Abstract
Two-dimensional semiconducting moiré superlattices provide a highly tunable platform for investigating strongly correlated and topological quantum phases1,2,3,4,5. As a prototypical example, twisted bilayer MoTe2 (tMoTe2) has been shown to host fractional topological phases at zero magnetic field6,7,8,9,10,11,12,13,14,15,16,17,18,19,20. However, their evolution with twist angle and competition with other correlated quantum states remain largely unexplored. Here we report a systematic transport study of twist-angle-dependent phase diagrams in tMoTe2 across a range of 3.79°–5.76°, revealing an evolution from valley-polarized, fractional topological states to valley-degenerate correlated states and superconductivity. At relatively small twist angles, partially filled Chern bands of tMoTe2 host fractional quantum anomalous Hall states following the Jain sequence, together with signatures of an anomalous composite Fermi liquid at moiré hole filling factor νh = 1/2. Increasing twist angle progressively suppresses fractional topological phases and reconstructs the half-filled Chern band into symmetry-breaking integer Chern insulating states. At νh = 1, we observe a transition from robust integer quantum anomalous Hall insulators at small angles to displacement-field-tuned, topologically trivial correlated insulators at larger angles. At twist angles above approximately 5.6°, superconductivity emerges adjacent to the νh = 1 correlated insulator, with a phase diagram closely resembling that recently reported in twisted bilayer WSe2 (refs. 21,22,23,24). Our results indicate a unified twist-angle-driven phase evolution linking fractional topology, symmetry breaking, magnetic order and superconductivity, providing new insight into the emergent quantum phenomena in moiré systems.
This is a preview of subscription content, access via your institution
Access options
/*# sourceMappingURL=buybox-fragment-31b50dd.css.map */
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
cancel any time
Subscribe to this journal
Receive 51 print issues and online access
only 3.90 € per issue
Buy this article
- Purchase on SpringerLink
- Instant access to the full article PDF.
39,95 €
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
Data availability
The data used in this study are available from the corresponding authors upon request. Source data are provided with this paper.
References
-
Mak, K. F. & Shan, J. Semiconductor moiré materials. Nat. Nanotechnol. 17, 686–695 (2022).
-
Li, B. H., Qiu, W.-X., Wu, F. & MacDonald, A. H. Quantum phases in twisted homobilayer transition metal dichalcogenides. Natl Sci. Rev. 13, nwaf570 (2025).
-
Cao, T., Fu, L., Ju, L., Xiao, D. & Xu, X. Fractional quantum anomalous Hall effect. Annu. Rev. Condens. Matter Phys. 17, 233–256 (2025).
-
Bernevig, B. A. et al. Fractional quantization in insulators from Hall to Chern. Nat. Phys. 21, 1702–1713 (2025).
-
Li, T., Liu, J., Xie, J. & Lu, X. Fractional quantum anomalous Hall effect in moiré fractional Chern insulators. Nat. Mater. https://doi.org/10.1038/s41563-026-02649-9 (2026).
-
Cai, J. et al. Signatures of fractional quantum anomalous Hall states in twisted MoTe2. Nature 622, 63–68 (2023).
-
Zeng, Y. et al. Thermodynamic evidence of fractional Chern insulator in moiré MoTe2. Nature 622, 69–73 (2023).
-
Park, H. et al. Observation of fractionally quantized anomalous Hall effect. Nature 622, 74–79 (2023).
-
Xu, F. et al. Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2. Phys. Rev. X 13, 031037 (2023).
-
Ji, Z. et al. Local probe of bulk and edge states in a fractional Chern insulator. Nature 635, 578–583 (2024).
-
Redekop, E. et al. Direct magnetic imaging of fractional Chern insulators in twisted MoTe2. Nature 635, 584–589 (2024).
-
Kang, K. et al. Evidence of the fractional quantum spin Hall effect in moiré MoTe2. Nature 628, 522–526 (2024).
-
Xu, F. et al. Interplay between topology and correlations in the second moiré band of twisted bilayer MoTe2. Nat. Phys. 21, 542–548 (2025).
-
Park, H. et al. Ferromagnetism and topology of the higher flat band in a fractional Chern insulator. Nat. Phys. 21, 549–555 (2025).
