- Open Access
Probing Quantum Anomalous Hall States in Twisted Bilayer via Attractive Polaron Spectroscopy
Phys. Rev. X 16, 021037 – Published 18 May, 2026
DOI: https://doi.org/10.1103/259w-bpxx
Abstract
Moiré superlattices in semiconductors exhibit a rich variety of interaction-induced topological states, including quantum anomalous Hall (QAH) effects [1–8]. A recent study hinted that twisted homobilayer () could host a QAH state but lacked direct evidence of ferromagnetism, a key hallmark of this phase [9]. Here, we report the first direct evidence of QAH states in with spontaneous ferromagnetism. Specifically, we employ polarization-resolved attractive polaron spectroscopy on a dual-gated, 2° and observe direct signatures of spontaneous time-reversal symmetry breaking at hole filling . Together with a Chern number () measurement via Streda formula analysis, we identify this magnetized state as a topological state, characterized by . Furthermore, we demonstrate that these topological and magnetic properties are tunable via a finite displacement field, between a QAH ferromagnetic state and an antiferromagnetic state. Our findings position as a highly versatile, stable, and optically addressable platform for investigating topological order and strong correlations in two-dimensional landscapes.
Physics Subject Headings (PhySH)
Popular Summary
Directly observing the quantum anomalous Hall effect in twisted has remained a challenge despite the material’s potential to host topological states that carry electric current along their edges without resistance. We addressed this by using magneto-optical spectroscopy to probe a twisted bilayer of at temperatures near absolute zero. By monitoring the behavior of attractive polarons, we detected spontaneous magnetism and confirmed the existence of a topological phase with a Chern index of one at specific electron fillings. We also found that the magnetic order can be reversibly switched between ferromagnetic and antiferromagnetic states through the application of a perpendicular electric field. These results establish twisted as a highly tunable and stable platform for engineering topological quantum phases. Our work provides a framework for utilizing optical signatures to identify and manipulate exotic electronic states in moiré semiconductors.
Article Text
Supplemental Material
References (59)
- J. Cai, E. Anderson, C. Wang, X. Zhang, X. Liu, W. Holtzmann, Y. Zhang, F. Fan, T. Taniguchi, K. Watanabe et al., Signatures of fractional quantum anomalous Hall states in twisted , Nature (London) 622, 63 (2023).
- Y. Zeng, Z. Xia, K. Kang, J. Zhu, P. Knüppel, C. Vaswani, K. Watanabe, T. Taniguchi, K. F. Mak, and J. Shan, Thermodynamic evidence of fractional Chern insulator in moiré , Nature (London) 622, 69 (2023).
- H. Park, J. Cai, E. Anderson, Y. Zhang, J. Zhu, X. Liu, C. Wang, W. Holtzmann, C. Hu, Z. Liu et al., Observation of fractionally quantized anomalous Hall effect, Nature (London) 622, 74 (2023).
- F. Xu, Z. Sun, T. Jia, C. Liu, C. Xu, C. Li, Y. Gu, K. Watanabe, T. Taniguchi, B. Tong et al., Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer , Phys. Rev. X 13, 031037 (2023).
- Z. Ji, H. Park, M. E. Barber, C. Hu, K. Watanabe, T. Taniguchi, J.-H. Chu, X. Xu, and Z.-X. Shen, Local probe of bulk and edge states in a fractional Chern insulator, Nature (London) 635, 578 (2024).
- E. Redekop, C. Zhang, H. Park, J. Cai, E. Anderson, O. Sheekey, T. Arp, G. Babikyan, S. Salters, K. Watanabe et al., Direct magnetic imaging of fractional Chern insulators in twisted , Nature (London) 635, 584 (2024).
- F. Xu, X. Chang, J. Xiao, Y. Zhang, F. Liu, Z. Sun, N. Mao, N. Peshcherenko, J. Li, K. Watanabe et al., Interplay between topology and correlations in the second moiré band of twisted bilayer , Nat. Phys. 21, 542 (2025).
- H. Park, J. Cai, E. Anderson, X.-W. Zhang, X. Liu, W. Holtzmann, W. Li, C. Wang, C. Hu, Y. Zhao et al., Ferromagnetism and topology of the higher flat band in a fractional Chern insulator, Nat. Phys. 21, 549 (2025).
