▎ 摘　　要

We demonstrate that for gapped bilayer graphene, the nonlinear nature of the screening of an external disorder potential and the resulting inhomogeneity of the electron liquid are crucial for describing the electronic compressibility. In particular, traditional diagrammatic methods of many-body theory do not include this inhomogeneity and therefore fail to reproduce experimental data accurately, particularly at low carrier densities. In contrast, a direct calculation of the charge landscape via a numerical Thomas-Fermi energy functional method along with the appropriate bulk averaging procedure captures all the essential physics, including the interplay between the band gap and the inhomogeneity.