Electronic compressibility of layer-polarized bilayer graphene

We report on a capacitance study of dual gated bilayer graphene. The measured capacitance allows us to probe the electronic compressibility as a function of carrier density, temperature, and applied perpendicular electrical displacement $\overline{D}$. As a band gap is induced with increasing $\overline{D}$, the compressibility minimum at charge neutrality becomes deeper but remains finite, suggesting the presence of localized states within the energy gap. Temperature dependent capacitance measurements show that compressibility is sensitive to the intrinsic band gap. For large displacements, an additional peak appears in the compressibility as a function of density, corresponding to the presence of a one-dimensional van Hove singularity (vHs) at the band edge arising from the quartic bilayer graphene band structure. For $\overline{D}>0$, the additional peak is observed only for electrons, while for $\overline{D}<0$ the peak appears only for holes. This asymmetry can be understood in terms of the finite interlayer separation and may be useful as a direct probe of the layer polarization.