- B. A. Foutty, C. R. Kometter, T. Devakul, A. P. Reddy, K. Watanabe, T. Taniguchi, L. Fu, and B. E. Feldman, Mapping twist-tuned multiband topology in bilayer , Science 384, 343 (2024).
- Y. Xia, Z. Han, K. Watanabe, T. Taniguchi, J. Shan, and K. F. Mak, Superconductivity in twisted bilayer , Nature (London) 637, 833 (2025).
- Y. Guo, J. Pack, J. Swann, L. Holtzman, M. Cothrine, K. Watanabe, T. Taniguchi, D. G. Mandrus, K. Barmak, J. Hone et al., Superconductivity in 5.0° twisted bilayer , Nature (London) 637, 839 (2025).
- A. Weston, E. G. Castanon, V. Enaldiev, F. Ferreira, S. Bhattacharjee, S. Xu, H. Corte-León, Z. Wu, N. Clark, A. Summerfield et al., Interfacial ferroelectricity in marginally twisted 2D semiconductors, Nat. Nanotechnol. 17, 390 (2022).
- E. C. Regan, D. Wang, C. Jin, M. I. Bakti Utama, B. Gao, X. Wei, S. Zhao, W. Zhao, Z. Zhang, K. Yumigeta, M. Blei, J. D. Carlström, K. Watanabe, T. Taniguchi, S. Tongay, M. Crommie, A. Zettl, and F. Wang, Mott and generalized Wigner crystal states in moiré superlattices, Nature (London) 579, 359 (2020).
- Y. Tang, L. Li, T. Li, Y. Xu, S. Liu, K. Barmak, K. Watanabe, T. Taniguchi, A. H. MacDonald, J. Shan et al., Simulation of Hubbard model physics in moiré superlattices, Nature (London) 579, 353 (2020).
- R. Xiong, J. H. Nie, S. L. Brantly, P. Hays, R. Sailus, K. Watanabe, T. Taniguchi, S. Tongay, and C. Jin, Correlated insulator of excitons in moiré superlattices, Science 380, 860 (2023).
- B. Gao, D. G. Suárez-Forero, S. Sarkar, T.-S. Huang, D. Session, M. J. Mehrabad, R. Ni, M. Xie, P. Upadhyay, J. Vannucci et al., Excitonic Mott insulator in a Bose-Fermi-Hubbard system of moiré heterobilayer, Nat. Commun. 15, 2305 (2024).
- Y. Xu, S. Liu, D. A. Rhodes, K. Watanabe, T. Taniguchi, J. Hone, V. Elser, K. F. Mak, and J. Shan, Correlated insulating states at fractional fillings of moiré superlattices, Nature (London) 587, 214 (2020).
- Y. Zhou, J. Sung, E. Brutschea, I. Esterlis, Y. Wang, G. Scuri, R. J. Gelly, H. Heo, T. Taniguchi, K. Watanabe et al., Bilayer Wigner crystals in a transition metal dichalcogenide heterostructure, Nature (London) 595, 48 (2021).
- K. Kang, B. Shen, Y. Qiu, Y. Zeng, Z. Xia, K. Watanabe, T. Taniguchi, J. Shan, and K. F. Mak, Evidence of the fractional quantum spin Hall effect in moiré , Nature (London) 628, 522 (2024).
- T. Li, S. Jiang, B. Shen, Y. Zhang, L. Li, Z. Tao, T. Devakul, K. Watanabe, T. Taniguchi, L. Fu et al., Quantum anomalous Hall effect from intertwined moiré bands, Nature (London) 600, 641 (2021).
- L. Ciorciaro, T. Smoleński, I. Morera, N. Kiper, S. Hiestand, M. Kroner, Y. Zhang, K. Watanabe, T. Taniguchi, E. Demler et al., Kinetic magnetism in triangular moiré materials, Nature (London) 623, 509 (2023).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/259w-bpxx for additional supporting figures, which includes Refs. [23,24].
- L. Zhang, L. Gu, R. Ni, M. Xie, S. Park, H. Jang, R. Ma, T. Taniguchi, K. Watanabe, and Y. Zhou, Electrical control and transport of tightly bound interlayer excitons in a heterostructure, Phys. Rev. Lett. 132, 216903 (2024).
