journal article·2026-05-04Open access

Magnetic and moiré proximity effects in WSe2/WSe2/CrI3 trilayers

Junyi Liu, Xu Zhang, Gang Lu

npj Computational Materials· Volume 12· Issue 1

Abstract

Integrating magnetic order to moiré superlattices is of significant scientific and technological interest. Based on first-principles calculations, we study the interplay of magnetic proximity and moiré proximity in WSe2/WSe2/CrI3 trilayers with different stackings and twist angles. Large valley splitting is observed due to redistribution of the exciton charge density across layers via a super-exchange-like mechanism, and its electric-field dependence bears similarity to electrically tunable and valley-selective Feshbach resonances. The valley splitting can be magnified in moiré superlattices owing to the superposition of Umklapp excitons folded from moiré minibands, yielding spatially modulated and enhanced magnetic proximity. The moiré proximity effect is demonstrated via an imprinted moiré potential on CrI3 layer and its feedback to the direct moiré potential on WSe2 bilayers is observed. The cooperation between the direct and imprinted moiré potentials is shown to yield novel topological and correlated states.
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OpenAlex topics: 2D Materials and Applications · Topological Materials and Phenomena · Graphene research and applications

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References (86)

Show source-provided references
1. Buzdin, A. I. Proximity effects in superconductor-ferromagnet heterostructures. Rev. Mod. Phys. 77, 935–976 (2005).10.1103/RevModPhys.77.935 ↗
2. Zhang, B., Lu, P., Tabrizian, R., Feng, P. X. L. & Wu, Y. 2D Magnetic heterostructures: spintronics and quantum future. npj Spintron. 2, 6 (2024).10.1038/s44306-024-00011-w ↗
3. Zhao, W. et al. Realization of the Haldane Chern insulator in a moiré lattice. Nat. Phys. 20, 275–280 (2024).10.1038/s41567-023-02284-0 ↗
4. Zhong, D. et al. Van der Waals engineering of ferromagnetic semiconductor heterostructures for spin and valleytronics. Sci. Adv. 3, e1603113 (2017).10.1126/sciadv.1603113 ↗
5. Huang, B. et al. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature 546, 270–273 (2017).10.1038/nature22391 ↗
6. Liu, J., Sun, Q., Kawazoe, Y. & Jena, P. Exfoliating biocompatible ferromagnetic Cr-trihalide monolayers. Phys. Chem. Chem. Phys. 18, 8777–8784 (2016).10.1039/C5CP04835D ↗
7. Heißenbüttel, M.-C., Deilmann, T., Krüger, P. & Rohlfing, M. Valley-dependent interlayer excitons in magnetic WSe2/CrI3. Nano Lett. 21, 5173–5178 (2021).10.1021/acs.nanolett.1c01232 ↗
8. Zhang, Z., Ni, X., Huang, H., Hu, L. & Liu, F. Valley splitting in the van der Waals heterostructure WSe2/CrI3: the role of atom superposition. Phys. Rev. B 99, 115441 (2019).10.1103/PhysRevB.99.115441 ↗
9. Zollner, K., Faria Junior, P. E. & Fabian, J. Proximity exchange effects in MoSe2 and WSe2 heterostructures with CrI3: twist angle, layer, and gate dependence. Phys. Rev. B 100, 085128 (2019).10.1103/PhysRevB.100.085128 ↗
10. Hu, T. et al. Manipulation of valley pseudospin in WSe2/CrI3 heterostructures by the magnetic proximity effect. Phys. Rev. B 101, 125401 (2020).10.1103/PhysRevB.101.125401 ↗
11. Zollner, K., Faria Junior, P. E. & Fabian, J. Strong manipulation of the valley splitting upon twisting and gating in MoSe2/CrI3 and WSe2/CrI3 van der Waals heterostructures. Phys. Rev. B 107, 035112 (2023).10.1103/PhysRevB.107.035112 ↗
