Non-Abelian fractional quantum Hall states at filling factor 3/4
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910028341968896 |
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| author | Huang, Kai-Wen Wu, Ying-Hai |
| author_facet | Huang, Kai-Wen Wu, Ying-Hai |
| contents | Fractional quantum Hall states have been observed at filling factor $ν=3/4$ 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 $ν=3/4$, which exhibit $12$ fold ground state degeneracy on the torus. The properties of $ν=3/4$ states can be analyzed using two complementary approaches. In the first one, they are treated as particle-hole conjugate of $ν=1/4$ 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 $ν=1/2$ Moore-Read type states. For bilayer graphene with appropriate Landau level mixing, numerical calculations found $12$ quasi-degenerate ground states on the torus at $ν=3/4$. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_16275 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-Abelian fractional quantum Hall states at filling factor 3/4 Huang, Kai-Wen Wu, Ying-Hai Strongly Correlated Electrons Mesoscale and Nanoscale Physics Fractional quantum Hall states have been observed at filling factor $ν=3/4$ 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 $ν=3/4$, which exhibit $12$ fold ground state degeneracy on the torus. The properties of $ν=3/4$ states can be analyzed using two complementary approaches. In the first one, they are treated as particle-hole conjugate of $ν=1/4$ 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 $ν=1/2$ Moore-Read type states. For bilayer graphene with appropriate Landau level mixing, numerical calculations found $12$ quasi-degenerate ground states on the torus at $ν=3/4$. 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. |
| title | Non-Abelian fractional quantum Hall states at filling factor 3/4 |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2408.16275 |