Non-Abelian fractional quantum Hall states at filling factor 3/4

doi:10.1088/1674-1056/ae3304

摘要/Abstract

摘要： 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.

关键词: fractional quantum Hall effect, non-Abelian anyon, bilayer graphene, topological order

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.

Key words: fractional quantum Hall effect, non-Abelian anyon, bilayer graphene, topological order

中图分类号: (Quantum Hall effects)

73.43.-f

71.10.Pm (Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.)) 72.80.Vp (Electronic transport in graphene) 03.65.Vf (Phases: geometric; dynamic or topological)

Kai-Wen Huang(黄楷文) and Ying-Hai Wu(吴英海)†. Non-Abelian fractional quantum Hall states at filling factor 3/4[J]. 中国物理B, 2026, 35(3): 37302-037302.

Kai-Wen Huang(黄楷文) and Ying-Hai Wu(吴英海)†. Non-Abelian fractional quantum Hall states at filling factor 3/4[J]. Chin. Phys. B, 2026, 35(3): 37302-037302.

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