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We present measurements of the electronic compressibility, $K$, of bilayergraphene in both zero and finite magnetic fields up to 14 T, and as a functionof both the carrier density and electric field perpendicular to the graphenesheet. The low energy hyperbolic band structure of bilayer graphene is clearlyrevealed in the data, as well as a sizable asymmetry between the conduction andvalence bands. A sharp increase in $K^{-1}$ near zero density is observed forincreasing electric field strength, signaling the controlled opening of a gapbetween these bands. At high magnetic fields, broad Landau level (LL)oscillations are observed, directly revealing the doubled degeneracy of thelowest LL and allowing for a determination of the disorder broadening of thelevels.

Measurement of the electronic compressibility of bilayer graphene