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

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 have 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.