12. Lyons, T. P. et al. Interplay between spin proximity effect and charge-dependent exciton dynamics in MoSe2/CrBr3 van der Waals heterostructures. Nat. Commun. 11, 6021 (2020).10.1038/s41467-020-19816-4 ↗
13. Seyler, K. L. et al. Valley manipulation by optically tuning the magnetic proximity effect in WSe2/CrI3 heterostructures. Nano Lett. 18, 3823–3828 (2018).10.1021/acs.nanolett.8b01105 ↗
14. Ciorciaro, L., Kroner, M., Watanabe, K., Taniguchi, T. & Imamoglu, A. Observation of magnetic proximity effect using resonant optical spectroscopy of an electrically tunable MoSe2/CrBr3 heterostructure. Phys. Rev. Lett. 124, 197401 (2020).10.1103/PhysRevLett.124.197401 ↗
15. Choi, J., Lane, C., Zhu, J.-X. & Crooker, S. A. Asymmetric magnetic proximity interactions in MoSe2/CrBr3 van der Waals heterostructures. Nat. Mater. 22, 305–310 (2023).10.1038/s41563-022-01424-w ↗
16. Zhong, D. et al. Layer-resolved magnetic proximity effect in van der Waals heterostructures. Nat. Nanotechnol. 15, 187–191 (2020).10.1038/s41565-019-0629-1 ↗
17. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).10.1038/nature26154 ↗
18. Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).10.1038/nature26160 ↗
19. Tran, K. et al. Evidence for moiré excitons in van der Waals heterostructures. Nature 567, 71–75 (2019).10.1038/s41586-019-0975-z ↗
20. Seyler, K. L. et al. Signatures of moiré-trapped valley excitons in MoSe2/WSe2 heterobilayers. Nature 567, 66–70 (2019).10.1038/s41586-019-0957-1 ↗
21. Jin, C. et al. Observation of moiré excitons in WSe2/WS2 heterostructure superlattices. Nature 567, 76–80 (2019).10.1038/s41586-019-0976-y ↗
22. Wang, Z. et al. Evidence of high-temperature exciton condensation in two-dimensional atomic double layers. Nature 574, 76–80 (2019).10.1038/s41586-019-1591-7 ↗
23. Fogler, M. M., Butov, L. V. & Novoselov, K. S. High-temperature superfluidity with indirect excitons in van der Waals heterostructures. Nat. Commun. 5, 1–5 (2014).10.1038/ncomms5555 ↗
24. Butov, L. V., Lai, C. W., Ivanov, A. L., Gossard, A. C. & Chemla, D. S. Towards Bose–Einstein condensation of excitons in potential traps. Nature 417, 47–52 (2002).10.1038/417047a ↗
25. Yu, H., Liu, G.-B., Tang, J., Xu, X. & Yao, W. Moiré excitons: from programmable quantum emitter arrays to spin-orbit–coupled artificial lattices. Sci. Adv. 3, e1701696 (2017).10.1126/sciadv.1701696 ↗
26. Du, L. et al. Moiré photonics and optoelectronics. Science 379, eadg0014 (2023).10.1126/science.adg0014 ↗
27. Ciarrocchi, A., Tagarelli, F., Avsar, A. & Kis, A. Excitonic devices with van der Waals heterostructures: valleytronics meets twistronics. Nat. Rev. Mater. 7, 449–464 (2022).10.1038/s41578-021-00408-7 ↗
28. Tong, Q., Chen, M. & Yao, W. Magnetic proximity effect in a van der Waals moiré superlattice. Phys. Rev. Appl. 12, 024031 (2019).10.1103/PhysRevApplied.12.024031 ↗
29. Ge, M. et al. Enhanced valley splitting of WSe2 in twisted van der Waals WSe2/CrI3 heterostructures. npj Comput. Mater. 8, 32 (2022).10.1038/s41524-022-00715-9 ↗
30. Arora, A. & Song, J. C. W. A moiré proximity effect. Nat. Mater. 23, 165–166 (2024).10.1038/s41563-023-01781-0 ↗
31. Gu, J. et al. Remote imprinting of moiré lattices. Nat. Mater. 23, 219–223 (2024).10.1038/s41563-023-01709-8 ↗
32. He, M. et al. Dynamically tunable moiré exciton Rydberg states in a monolayer semiconductor on twisted bilayer graphene. Nat. Mater. 23, 224–229 (2024).10.1038/s41563-023-01713-y ↗
