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Bilayer graphene has been predicted to give unprecedented tunability of theelectron-electron interaction with the help of external parameters, allowingone to stabilize different fractional quantum Hall states. Recent experimentalworks make theoretical analysis of such systems extremely relevant. In thispaper we describe a methodology for investigating the possibility of realizingspecific fractional quantum Hall states in bilayer graphene taking into accountpolarization effects and virtual interband transitions. We apply thismethodology to explore the possibility of realizing the Moore-Read Pfaffianstate in bilayer graphene.

Fractional quantum Hall effect in bilayer graphene beyond the single Landau level approximation