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Non-Abelian fractional quantum Hall states at filling factor 3/4 |
| Kai-Wen Huang(黄楷文) and Ying-Hai Wu(吴英海)† |
| School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China |
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Abstract Fractional quantum Hall states have been observed at filling factor $\nu=3/4$ in GaAs hole system and bilayer graphene. In theoretical bootstrap analysis, it was revealed that non-Abelian topological orders with Ising anyons can be realized at $\nu=3/4$, which exhibit $12$ fold ground state degeneracy on the torus. The properties of $\nu=3/4$ states can be analyzed using two complementary approaches. In the first one, they are treated as particle-hole conjugate of $\nu=1/4$ Moore-Read types states. In the second one, they are mapped to composite fermions with reverse flux attachment at effective filling factor $3/2$, whose integral part realizes an integer quantum Hall state and the fractional part realizes $\nu=1/2$ Moore-Read type states. For bilayer graphene with appropriate Landau level mixing, numerical calculations have found $12$ quasi-degenerate ground states on the torus at $\nu=3/4$. Chiral graviton spectral functions of these states have one low energy peak with negative chirality and one high energy peak with positive chirality. This points to a specific member of the Moore-Read type states and agrees with the deduction based on daughter states.
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Received: 21 October 2025
Revised: 30 December 2025
Accepted manuscript online: 04 January 2026
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PACS:
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73.43.-f
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(Quantum Hall effects)
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71.10.Pm
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(Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.))
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72.80.Vp
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(Electronic transport in graphene)
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03.65.Vf
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(Phases: geometric; dynamic or topological)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 12174130). |
Corresponding Authors:
Ying-Hai Wu
E-mail: yinghaiwu88@hust.edu.cn
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Cite this article:
Kai-Wen Huang(黄楷文) and Ying-Hai Wu(吴英海)† Non-Abelian fractional quantum Hall states at filling factor 3/4 2026 Chin. Phys. B 35 037302
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