Direct chemical potential measurements of fractional quantum Hall states in bilayer graphene

We report measurements of the chemical potential in high quality bilayer graphene (BLG) in the quantum Hall regime as a function of magnetic field, interlayer bias, and charge carrier density. To maintain sample quality while also enabling quantitative determination of the chemical potential of the BLG flake, we use a four plate capacitor heterostructure consisting of graphite top and bottom gates,BLG, and an integrated charge sensing graphene monolayer. The resulting devices show fractional quantum Hall states at odd-denominator filling fractions as large as 11 as well as even-denominator states at fillings ν=-5/2, -1/2, 3/2 and 7/2. Changes in the chemical potential of the BLG flake generate modulations of the charge density in the monolayer graphene sensor layer, which we detect capacitively. These modulations form the error signal for a feedback loop whose control voltage is the BLG chemical potential. We demonstrate chemical potential sensitivity better than 10uV/
√Hz, allowing determination of fractional quantum Hall energy gaps in this system. We then use the measured temperature dependence of the chemical potential to estimate the entropy of the electron system, and compare our results to predictions for abelian and nonabelian quasiparticles near fractional filling factors