  Bernal bilayer graphene hosts even denominator fractional quantum Hall states
thought to be described by a Pfaffian wave function with nonabelian
quasiparticle excitations. Here we report the quantitative determination of
fractional quantum Hall energy gaps in bilayer graphene using both thermally
activated transport and by direct measurement of the chemical potential. We
find a transport activation gap of 5.1K at B = 12T for a half-filled N=1 Landau
level, consistent with density matrix renormalization group calculations for
the Pfaffian state. However, the measured thermodynamic gap of 11.6K is smaller
than theoretical expectations for the clean limit by approximately a factor of
two. We analyze the chemical potential data near fractional filling within a
simplified model of a Wigner crystal of fractional quasiparticles with
long-wavelength disorder, explaining this discrepancy. Our results
quantitatively establish bilayer graphene as a robust platform for probing the
non-Abelian anyons expected to arise as the elementary excitations of the
even-denominator state.
