Space charge and screening in bilayer graphene

Undoped bilayer graphene is a two-dimensional semimetal with a low-energy excitation spectrum that is parabolic in the momentum. As a result, the screening of an arbitrary external charge $Ze$ is accompanied by a reconstruction of the ground state: valence band electrons (for $Z>0$) are promoted to form a space charge around the charge while the holes leave the physical picture. The outcome is flat neutral object resembling the regular atom except that for $Z \gg 1$ it is described by a strictly linear Thomas-Fermi theory. This theory also predicts that the bilayer's static dielectric constant is the same as that of a two-dimensional electron gas in the long-wavelength limit.