- L. A. Jauregui, A. Y. Joe, K. Pistunova, D. S. Wild, A. A. High, Y. Zhou, G. Scuri, K. De Greve, A. Sushko, C.-H. Yu et al., Electrical control of interlayer exciton dynamics in atomically thin heterostructures, Science 366, 870 (2019).
- L. Wang, E.-M. Shih, A. Ghiotto, L. Xian, D. A. Rhodes, C. Tan, M. Claassen, D. M. Kennes, Y. Bai, B. Kim et al., Correlated electronic phases in twisted bilayer transition metal dichalcogenides, Nat. Mater. 19, 861 (2020).
- H. Pan, F. Wu, and S. Das Sarma, Band topology, Hubbard model, Heisenberg model, and Dzyaloshinskii-Moriya interaction in twisted bilayer , Phys. Rev. Res. 2, 033087 (2020).
- J. Zang, J. Wang, J. Cano, and A. J. Millis, Hartree-fock study of the moiré Hubbard model for twisted bilayer transition metal dichalcogenides, Phys. Rev. B 104, 075150 (2021).
- D. Muñoz-Segovia, V. Crépel, R. Queiroz, and A. J. Millis, Twist-angle evolution of the intervalley-coherent antiferromagnet in twisted , Phys. Rev. B 112, 085111 (2025).
- F. Wu, T. Lovorn, E. Tutuc, I. Martin, and A. H. MacDonald, Topological insulators in twisted transition metal dichalcogenide homobilayers, Phys. Rev. Lett. 122, 086402 (2019).
- Y. Xie, A. T. Pierce, J. M. Park, D. E. Parker, E. Khalaf, P. Ledwith, Y. Cao, S. H. Lee, S. Chen, P. R. Forrester et al., Fractional Chern insulators in magic-angle twisted bilayer graphene, Nature (London) 600, 439 (2021).
- K. P. Nuckolls, M. Oh, D. Wong, B. Lian, K. Watanabe, T. Taniguchi, B. A. Bernevig, and A. Yazdani, Strongly correlated Chern insulators in magic-angle twisted bilayer graphene, Nature (London) 588, 610 (2020).
- E. M. Spanton, A. A. Zibrov, H. Zhou, T. Taniguchi, K. Watanabe, M. P. Zaletel, and A. F. Young, Observation of fractional Chern insulators in a van der Waals heterostructure, Science 360, 62 (2018).
- X.-W. Zhang, C. Wang, X. Liu, Y. Fan, T. Cao, and D. Xiao, Polarization-driven band topology evolution in twisted and , Nat. Commun. 15, 4223 (2024).
- T. Devakul, V. Crépel, Y. Zhang, and L. Fu, Magic in twisted transition metal dichalcogenide bilayers, Nat. Commun. 12, 6730 (2021).
- P. Knüppel, J. Zhu, Y. Xia, Z. Xia, Z. Han, Y. Zeng, K. Watanabe, T. Taniguchi, J. Shan, and K. F. Mak, Correlated states controlled by a tunable van Hove singularity in moiré bilayers, Nat. Commun. 16, 1959 (2025).
- K. Kang, Y. Qiu, K. Watanabe, T. Taniguchi, J. Shan, and K. F. Mak, Double quantum spin Hall phase in moiré , Nano Lett. 24, 14901 (2024).
- A. Abouelkomsan and L. Fu, Non-Abelian spin Hall insulator, Phys. Rev. Res. 7, 023083 (2025).
- E. Anderson, F.-R. Fan, J. Cai, W. Holtzmann, T. Taniguchi, K. Watanabe, D. Xiao, W. Yao, and X. Xu, Programming correlated magnetic states with gate-controlled moiré geometry, Science 381, 325 (2023).
- V. Crépel and L. Fu, Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides, Phys. Rev. B 107, L201109 (2023).
- X. Chang et al., Emergent charge-transfer ferromagnetism and fractional Chern states in moiré , arXiv:2503.13213.
