Abstract
Topological flat bands formed in two-dimensional lattice systems offer an opportunity to study fractional phases of matter in the absence of an external magnetic field. Examples include fractional quantum anomalous Hall effects and fractional topological insulators. Recently, fractional quantum anomalous Hall effects have been experimentally realized in both twisted bilayer MoTe2 and rhombohedral-stacked multilayer graphene on hexagonal boron nitride. These studies focus mainly on the first moiré flat band, but there is a possibility that non-Abelian states could occur in the second moiré band. Here we present a systematic transport study of twisted bilayer MoTe2 devices, focusing on the second moiré band. We observe ferromagnetism in the second moiré band, and a Chern insulator state driven by out-of-plane magnetic fields at a filling factor of three holes per moiré unit cell. Between fillings of 2.2 and 2.7 holes per moiré unit cell, we observe a finite temperature resistivity minimum with a 1/T scaling law at low temperatures and a large out-of-plane negative magnetoresistance. Applying an out-of-plane electric field can induce quantum phase transitions at both integer and fractional filling factors. Our studies lay the groundwork for realizing tunable topological states and other unexpected magnetic phases beyond the first moiré flat band based in twisted MoTe2.
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Acknowledgements
We thank F. Wu, Z. Liu, X. Xu and M. Qin for helpful discussions. This work is supported by the National Key R&D Program of China (grant nos. 2022YFA1402702, 2022YFA1405400, 2021YFA1401400, 2021YFA1400100, 2022YFA1402404, 2019YFA0308600, 2022YFA1402400, 2020YFA0309000 and 2021YFA1202902), the National Natural Science Foundation of China (grant nos. 12350403, 92265102, 12174249, 12174250, 12141404, 12374045, 12374292 and 124B1030), the Innovation Program for Quantum Science and Technology (grant nos. 2021ZD0302600 and 2021ZD0302500), the Natural Science Foundation of Shanghai (grant nos. 24QA2703700, 22PJ1406700, 24LZ1401100 and 22ZR1430900). T.L., S.J. and X.L. acknowledge the Shanghai Jiao Tong University 2030 Initiative Program. T.L. and S.J. acknowledge the Yangyang Development Fund. N.M. acknowledges the financial support from the Alexander von Humboldt Foundation. Yixin Zhang and Yang Zhang acknowledge support from Max Planck partner lab grant for quantum materials. K.W. and T.T. acknowledge support from the JSPS KAKENHI (grant nos. 21H05233 and 23H02052) and World Premier International Research Center Initiative (WPI), MEXT, Japan. A portion of this work was carried out at the Synergetic Extreme Condition User Facility (SECUF, https://cstr.cn/31123.02.SECUF).
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T.L., S.J. and X.L. designed and supervised the experiment. J.X., F.L., F.X., X.C. and Z. Sun fabricated the devices. F.X., Z. Sun and J.L. performed the transport measurements. X.C and J.X. performed the optical measurements. F.X., X.C., T.L., S.J. and X.L. analysed the data. Yixin Zhang, N.M., N.P. and Yang Zhang performed theoretical studies. K.W. and T.T. grew the bulk hBN crystals. T.L. and Yang Zhang wrote the paper. All authors discussed the results and commented on the paper.
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Extended data
Extended Data Fig. 1 Twist angle calibrations and contact resistance.
a, ρxx versus ν and B⊥ at T = 300 mK and D ≈ −275 mV/nm of device A. Clear quantum oscillations can be observed around ν = −1 when B⊥ above about 6 T, corresponding to a quantum mobility about 1500 cm2/V·s. The Landau Level filling factor νLL can be determined from the Hall resistance, which allows us to derive the gate geometric capacitance accurately. b, ρxx versus ν and B⊥ at T = 300 mK and D ≈ −410 mV/nm of device B. The twisted angles for device A and B are determined to be 3.15° ± 0.1° and 3.0° ± 0.1°, respectively. c, Two-terminal resistance as a function of ν at T = 1.2 K and B⊥= 0.1 T around D = 0. It is measured with contact 21 and contact 4 of device A with a constant bias current of approximately 1 nA. The measured two-terminal resistance includes contributions from both the sample resistance and the contact resistance of the two contacts used as the source and drain for transport measurements. Given that the contact resistance is in general high in TMDc devices, we can reasonably assume that it dominates the two-terminal resistance, except when the sample is tuned into an insulating state. d,e, Contact resistance in device A (d) and device B (e) at 1.7 K. For device A, the contact resistance is measured at ν = −1.4 and D = −116 mV/nm. For device B, the contact resistance is measured at ν = −4.2 and D = −30 mV/nm. During the measurement of contact resistance, only the specific contact is biased with a 1 mV dc voltage while all other contacts are grounded.
Extended Data Fig. 2 Characterizations of device B (3.0°).
a, Optical image of device B (3.0°). b, The schematic transport measurement configuration. Contacts in a and b are labeled by numbers. c,d, Longitudinal resistivity ρxx (c) and Hall resistivity ρxy (d) as a function of ν and D. ρxx is measured under zero magnetic field at 500 mK; ρxy is the antisymmetrized results under an out-of-plane magnetic field B⊥= ± 0.3 T at 500 mK. A built-in electric field D0 about 50 mV/nm has been subtracted for device B (3.0°).
Extended Data Fig. 3 Characterizations of device C (3.7°).
a, Optical image of device C (3.7°). b-f, MCD map as a function of ν and D measured at B⊥≈ 10 mT and T = 1.6 K (b), 2 K (c), 3 K (d), 4 K (e), 5 K (f). Ferromagnetism in the second moiré band spans approximately from ν ≈ −2.65 to −3.2. The maximum Cuire temperature of the second moiré band magnetism is about 5 K.