-
Park, H. et al. Observation of dissipationless fractional Chern insulator. Nat. Phys. 22, 389–395 (2026).
-
Xu, F. et al. Signatures of unconventional superconductivity near reentrant and fractional quantum anomalous Hall insulators. Preprint at arxiv.org/abs/2504.06972 (2025).
-
Li, W. et al. Universal magnetic phases in twisted bilayer MoTe2. Nano Lett. 25, 18044–18050 (2025).
-
Anderson, E. et al. Trion sensing of a zero-field composite Fermi liquid. Nature 635, 590–595 (2024).
-
Wang, Y. et al. Hidden states and dynamics of fractional fillings in twisted MoTe2 bilayers. Nature 641, 1149–1155 (2025).
-
Pan, H. et al. Optical signatures of (-frac{1}{3}) fractional quantum anomalous Hall state in twisted MoTe2. Phys. Rev. Lett. 136, 056601 (2026).
-
Xia, Y. et al. Superconductivity in twisted bilayer WSe2. Nature 637, 833–838 (2025).
-
Guo, Y. et al. Superconductivity in 5.0° twisted bilayer WSe2. Nature 637, 839–845 (2025).
-
Xia, Y. et al. Bandwidth-tuned Mott transition and superconductivity in moiré WSe2. Nature 650, 585–591 (2026).
-
Guo, Y. et al. Angle evolution of the superconducting phase diagram in twisted bilayer WSe2. Nature 652, 622–627 (2026).
-
Wu, F., Lovorn, T., Tutuc, E., Martin, I. & MacDonald, A. H. Topological insulators in twisted transition metal dichalcogenide homobilayers. Phys. Rev. Lett. 122, 086402 (2019).
-
Yu, H., Chen, M. & Yao, W. Giant magnetic field from moiré induced Berry phase in homobilayer semiconductors. Natl Sci. Rev. 7, 12–20 (2020).
-
Li, H., Kumar, U., Sun, K. & Lin, S.-Z. Spontaneous fractional Chern insulators in transition metal dichalcogenide moiré superlattices. Phys. Rev. Res. 3, L032070 (2021).
-
Devakul, T., Crépel, V., Zhang, Y. & Fu, L. Magic in twisted transition metal dichalcogenide bilayers. Nat. Commun. 12, 6730 (2021).
-
Kane, C. L. & Mele, E. J. Quantum spin Hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005).
-
Crépel, V. & Fu, L. Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides. Phys. Rev. B 107, L201109 (2023).
-
Dong, J., Wang, J., Ledwith, P. J., Vishwanath, A. & Parker, D. E. Composite Fermi liquid at zero magnetic field in twisted MoTe2. Phys. Rev. Lett. 131, 136502 (2023).
-
Wang, C. et al. Fractional Chern insulator in twisted bilayer MoTe2. Phys. Rev. Lett. 132, 036501 (2024).
-
Reddy, A. P., Alsallom, F., Zhang, Y., Devakul, T. & Fu, L. Fractional quantum anomalous Hall states in twisted bilayer MoTe2 and WSe2. Phys. Rev. B 108, 085117 (2023).
-
Morales-Durán, N., Wei, N., Shi, J. & MacDonald, A. H. Magic angles and fractional Chern insulators in twisted homobilayer transition metal dichalcogenides. Phys. Rev. Lett. 132, 096602 (2024).
-
Sheng, D. N., Reddy, A. P., Abouelkomsan, A., Bergholtz, E. J. & Fu, L. Quantum anomalous Hall crystal at fractional filling of Moiré superlattices. Phys. Rev. Lett. 133, 066601 (2024).
-
Reddy, A. P. & Fu, L. Toward a global phase diagram of the fractional quantum anomalous Hall effect. Phys. Rev. B 108, 245159 (2023).
-
Muñoz-Segovia, D., Crépel, V., Queiroz, R. & Millis, A. J. Twist-angle evolution of the intervalley-coherent antiferromagnet in twisted WSe2. Phys. Rev. B 112, 085111 (2025).
