Dynamical Screening and Excitonic Instability in Bilayer Graphene

Electron interactions in undoped bilayer graphene lead to an instability of the gapless state, "which-layer'' symmetry breaking, and energy gap opening at the Dirac point. In contrast with single-layer graphene, the bilayer system exhibits instability even for an arbitrarily weak interaction. A controlled theory of this instability for realistic dynamically screened Coulomb interactions is developed, with full account of the dynamically generated ultraviolet cutoff. This leads to an energy gap that scales as a power law of the interaction strength, making the excitonic instability readily observable.