Wannier excitons signalling strong Coulomb coupling in graphene

The Wannier equation for quasiparticles with a linear dispersion is investigated. It is shown that Coulomb bound compounds of mass less electron-hole pairs can only exist if the effective coupling strength exceeds the critical value of approximately 0.46. At the critical value, a second-order transition to a weak Coulomb regime is found. It is shown that the existence of bound excitons indicates an instability of the noninteracting ground state.