-
Li, B. H., Qiu, W.-X. & Wu, F. Electrically tuned topology and magnetism in twisted bilayer MoTe2 at νh = 1. Phys. Rev. B 109, L041106 (2024).
-
Pan, H., Wu, F. & Sarma, S. D. Band topology, Hubbard model, Heisenberg model, and Dzyaloshinskii-Moriya interaction in twisted bilayer WSe2. Phys. Rev. Res. 2, 033087 (2020).
-
Qiu, W.-X., Li, B., Luo, X.-J. & Wu, F. Interaction-driven topological phase diagram of twisted bilayer MoTe2. Phys. Rev. X 13, 041026 (2023).
-
Wang, T., Devakul, T., Zaletel, M. P. & Fu, L. Diverse magnetic orders and quantum anomalous Hall effect in twisted bilayer MoTe2 and WSe2. Preprint at arxiv.org/abs/2306.02501 (2024).
-
Yu, J. et al. Fractional Chern insulators versus nonmagnetic states in twisted bilayer MoTe2. Phys. Rev. B 109, 045147 (2024).
-
Abouelkomsan, A., Reddy, A. P., Fu, L. & Bergholtz, E. J. Band mixing in the quantum anomalous Hall regime of twisted semiconductor bilayers. Phys. Rev. B 109, L121107 (2024).
-
Foutty, B. A. et al. Mapping twist-tuned multiband topology in bilayer WSe2. Science 384, 343–347 (2024).
-
Gao, B. et al. Probing quantum anomalous Hall states in twisted bilayer WSe2 via attractive polaron spectroscopy. Phys. Rev. X 16, 021037 (2026).
-
Knüppel, P. et al. Correlated states controlled by a tunable van Hove singularity in moiré WSe2 bilayers. Nat. Commun. 16, 1959 (2025).
-
Schrade, C. & Fu, L. Nematic, chiral, and topological superconductivity in twisted transition metal dichalcogenides. Phys. Rev. B 110, 035143 (2024).
-
Fischer, A. et al. Theory of intervalley-coherent AFM order and topological superconductivity in tWSe2. Phys. Rev. X 15, 041055 (2025).
-
Qin, W., Qiu, W.-X. & Wu, F. Topological chiral superconductivity mediated by intervalley antiferromagnetic fluctuations in twisted bilayer WSe2. Phys. Rev. Lett. 135, 246002 (2025).
-
Chubukov, A. V. & Varma, C. M. Quantum criticality and superconductivity in twisted transition metal dichalcogenides. Phys. Rev. B 111, 014507 (2025).
-
Christos, M., Bonetti, P. M. & Scheurer, M. S. Approximate symmetries, insulators, and superconductivity in the continuum-model description of twisted WSe2. Phys. Rev. Lett. 135, 046503 (2025).
-
Goldman, H., Reddy, A. P., Paul, N. & Fu, L. Zero-field composite Fermi liquid in twisted semiconductor bilayers. Phys. Rev. Lett. 131, 136501 (2023).
-
Stern, A. & Fu, L. Transport properties of a half-filled Chern band at the electron and composite fermion phases. Phys. Rev. Lett. 133, 246602 (2024).
-
Lu, T. & Santos, L. H. Fractional Chern insulators in twisted bilayer MoTe2: a composite fermion perspective. Phys. Rev. Lett. 133, 186602 (2024).
-
Zhang, M. et al. Transport evidence for Wigner crystals in monolayer MoTe2. Preprint at arxiv.org/abs/2506.20392 (2025).
-
Fallahazad, B. et al. Shubnikov–de Haas oscillations of high-mobility holes in monolayer and bilayer WSe2: Landau level degeneracy, effective mass, and negative compressibility. Phys. Rev. Lett. 116, 086601 (2016).
-
Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).
-
Puotinen, D. & Newnham, R. E. The crystal structure of MoTe2. Acta Crystallogr. 14, 691–692 (1961).
-
Mao, N. et al. Transfer learning relaxation, electronic structure and continuum model for twisted bilayer MoTe2. Commun. Phys. 7, 262 (2024).
-
Tuo, C., Li, M.-R., Wu, Z., Sun, W. & Yao, H. Theory of topological superconductivity and antiferromagnetic correlated insulators in twisted bilayer WSe2. Nat. Commun. 16, 9525 (2025).