Extended Data Fig. 4 More characterizations of device A (3.15°).
a, Optical image of device A (3.15°). Contacts are labeled by numbers. b, MCD map as a function of ν and D measured at 1.6 K. c,d, Symmetrized ρxx (c) and antisymmetrized ρxy (d) at varying temperatures at ν ≈ −2.8. e, Symmetrized ρxx and antisymmetrized ρxy under \({B}_{\perp }\)= ± 0.3 T at D ≈ 0 V/nm and T = 0.6 K, 0.9 K, 1.2 K, respectively. f, Symmetrized ρxx and antisymmetrized ρxy under at D ≈ 0 V/nm and T =1.6 K with B⊥= 0.25 T, 0.5 T, 1 T, respectively.
Extended Data Fig. 5 Magnetoresistance at ν = −2 and −4 of device A (3.15°), and the transport gap fitting at ν = −2.
a-c, Rxx versus B|| and B⊥ at ν = −2 and D = −20 mV/nm (a), D = 260 mV/nm (b) and D = −300 mV/nm (c). d, Rxx versus B|| and B⊥ at ν = −4 at D = −200 mV/nm. The measurement temperature for a-d is 300 mK. e, Temperature dependence of Rxx at ν = −2 and D = −20 mV/nm of device A (3.15°). f, Temperature dependence of Rxx at ν = −2 and D = −650 mV/nm of device B (3.0°). Dashed lines in e and f are the fit to \({\rho }_{{xx}}{\propto e}^{-\varDelta /2{k}_{B}T}\), with \(\varDelta\) and \({k}_{B}\) denoting the transport gap and Boltzmann constant, respectively. We observe that below about 40 K, the temperature dependence of Rxx shown in e becomes metallic-like, presumably due to the interplay between bulk transport and edge transport of an IQSH insulator. Consequently, the thermal activation fitting range is very narrow in e, leading to a substantial uncertainty of the estimation for the real charge gap.
Extended Data Fig. 6 Magnetoresistance at ν = −2 and −4 of device B (3.0°) and at ν = −2 of device C (3.7°).
a,b, Angle-dependent magnetoresistance at ν = −2 (a) and ν = −4 (b) of device B (3.0°) at 300 mK. The definition of the tilt angle θ is schematically illustrated in the inset of a, where θ = 90° corresponds to the in-plane magnetic field configuration. c, Rxx versus B|| and B⊥ at ν = −2 and D ≈ 0 V/nm of device C (3.7°). d, Rxx as a function of θ at ν = −2 and D ≈ 0 V/nm of device C. The applied magnetic field Btotal is fixed at 0.4 T.
Extended Data Fig. 7 In-plane Magnetoresistance and nonlocal transport of device B (3.0°).
a, The in-plane magnetoresistance Rxx(B|| =0.3 T)/Rxx(B =0) versus ν and D measured at T = 500 mK. c, The ratio between nonlocal resistance and local resistance as a function of ν and D measured at T = 500 mK and zero magnetic field. b and d illustrate the measurement configurations in a and c, respectively.
Extended Data Fig. 8 Hartree-Fock simulation and schematic band structures of integer topological phases.
a, Hartree-Fock phase diagram at v = −2 and \(\epsilon =30\); b, Hartree-Fock band structure at v = −3 and \(\epsilon =20\) without magnetic field with non-polarized initial state, showing a partially polarized anomalous Hall metal; c, Hartree-Fock band structure with the same configuration but with \(\epsilon =30\), showing a nearly gapless IQAH state. d, Hartree-Fock band structure at and \(\epsilon =30\) with Zeeman energy \({E}_{z}\)= 2 meV, displaying a C = −1 Chern insulator from two occupied K valley bands with C = (1,−1), and one occupied K′ valley band with C = −1.
Extended Data Fig. 9 Chern state at ν = −3 of device B (3.0°).
a,b, ρxx (a) and ρxy (b) versus ν and B⊥ at T = 1.6 K and D ≈ 0 V/nm. Dashed lines represent the expected dispersions based on Streda formula for the IQAH state at ν = −1 with C = 1, the FQAH state at ν = −2/3 with C = 2/3, and the Chern state emerged under B⊥ at ν = −3 with C = −1, respectively. c, ρxx and ρxy versus B⊥ alone the Streda dispersion line of the Chern state at ν = −3. The ρxy approaches the expected quantized value of h/e2, and the ρxx is gradually vanishing with increasing B⊥. d, Temperature dependence of ρxx versus D at ν = −3 from T = 1.6 K to 30 K.
Extended Data Fig. 10 Out-of-plane magnetoresistance fitting, T dependence of ρxx under B⊥ at ν ≈ −5/2 of device A (3.15°).
a-c, ρxx versus B⊥ at ν = −2.3 (a), ν = −2.5 (b), ν = −2.7 (c). Dashed lines in a-c are the fitting curves of magnetoresistance with \({\rho }_{{\rm{xx}}}\left({B}_{\perp }\right)=a/{B}_{\perp }-b/{B}_{\perp }^{2}+c\). The measurements in a-c were performed at T = 300 mK and D ≈ 0 V/nm. d, Temperature dependent ρxx at ν ≈ −2.5 and D ≈ 0 V/nm under B⊥ = 0 T and 1 T, respectively.
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Xu, F., Chang, X., Xiao, J. et al. Interplay between topology and correlations in the second moiré band of twisted bilayer MoTe2. Nat. Phys. 21, 542–548 (2025). https://doi.org/10.1038/s41567-025-02803-1
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DOI: https://doi.org/10.1038/s41567-025-02803-1
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