We analyze the phase diagram of the zeroth Landau level of bilayer graphene, taking into account the realistic effects of screening of the Coulomb interaction and the strong mixing between two degenerate sublevels. We identify robust quantum Hall states at filling factors ν = −1, − 4 3 , − 5 3 , − 8 5 , − 1 2 , and discuss the nature of their ground states, collective excitations, and relation to the more familiar states in GaAs using a tractable model. In particular, we present evidence that the ν = − 1 2 state, which was recently reported experimentally, is nonAbelian, and described by either the Moore-Read Pfaffian wave function or its particle-hole conjugate, while ruling out other candidates such as the 331 state. Introduction. Following a rapid progress in graphene sample quality, the fractional quantum Hall effect (FQHE) was discovered in this material [1][2][3][4][5][6]. A novel feature of graphene [7] compared to GaAs-based two-dimensional electron gas (2DEG) is the four-fold degeneracy of Landau levels (LLs) due to spin and valley degrees of freedom. The interplay of long-range SU(4)-symmetric Coulomb interactions and smaller symmetry-breaking terms gives rise to an unusual sequence of FQHEs in the zeroth LL, in which certain states are absent or weak, while others exhibit phase transitions as a function of the magnetic field [4,6,8]. It was suggested [9][10][11][12] that SU(4)-symmetry may give rise to new states not found in GaAs 2DEG and other semiconducting systems (see Ref.[13] for a review).
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