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Bernal bilayer graphene hosts even denominator fractional quantum Hall statesthought to be described by a Pfaffian wave function with nonabelianquasiparticle excitations. Here we report the quantitative determination offractional quantum Hall energy gaps in bilayer graphene using both thermallyactivated transport and by direct measurement of the chemical potential. Wefind a transport activation gap of 5.1K at B = 12T for a half-filled N=1 Landaulevel, consistent with density matrix renormalization group calculations forthe Pfaffian state. However, the measured thermodynamic gap of 11.6K is smallerthan theoretical expectations for the clean limit by approximately a factor oftwo. We analyze the chemical potential data near fractional filling within asimplified model of a Wigner crystal of fractional quasiparticles withlong-wavelength disorder, explaining this discrepancy. Our resultsquantitatively establish bilayer graphene as a robust platform for probing thenon-Abelian anyons expected to arise as the elementary excitations of theeven-denominator state.

Energy gap of the even-denominator fractional quantum Hall state in bilayer graphene