-
Xie, F. et al. Superconductivity in twisted WSe2 from topology-induced quantum fluctuations. Phys. Rev. Lett. 134, 136503 (2025).
-
Zhu, J., Chou, Y.-Z., Xie, M. & Sarma, S. D. Superconductivity in twisted transition metal dichalcogenide homobilayers. Phys. Rev. B 111, L060501 (2025).
-
Kim, S., Mendez-Valderrama, J. F., Wang, X. & Chowdhury, D. Theory of correlated insulators and superconductor at ν = 1 in twisted WSe2. Nat. Commun. 16, 1701 (2025).
-
Akbar, W., Biborski, A., Rademaker, L. & Zegrodnik, M. Topological superconductivity with mixed singlet-triplet pairing in moiré transition metal dichalcogenide bilayers. Phys. Rev. B 110, 064516 (2024).
-
Zegrodnik, M. & Biborski, A. Mixed singlet-triplet superconducting state within the moiré t−J−U model applied to twisted bilayer WSe2. Phys. Rev. B 108, 064506 (2023).
-
Zang, J., Wang, J., Cano, J. & Millis, A. J. Hartree-Fock study of the moiré Hubbard model for twisted bilayer transition metal dichalcogenides. Phys. Rev. B 104, 075150 (2021).
-
Zegrodnik, M., Akbar, W., Biborski, A. & Rademaker, L. Optimal superconductivity in twisted bilayer WSe2 where the Van Hove singularity crosses half-filling. Phys. Rev. Res. 8, L012070 (2026).
-
Xu, C. et al. Chiral superconductivity from spin polarized Chern band in twisted MoTe2. Phys. Rev. Lett. 135, 266005 (2025).
-
Guerci, D., Abouelkomsan, A. & Fu, L. From fractionalization to Chiral topological superconductivity in a flat Chern band. Phys. Rev. Lett. 135, 186601 (2025).
-
Shi, Z. D. & Senthil, T. Anyon delocalization transitions out of a disordered fractional quantum anomalous Hall insulator. Proc. Natl Acad. Sci. USA 122, e2520608122 (2025).
-
Nosov, P. A., Han, Z. & Khalaf, E. Anyon superconductivity and plateau transitions in doped fractional quantum anomalous Hall insulators. Phys. Rev. Lett. 136, 106501 (2026).
-
Wang, T. & Zaletel, M. P. Chiral superconductivity near a fractional Chern insulator. Preprint at arxiv.org/abs/2507.07921 (2025).
-
Pichler, F., Kuhlenkamp, C., Knap, M. & Vishwanath, A. Microscopic mechanism of anyon superconductivity emerging from fractional Chern insulators. Newton 2, 100340 (2026).
-
Liu, F. et al. From fractional Chern insulators to topological electronic crystals in moiré MoTe2: quantum geometry tuning via remote layer. Preprint at arxiv.org/abs/2512.03622 (2025).
-
Wu, M. et al. Reconstructed Chern insulator in moderately correlated twisted bilayer MoTe2. Natl Sci. Rev. https://doi.org/10.1093/nsr/nwag610 (2026).
Acknowledgements
We thank J. Shan, K. F. Mak and F. Wu for their discussions. Device fabrication is supported by the Micro-nano Fabrication Platform of the School of Physics and Astronomy at Shanghai Jiao Tong University.
