Bound states in gapped graphene with impurities: Effective low-energy description of short-range interactions

We obtain a bound-state spectrum of low-energy excitations near the Fermi points of gapped graphene in the presence of a charge impurity. The effects of possible short-range interactions induced by the impurity are modeled by suitable boundary conditions. The spectrum in the subcritical region of the effective Coulomb coupling is labeled by a parameter which characterizes the boundary conditions and determines the inequivalent quantizations of the system. In the supercritical region we obtain a renormalization-group flow for the effective Coulomb coupling.