Stable Pfaffian State in Bilayer Graphene

Here, we show that the incompressible Pfaffian state originally proposed for the 5 2 fractional quantum Hall states in conventional two-dimensional electron systems can actually be found in a bilayer graphene at one of the Landau levels. The properties and stability of the Pfaffian state at this special Landau level strongly depend on the magnetic field strength. The graphene system shows a transition from the incompressible to a compressible state with increasing magnetic field. At a finite magnetic field of similar to 10 T, the Pfaffian state in bilayer graphene becomes more stable than its counterpart in conventional electron systems.