Funding
This work is supported by the National Key R&D Program of China (nos. 2022YFA1405400, 2022YFA1402404, 2022YFA1402702 and 2022YFA1403301), the National Natural Science Foundation of China (nos. 12350403, 92565302, 12621003, 12374045, 12350404, 12204115, 92265102, 12550403 and 12674229), the Quantum Science and Technology–National Science and Technology Major Project (nos. 2021ZD0302600, 2021ZD0302500, 2023ZD0300500, 2024ZD0300104 and 2025ZD0300500), the Natural Science Foundation of Shanghai (nos. 24LZ1401100 and 24QA2703700), and the Shanghai Jiao Tong University 2030 Initiative Program. J.G., J.Z. and Yuanbo Zhang acknowledge support from the Fundamental and Interdisciplinary Disciplines Breakthrough Plan of the Ministry of Education of China (grant no. JYB2025XDXM120), the Shanghai Municipal Science and Technology Commission (nos. 23JC1400600 and 2019SHZDZX01), and the China Postdoctoral Science Foundation (grant no. 2022M720812). S.L. acknowledges support by the Hong Kong RGC (no. 26308524, AoE/P-604/25R), the Hong Kong Collaborative Research Fund (no. C6053-23G), and the Guangdong Provincial Quantum Science Strategic Initiative (nos. GDZX2501003 and GDZX2601002). K.W. and T.T. acknowledge support from the CREST (JPMJCR24A5), JST and World Premier International Research Center Initiative (WPI), MEXT, Japan. T.L. acknowledges support from the New Cornerstone Science Foundation through the XPLORER PRIZE and the Asian Young Scientist Fellowship. X.L. acknowledges ‘Shuguang Program’ supported by Shanghai Education Development Foundation. F.X. are supported by T.D. Lee scholarship.
Author information
Authors and Affiliations
Contributions
Z.S., F.X., J.L., T.J., K.C. and W.T. fabricated the devices and performed the electrical transport measurements. Z.S., F.X., J.L., T.J., K.C., J.J., X.L. and T.L. analysed the data. Y.J., J.G., J.Z., Yuanbo Zang and S.L. grew the bulk MoTe2 crystals. C.X. and Yang Zhang performed the band-structure calculations. S.W. and S.J. performed optical characterizations. K.W. and T.T. grew the bulk hBN crystals. T.L. and X.L. supervised the project.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature thanks Tiancheng Song and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Extended data figures and tables
Extended Data Fig. 1 Device image and twist angle calibration for device 11 (5.18°).
a, Optical micrograph image of device 11 (5.18°). Yellow dashed lines indicate the TaSe2 contacts. Red dashed lines outline the tMoTe2 region. Blue and purple dashed lines denote the top-gate and bottom-gate regions, respectively. b, Two-terminal resistance R2 as a function of νh for device 2 (3.96°) and device 11 (5.18°), shown by the black and red curves, respectively. The measured R2 is primarily limited by contact resistance. In general, devices with larger twist angles exhibit better contacts, possibly due to the less flat moiré bands. c, Map of ρxx as a function of νh and D for device 11 (5.18°) measured at T = 10 mK and B = 8 T. d, Linear fit of the Landau-level filling factor νLL a function of νh (along the dashed line in c), from which the moiré density ({n}_{{rm{M}}}) is extracted. e, ρxx as a function of B at D = 290 mV/nm and νh = 0.25, corresponding to the black dot marked in c. The onset of Shubnikov–de Haas oscillations occurs at B ≈ 1.3 T, reflecting the high quality of the device. f, ρxx as a function of νh and D at T = 10 mK and B = 0 T. No superconducting state is observed in this device. Grey regions indicate areas inaccessible to electrical transport measurements.
Extended Data Fig. 2 Transport phase diagrams of device 1 (3.79°), device 3 (4.08°), device 5 (4.22°), device 8 (4.69°), and device 9 (4.82°).
a,c,e,g,i, Symmetrized ρxx as a function of D and νh for device 1 (a), 3 (c), 5 (e), 8 (g), and 9 (i). b,d,f,h,j, Antisymmetrized ρxy as a function of D and νh for device 1 (b), 3 (d), 5 (f), 8 (h), and 9 (j). All maps measured at T = 1.6 K and with B = 0.1 T (a–f) or 0.3 T (g–j). Device 1 (3.79°) host multiple FQAH states. As the twist angle increases, only IQAH states remain in device 5 (4.22°) and 8 (4.69°), while no quantum anomalous Hall states are observed in device 9 (4.82°). Grey regions in a,c,e indicate areas inaccessible to electrical transport measurements.