33. Zhang, Z. et al. Engineering correlated insulators in bilayer graphene with a remote Coulomb superlattice. Nat. Mater. 23, 189–195 (2024).10.1038/s41563-023-01754-3 ↗
34. Liu, J., Lu, G. & Zhang, X. Exciton dispersion and exciton–phonon interaction in solids by time-dependent density functional theory. J. Chem. Phys. 158, 044116 (2023).10.1063/5.0137326 ↗
35. Refaely-Abramson, S., Jain, M., Sharifzadeh, S., Neaton, J. B. & Kronik, L. Solid-state optical absorption from optimally tuned time-dependent range-separated hybrid density functional theory. Phys. Rev. B 92, 081204(R) (2015).10.1103/PhysRevB.92.081204 ↗
36. Refaely-Abramson, S. et al. Gap renormalization of molecular crystals from density-functional theory. Phys. Rev. B 88, 081204 (2013).10.1103/PhysRevB.88.081204 ↗
37. Refaely-Abramson, S. et al. Quasiparticle spectra from a nonempirical optimally tuned range-separated hybrid density functional. Phys. Rev. Lett. 109, 226405 (2012).10.1103/PhysRevLett.109.226405 ↗
38. Wing, D. et al. Comparing time-dependent density functional theory with many-body perturbation theory for semiconductors: Screened range-separated hybrids and the GW plus Bethe-Salpeter approach. Phys. Rev. Mater. 3, 064603 (2019).10.1103/PhysRevMaterials.3.064603 ↗
39. Liu, J., Zhang, X. & Lu, G. Moiré magnetism and moiré excitons in twisted CrSBr bilayers. Proc. Natl. Acad. Sci. USA. 122, e2413326121 (2025).10.1073/pnas.2413326121 ↗
40. Guo, H., Zhang, X. & Lu, G. Shedding light on moiré excitons: a first-principles perspective. Sci. Adv. 6, eabc5638 (2020).10.1126/sciadv.abc5638 ↗
41. Guo, H., Zhang, X. & Lu, G. Moiré excitons in defective van der Waals heterostructures. Proc. Natl. Acad. Sci. USA. 118, e2105468118 (2021).10.1073/pnas.2105468118 ↗
42. Guo, H., Zhang, X. & Lu, G. Tuning moiré excitons in Janus heterobilayers for high-temperature Bose-Einstein condensation. Sci. Adv. 8, eabp9757 (2022).10.1126/sciadv.abp9757 ↗
43. Guo, H., Zhang, X. & Lu, G. Pseudo-heterostructure and condensation of 1D moiré excitons in twisted phosphorene bilayers. Sci. Adv. 9, eadi5404 (2023).10.1126/sciadv.adi5404 ↗
44. Schwartz, I. et al. Electrically tunable Feshbach resonances in twisted bilayer semiconductors. Science 374, 336–340 (2021).10.1126/science.abj3831 ↗
45. Kuhlenkamp, C., Knap, M., Wagner, M., Schmidt, R. & Imamoğlu, A. Tunable Feshbach resonances and their spectral signatures in bilayer semiconductors. Phys. Rev. Lett. 129, 037401 (2022).10.1103/PhysRevLett.129.037401 ↗
46. Yu, H., Liu, G.-B. & Yao, W. Brightened spin-triplet interlayer excitons and optical selection rules in van der Waals heterobilayers. 2D Mater 5, 035021 (2018).10.1088/2053-1583/aac065 ↗
47. Xuan, F. & Quek, S. Y. Valley-filling instability and critical magnetic field for interaction-enhanced Zeeman response in doped WSe2 monolayers. npj Comput. Mater. 7, 198 (2021).10.1038/s41524-021-00665-8 ↗
48. Xuan, F. & Quek, S. Y. Valley Zeeman effect and Landau levels in two-dimensional transition metal dichalcogenides. Phys. Rev. Res. 2, 033256 (2020).10.1103/PhysRevResearch.2.033256 ↗
49. Förste, J. et al. Exciton g-factors in monolayer and bilayer WSe2 from experiment and theory. Nat. Commun. 11, 4539 (2020).10.1038/s41467-020-18019-1 ↗
50. Liang, J. et al. Nanosecond ferroelectric switching of intralayer excitons in bilayer 3R-MoS2 through Coulomb engineering. Phys. Rev. X 15, 021081 (2025).