- Y. Wang, J. Choe, E. Anderson, W. Li, J. Ingham, E. A. Arsenault, Y. Li, X. Hu, T. Taniguchi, K. Watanabe, X. Roy, D. Basov, D. Xiao, R. Queiroz, J. C. Hone, X. Xu, and X. Y. Zhu, Hidden states and dynamics of fractional fillings in moiré superlattices, arXiv:2502.21153.
- E. Anderson, H. Park, K. Yang, J. Cai, T. Taniguchi, K. Watanabe, L. Fu, T. Cao, D. Xiao, and X. Xu, Magnetoelectric control of helical light emission in a moiré Chern magnet, arXiv:2503.02810.
- F. Xu, Z. Sun, J. Li, C. Zheng, C. Xu, J. Gao, T. Jia, K. Watanabe, T. Taniguchi, B. Tong, L. Lu, J. Jia, Z. Shi, S. Jiang, Y. Zhang, Y. Zhang, S. Lei, X. Liu, and T. Li, Signatures of unconventional superconductivity near reentrant and fractional quantum anomalous Hall insulators, arXiv:2504.06972.
- M. Xie, M. Hafezi, and S. Das Sarma, Long-lived topological flatband excitons in semiconductor moiré heterostructures: A bosonic Kane-Mele model platform, Phys. Rev. Lett. 133, 136403 (2024).
- H. Park, J. Zhu, X. Wang, Y. Wang, W. Holtzmann, T. Taniguchi, K. Watanabe, J. Yan, L. Fu, T. Cao et al., Dipole ladders with large hubbard interaction in a moiré exciton lattice, Nat. Phys. 19, 1286 (2023).
- Z. Lian, Y. Meng, L. Ma, I. Maity, L. Yan, Q. Wu, X. Huang, D. Chen, X. Chen, X. Chen et al., Valley-polarized excitonic Mott insulator in moiré superlattice, Nat. Phys. 20, 34 (2024).
- M. Hafezi, A. S. Sørensen, E. Demler, and M. D. Lukin, Fractional quantum Hall effect in optical lattices, Phys. Rev. A 76, 023613 (2007).
- G. Möller and N. R. Cooper, Composite fermion theory for bosonic quantum Hall states on lattices, Phys. Rev. Lett. 103, 105303 (2009).
- Y.-F. Wang, Z.-C. Gu, C.-D. Gong, and D. N. Sheng, Fractional quantum Hall effect of hard-core bosons in topological flat bands, Phys. Rev. Lett. 107, 146803 (2011).
- N. Regnault and B. A. Bernevig, Fractional Chern insulator, Phys. Rev. X 1, 021014 (2011).
- T. Neupert, L. Santos, C. Chamon, and C. Mudry, Fractional quantum Hall states at zero magnetic field, Phys. Rev. Lett. 106, 236804 (2011).
- D. Sheng, Z.-C. Gu, K. Sun, and L. Sheng, Fractional quantum Hall effect in the absence of Landau levels, Nat. Commun. 2, 389 (2011).
- E. Tang, J.-W. Mei, and X.-G. Wen, High-temperature fractional quantum Hall states, Phys. Rev. Lett. 106, 236802 (2011).
- K. Sun, Z. Gu, H. Katsura, and S. Das Sarma, Nearly flatbands with nontrivial topology, Phys. Rev. Lett. 106, 236803 (2011).
- J. Bloch, A. Cavalleri, V. Galitski, M. Hafezi, and A. Rubio, Strongly correlated electron–photon systems, Nature (London) 606, 41 (2022).
- D. N. Basov, R. D. Averitt, D. Van Der Marel, M. Dressel, and K. Haule, Electrodynamics of correlated electron materials, Rev. Mod. Phys. 83, 471 (2011).
- M. McGinley, M. Fava, and S. A. Parameswaran, Signatures of fractional statistics in nonlinear pump-probe spectroscopy, Phys. Rev. Lett. 132, 066702 (2024).
- G. Nambiar, A. Grankin, and M. Hafezi, Diagnosing electronic phases of matter using photonic correlation functions, Phys. Rev. X 15, 041020 (2025).
- J. R. Vannucci, Magneto-optical response of excitons in sub-Kelvin regime, Ph.D. dissertation, University of Maryland, College Park, College Park, USA, 2022.