Extended Data Fig. 3 Magnetism and Chern insulators in device 1 (3.79°), device 4 (4.14°) and device 7 (4.63°).
a–c, Magnetic hysteresis loop scans at νh = 4/7, 3/5, and 2/3, respectively, measured at D = 0 in device 1. Clear FQAH effects are observed at these fillings. d–i, Magnetic hysteresis loop scans at νh = 0.55, 3/5, 2/3, 0.8, 0.9 and 1, respectively, measured at D = 0 in device 4. In this device, robust ferromagnetism persists over the filling range of νh ≈ 1/2 to 1 at D = 0, and IQAH effects are observed around both νh = 1 and νh ≈ 0.62. Panels a–i were measured at T = 600 mK. j, Magnetic hysteresis loop scans measured at νh = 1 and D = 175 mV/nm in device 7 at T = 10 mK. k, Symmetrized ρxx and antisymmetrized ρxy as a function of νh at D = 175 mV/nm measured at T = 10 mK (red and black curves) and at T = 1.6 K (green and blue curves), the applied B-field is 0.1 T. At T = 10 mK, ρxx at the IQAH state nearly vanishes, while at T = 1.6 K, the residual ρxx increases to approximately 5 kΩ and ρxy deviates from the quantized value of h/e2.
Extended Data Fig. 4 Magnetism and Chern insulators in device 6 (4.55°).
a,b, Temperature dependence of magnetic hysteresis loop scans of ρxx (a) and ρxy (b) at νh = 1 and D = 130 mV/nm. Integer quantum anomalous Hall effect is observed at low temperatures and at B = 0. The Curie temperature for the ferromagnetism at νh = 1 is approximately 4 K. c,d, The same as a and b, respectively, but measured at νh = 1/2 and D = 0. Clear magnetic hysteresis loop is observed at low temperatures, but zero-field quantization is not achieved. A small magnetic field B ≈ 0.2 T is required to stabilize the SBCI state. The Curie temperature at νh = 1/2 is approximately 2 K. e–i, Magnetic hysteresis loop scans at νh = 1, 0.9, 0.8, 0.7, and 0.6, respectively, measured at T = 300 mK and D = 0, respectively. Ferromagnetism is absent around νh = 1 and 0.6 at D = 0.
Extended Data Fig. 5 Středa formula for integer, fractional, and symmetry-broken Chern insulators.
a-b, ρxx as a function of νh and B for device 1 (a) and device 7 (b). Panel a was measured at 1.6 K and Panel b at 0.3 K. In device 1 (3.79°), the integer and fractional Chern insulators follows the expected dispersions based on the Středa formula ({n}_{M}frac{d{nu }_{{rm{h}}}}{{dB}}=Cfrac{e}{h}), as indicated by the dashed lines. In device 7 (4.63°), the SBCI states at νh = 1/2 also approximately follows the Streda formula with C = 1, consistent with the measured quantized ρxy of h/e2. c–d, ρxx (c) and ρxy (d) as a function of νh and B for device 8 (4.69°). Grey regions in maps indicate areas inaccessible to electrical transport measurements. In addition to the SBCI state at νh = 1/2, a new state emerges from νh ≈ 0.52. This state also exhibits a quantized anomalous Hall resistance of h/e² but does not follow the Středa relation. Interestingly, a closely related state (at νh ≈ 0.53) was recently reported in a 3.7° twisted mono-bilayer MoTe2 device74, indicating that both twist-angle tuning and remote-layer engineering can give rise to analogous modifications of the band quantum geometry. We also note a very recent study reporting similar observation in a 4.54° tMoTe275.
Extended Data Fig. 6 Calculated DOS compared with experiments.
a,c, Calculated DOS as a function of interlayer potential difference Δ and νh at θ = 4.6° (a) and θ = 5.8° (c). b, ρxx as a function of νh and D at B = 0 and T = 1.6 K for device 7 (4.63°). The red solid line marks the calculated VHS from a. We approximately convert Δ into D using (D=E{varepsilon }_{{rm{hBN}}}=Delta {varepsilon }_{{{rm{MoTe}}}_{2}}/(ed)), where d is the interlayer separation in MoTe2, and ({varepsilon }_{{rm{hBN}}}), ({varepsilon }_{{{rm{MoTe}}}_{2}}) are the dielectric constant for hBN and MoTe2, respectively (Methods). It illustrates that the emergence of the IQAH state roughly coincides with the D-field at which the VHS crosses νh = 1. Dashed lines mark the local ρxx peaks beyond single-particle VHS, which is likely associated with interaction-induced Fermi-surface reconstruction. d, Comparison between the calculated VHS (red) and the experimentally extracted VHS (green) from the ρxy–νh–D map of device 15 (shown in Fig. 3h), shown on the ρxx–νh–D map at B = 0 T and T = 10 mK. The calculated VHS across the superconducting and correlated insulating states, also agree reasonably well with the experimentally extracted VHS.
