Electronic compressibility of graphene: The case of vanishing electron correlations and the role of chirality

A recent surprising finding that electronic compressibility measured experimentally in monolayer graphene can be described solely in terms of the kinetic energy [J. Martin, et al., Nat. Phys. 4, 144 (2008)] is explained theoretically as a direct consequence of the linear energy dispersion and the chirality of massless Dirac electrons. For bilayer graphene we show that contributions to the compressibility from the electron correlations are restored. We attribute the difference to the respective momentum dependence of the low energy band structures of the two materials.