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A two-dimensional electron system placed in a magnetic field develops Landaulevels, where strong Coulomb interactions lead to the appearance of many-bodycorrelated ground states. Quantum numbers similar to the electron spin enablethe understanding and control of complex ground state order and collectiveexcitations. Owing to its spin, valley and orbital degrees of freedom,Bernal-stacked bilayer graphene offers a rich platform to pursue correlatedphenomena in two dimensions. In this work, we fabricate dual-gatedBernal-stacked bilayer graphene devices and demonstrate unprecedented finecontrol over its valley isospin degrees of freedom using a perpendicularelectric field. Higher sample quality enables us to probe regimes obscured bydisorder in previous studies. We present evidence for a new even-denominatorfractional quantum Hall state at filling factor {\nu} = 5/2. The 5/2 state isfound to be spontaneously valley polarized in the limit of vanishing valleyZeeman splitting, consistent with a theoretical prediction made regarding thespin polarization of the Moore-Read state. In the vicinity of theeven-denominator fractional quantum Hall states, we observe the appearance ofthe predicted Levin-Halperin daughter states of the Moore-Read Pfaffian wavefunction at {\nu}= 3/2, 7/2, and -1/2 and of the anti-Pfaffian at {\nu}= 5/2.These observations suggest the breaking of particle-hole symmetry in bilayergraphene. We construct a comprehensive valley polarization phase diagram forthe Jain sequence fractional states surrounding filling factor 3/2. Theseresults are well explained by a two-component composite fermion model, furtherdemonstrating the SU(2) nature of the valley isospin in bilayer graphene. Ourexperiment paves the path for future efforts of manipulating the valley isospinin bilayer graphene to engineer exotic topological orders and quantuminformation processes.

Valley Isospin Controlled Fractional Quantum Hall States in Bilayer Graphene