Extended Data Fig. 7 T-dependent ρxx maps in device 15 (5.76°).
a–d, Maps of ρxx at zero magnetic field as a function of νh and D, measured at T = 100 mK, 150 mK, 200 mK, 300 mK, respectively. Observed superconductivity is most robust at fillings slightly below νh = 1, adjacent to the νh = 1 correlated insulator.
Extended Data Fig. 8 D-dependent transport behaviors at νh = 1 in device 15 (5.76°).
a, ρxx as a function of T and D at zero magnetic field, the same dataset as shown in Fig. 4b. Line cuts shown in b–f are indicated by the vertical dashed lines. b, ρxx as a function of T at D = −432 mV/nm. A non-monotonic temperature dependence is observed, with a local ρxx minimum around 4 K. Similar behaviors have been reported in tWSe223, where the local ρxx minimum roughly indicate the Néel temperature of the valley-coherent antiferromagnetic order. c, ρxx as a function of 1/T at D = −324 mV/nm. Thermal activation behavior corresponding to a correlated insulator gap is observed. The fit yields a gap of ~ 2.5 meV. d-f, ρxx as a function of T at D = −277, −261, and −160 mV/nm, respectively. Strange-metal behaviors with linear-in-T resistivity are observed in the superconducting normal state (d) and adjacent to the superconducting region (e). Away from the superconducting region at smaller D, Fermi liquid behaviors are observed at low temperatures (f).
Extended Data Fig. 9 Superconducting states in device 13 (5.67°) and device 14 (5.69°).
a-b, ρxx map as a function of νh and D for device 13 (5.67°), measured at T = 10 mK and B = 0. c, ρxx as a function of T and νh at D = −220 mV/nm. d, Differential resistivity dV/dI as a function of Idc and T at B = 0 for the superconducting state. e, The B-dV/dI –Idc map measured at T = 10 mK. f, ρxx as a function of T under different B. Measurements in panels d–f were performed at the optimal superconducting condition for device 13 (νh = 0.965, D = −227 mV/nm), as marked by the red dot in b. g, Local ρxx map as a function of νh and D for device 14 (5.69°), measured at T = 10 mK and B = 0. The range shown in g is limited by gate leakage, which prevents us from accessing a more complete phase diagram in this device. h, The B-dV/dI –Idc map measured at T = 10 mK. i, ρxx as a function of T at B = 0. Measurements in panels h,i were performed at the optimal superconducting condition for device 14 (νh = 0.97, D = −230 mV/nm), as marked by the green dot in g. The optimal superconducting transition temperature Tc (determined by 50% Rn) is approximately 175 mK in device 13 and 165 mK in device 14, respectively, which is slightly lower than that observed in device 15 with a larger twist angle of 5.76°.
Extended Data Fig. 10 Fermi surface reconstructions near the superconducting state in device 15 (5.76°).
a–b, Antisymmetrized ρxy as a function of D and νh measured at B = 0.2 T and T = 10 mK (a), and at B = 0.5 T and T = 1.6 K (b). The red dashed lines delineate the superconducting region based on the ρxx map shown in Fig. 4a. Fermi Surface reconstructions (FSR) are observed near the correlated insulator at νh = 1, resembling those recently reported in tWSe223,24. c, ρxy as a function of B at different νh following the black dashed line shown in b, measured at T = 1.6 K.
Supplementary information
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Sun, Z., Xu, F., Li, J. et al. Twist-angle-dependent quantum phase diagrams in moiré bilayer MoTe2.
Nature (2026). https://doi.org/10.1038/s41586-026-11274-0
-
Received:
-
Accepted:
-
Published:
-
Version of record:
-
DOI: https://doi.org/10.1038/s41586-026-11274-0