51. Wang, X. et al. Light-induced ferromagnetism in moiré superlattices. Nature 604, 468–473 (2022).10.1038/s41586-022-04472-z ↗
52. Zhu, J. et al. Moiré exchange effect in twisted WSe2/WS2 heterobilayer. Phys. Rev. Lett. 133, 086501 (2024).10.1103/PhysRevLett.133.086501 ↗
53. Ruiz-Tijerina, D. A. & Fal’ko, V. I. Interlayer hybridization and moiré superlattice minibands for electrons and excitons in heterobilayers of transition-metal dichalcogenides. Phys. Rev. B 99, 125424 (2019).10.1103/PhysRevB.99.125424 ↗
54. Kundu, S., Naik, M. H., Krishnamurthy, H. R. & Jain, M. Moiré induced topology and flat bands in twisted bilayer WSe2: a first-principles study. Phys. Rev. B 105, L081108 (2022).10.1103/PhysRevB.105.L081108 ↗
55. Salvador, A. G., Kuhlenkamp, C., Ciorciaro, L., Knap, M. & İmamoğlu, A. Optical signatures of periodic magnetization: the moiré Zeeman effect. Phys. Rev. Lett. 128, 237401 (2022).10.1103/PhysRevLett.128.237401 ↗
56. Broholm, C. et al. Quantum spin liquids. Science 367, eaay0668 (2020).10.1126/science.aay0668 ↗
57. Han, T.-H. et al. Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet. Nature 492, 406–410 (2012).10.1038/nature11659 ↗
58. Ghimire, N. J. & Mazin, I. I. Topology and correlations on the kagome lattice. Nat. Mater. 19, 137–138 (2020).10.1038/s41563-019-0589-8 ↗
59. Wu, M., Li, Z., Cao, T. & Louie, S. G. Physical origin of giant excitonic and magneto-optical responses in two-dimensional ferromagnetic insulators. Nat. Commun. 10, 2371 (2019).10.1038/s41467-019-10325-7 ↗
60. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953 (1994).10.1103/PhysRevB.50.17953 ↗
61. Dal Corso, A. Projector augmented-wave method: application to relativistic spin-density functional theory. Phys. Rev. B 82, 075116 (2010).10.1103/PhysRevB.82.075116 ↗
62. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).10.1103/PhysRevB.54.11169 ↗
63. Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comp. Mater. Sci. 6, 15–50 (1996).10.1016/0927-0256(96)00008-0 ↗
64. Dudarev, S. L., Botton, G. A., Savrasov, S. Y., Humphreys, C. J. & Sutton, A. P. Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study. Phys. Rev. B 57, 1505–1509 (1998).10.1103/PhysRevB.57.1505 ↗
65. Hedin, L. New method for calculating the one-particle Green’s function with application to the electron-gas problem. Phys. Rev. 139, A796 (1965).10.1103/PhysRev.139.A796 ↗
66. Hybertsen, M. S. & Louie, S. G. Electron correlation in semiconductors and insulators: band gaps and quasiparticle energies. Phys. Rev. B 34, 5390 (1986).10.1103/PhysRevB.34.5390 ↗
67. Rohlfing, M. & Louie, S. G. Electron-hole excitations in semiconductors and insulators. Phys. Rev. Lett. 81, 2312–2315 (1998).10.1103/PhysRevLett.81.2312 ↗
68. Gross, E. K. U. & Kohn, W. Local density-functional theory of frequency-dependent linear response. Phys. Rev. Lett. 55, 2850 (1985).10.1103/PhysRevLett.55.2850 ↗
69. Marques, M. A., Maitra, N. T., Nogueira, F. M., Gross, E. K. & Rubio, A. Fundamentals of time-dependent density functional theory (Springer Science & Business Media, 2012).10.1007/978-3-642-23518-4 ↗
