▎ 摘　　要

In the low-energy two-band as well as four-band continuum models, we study the supercritical charge instability in gapped bilayer graphene in the field of an impurity charge when the lowest-energy bound state dives into the hole continuum. It is found that the screening effects are crucially important in bilayer graphene. If they are neglected, then the critical value for the impurity charge tends to zero as the gap Delta vanishes. If the screened Coulomb interaction is considered, then the critical charge tends to a finite value for Delta -> 0. The different scalings of the kinetic energy of quasiparticles and the Coulomb interaction with respect to the distance to the charged impurity ensure that the wave function of the electron bound state does not shrink toward the impurity as its charge increases. This results in the absence of the fall-to-center phenomenon in bilayer graphene although the supercritical charge instability is realized.