Excitonic instability and gap generation in monolayer graphene

We analyze the excitonic instability in graphene by solving the Bethe-Salpeter equation for the electron hole bound state. In the supercritical regime, we show that this equation has a tachyon in its spectrum. We argue that the excitonic instability is resolved through the formation of an electron-hole condensate leading to the gap (mass) generation in the quasiparticle spectrum. Such a gap could be observed in a free standing clean graphene.