70. Liu, J., Zhang, X. & Lu, G. Excitonic effect drives ultrafast dynamics in van der Waals heterostructures. Nano Lett. 20, 4631–4637 (2020).10.1021/acs.nanolett.0c01519 ↗
71. Liu, J. et al. Charge separation boosts exciton diffusion in fused ring electron acceptors. J. Mater. Chem. A 8, 23304–23312 (2020).10.1039/D0TA08666E ↗
72. Liu, J., Zhang, X. & Lu, G. Non-adiabatic exciton dynamics in van der Waals heterostructures. J. Phys. Chem. Lett. 13, 11760–11769 (2022).10.1021/acs.jpclett.2c03148 ↗
73. Liu, J., Li, Z., Zhang, X. & Lu, G. Unraveling energy and charge transfer in type-II van der Waals heterostructures. npj Comput. Mater. 7, 191 (2021).10.1038/s41524-021-00663-w ↗
74. Liu, J., Zhang, X. & Lu, G. Auger processes and excited state dynamics in WS2/Graphene heterostructures: A first-principles perspective. J. Phys. Chem. Lett. 13, 7371–7379 (2022).10.1021/acs.jpclett.2c01937 ↗
75. Zhang, L., Zhang, X. & Lu, G. Predictions of moiré excitons in twisted two-dimensional organic–inorganic halide perovskites. Chem. Sci. 12, 6073–6080 (2021).10.1039/D1SC00359C ↗
76. Chong, D. P. Recent advances in density functional methods (World Scientific, 1995).10.1142/2914 ↗
77. Zhang, X. & Lu, G. First-order nonadiabatic couplings in extended systems by time-dependent density functional theory. J. Chem. Phys. 149, 244103 (2018).10.1063/1.5065504 ↗
78. Zhang, X., Li, Z. & Lu, G. First-principles simulations of exciton diffusion in organic semiconductors. Phys. Rev. B 84, 235208 (2011).10.1103/PhysRevB.84.235208 ↗
79. Yankowitz, M., McKenzie, D. & LeRoy, B. J. Local spectroscopic characterization of spin and layer polarization in WSe2. Phys. Rev. Lett. 115, 136803 (2015).10.1103/PhysRevLett.115.136803 ↗
80. Zhang, C. et al. Probing critical point energies of transition metal dichalcogenides: Surprising indirect gap of single layer WSe2. Nano Lett. 15, 6494–6500 (2015).10.1021/acs.nanolett.5b01968 ↗
81. Li, Z. et al. Emerging photoluminescence from the dark-exciton phonon replica in monolayer WSe2. Nat. Commun. 10, 2469 (2019).10.1038/s41467-019-10477-6 ↗
82. Mouri, S. et al. Nonlinear photoluminescence in atomically thin layered WSe2 arising from diffusion-assisted exciton-exciton annihilation. Phys. Rev. B 90, 155449 (2014).10.1103/PhysRevB.90.155449 ↗
83. Adolph, B., Gavrilenko, V. I., Tenelsen, K., Bechstedt, F. & Del Sole, R. Nonlocality and many-body effects in the optical properties of semiconductors. Phys. Rev. B 53, 9797–9808 (1996).10.1103/PhysRevB.53.9797 ↗
84. Rohlfing, M. & Louie, S. G. Electron-hole excitations and optical spectra from first principles. Phys. Rev. B 62, 4927–4944 (2000).10.1103/PhysRevB.62.4927 ↗
85. Gajdoš, M., Hummer, K., Kresse, G., Furthmüller, J. & Bechstedt, F. Linear optical properties in the projector-augmented wave methodology. Phys. Rev. B 73, 045112 (2006).10.1103/PhysRevB.73.045112 ↗
86. Adolph, B., Furthmüller, J. & Bechstedt, F. Optical properties of semiconductors using projector-augmented waves. Phys. Rev. B 63, 125108 (2001).10.1103/PhysRevB.63.125108 ↗