -1 (b), respectively, at selected temperatures from 1 K to 12 K. c-d, Extracted Rxx as a function of inverse temperature (T-1) at ν = -3 (c) and ν = -1 (d). The thermal activation gap is found to be 46(4) K for ν = -1, while it appears that ν = -3 is not fully gapped. e, -Rxy as a function of magnetic field near ν = -2 and D/ε0 = 0, measured at T < 100 mK.

Extended Data Fig. 6 Filling factor dependent anomalous Hall effect near v = -3 for different twist angles.

a, Magnetic field dependence of Rxx (top) and Rxy (bottom) at selected filling factors near ν = -3 for 2.6° twisted MoTe2 device. b, ∆Rxy versus magnetic field and filling factor. Here, ∆Rxy is obtained by taking the difference of Rxy between sweeping magnetic field up and down. The data in a and b are taken at T = 15 mK and D/ε0 = 0 from a different cool down of the same sample in the main Fig. 2. c, d, Similar data for a 3.1° twisted MoTe2 device, and e, f, similar data for a 3.8° twisted MoTe2 device. The ∆Rxy is positive (red) at the ν = -1 Chern insulator state (C = -1) for all devices. A sign reversal of the AHE at ν = -3 is evident between the 2.6° device and the devices with twist angles of 3.1° and 3.8°.

Extended Data Fig. 7 Dual gate maps at high magnetic fields and Landau fan at high electric field for filling factor assignment of the 2.6° device.

a, b, c, Longitudinal resistance Rxx as a function of filling factor ν and electric field D/ε0 at out-of-plane magnetic fields (μ0H) of 7 T (a), 9 T (b), and 13 T (c). The regions in black are inaccessible due to their high resistance. A resistive state at ν = -3/2 is visible near D/ε0 = 0. d, Linecuts of Rxx at selected magnetic fields. Each curve is displaced by 10 kΩ for clarity and the arrow highlights the non-dispersing resistive maximum at the v = -3/2 state. e, The Landau fan of Rxx measured as a function of ν and μ0H at a finite electric field of D/ε0 = 190 mV/nm, denoted as the white line in a. Clear quantum oscillations are visible stemming from the filling factor of ν = -3 and ν = -1, which allows accurate filling factor assignment for the main figures. The degeneracy of the Landau levels is denoted on the top axis. Data are taken at a temperature of 15 mK.

Extended Data Fig. 8 Magnetoresistance and first order phase transition near ν = -2.

a, Zoom in of the Landau fan diagram in the main Fig. 4e near ν = -2. b, Magnetoresistance as a function of sweeping the field up and down near the filling factor of near ν = -2. A clear hysteresis can be seen, which is a signature of a first order spin-flip transition due to Zeeman splitting.

Extended Data Fig. 9 Temperature dependence of C = -2 Chern insulator state at high magnetic fields.

a, b, Filling factor dependent Rxx (a) and −Rxy (b) at selected temperatures at a fixed field of 13 T. Data are symmetrized and anti-symmetrized at ±13 T. Note that at low doping levels the contact resistance does not become negligible, hence the deviation from FCI behavior. c, Thermal activation behavior of Rxx near the filling factor of ν = -2.3, which indicates an energy gap of 13(3) K.

Source data

Source Data Fig. 1

Statistical data for Fig. 1.

Source Data Fig. 2

Statistical data for Fig. 2.

Source Data Fig. 3

Statistical data for Fig. 3.

Source Data Fig. 4

Statistical data for Fig. 4.

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Park, H., Cai, J., Anderson, E. et al. Ferromagnetism and topology of the higher flat band in a fractional Chern insulator. Nat. Phys. 21, 549–555 (2025). https://doi.org/10.1038/s41567-025-02804-0

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