▎ 摘　　要

It is well known that there are resonant states with complex energy for the supercritical Coulomb impurity in graphene. We show that opening of a quasiparticle gap decreases the imaginary part of energy, vertical bar Im E vertical bar, of these states and stabilizes the system. For gapless quasiparticles with strong Coulomb interaction in graphene, we solve the Bethe-Salpeter equation for the electron-hole bound state and show that it has a tachyonic solution for strong enough coupling alpha=e(2)/kappa(h) over barv(F) leading to instability of the system. In the random-phase approximation, the critical coupling is estimated to be alpha(c)=1.62 and is an analog of the critical charge in the Coulomb center problem. We argue that the excitonic instability should be resolved through the formation of an excitonic condensate and gap generation in the quasiparticle spectrum.