  In this paper, we numerically study the bound electron states induced by long
range Coulomb impurity in gapped graphene and the quasi-bound states in
supercritical region based on the lattice model. We present a detailed
comparison between our numerical simulations and the prediction of the
continuum model which is described by the Dirac equation in (2+1)-dimensional
Quantum Electrodynamics (QED). We also use the Fano's formalism to investigate
the quasi-bound state development and design an accessible experiments to test
the decay of the supercritical vacuum in the gapped graphene.
