  We study the problem of Coulomb field-induced charging of the ground state in
a system of 2D massive Dirac particles (gapped graphene). As in its 3D QED
counterpart, the critical Coulomb coupling is renormalized to higher values,
compared to the massless case. We find that in gapped graphene a novel
supercritical regime is possible, where the screening charge is comparable to
the impurity charge, thus leading to suppression of the Coulomb field at
nanometer scales. We corroborate this with numerical solution of the
tight-binding problem in the honeycomb lattice.
