Many-body instability of Coulomb interacting bilayer graphene: Renormalization group approach

Low-energy electronic structure of (unbiased and undoped) bilayer graphene consists of two Fermi points with quadratic dispersions if trigonal warping is ignored. We show that short-range (or screened Coulomb) interactions are marginally relevant and use renormalization group to study their effects on low-energy properties of the system. We find that the two quadratic Fermi points spontaneously split into four Dirac points. This results in a nematic state that spontaneously breaks the sixfold lattice rotation symmetry (combined with layer permutation) down to a twofold one, with a finite transition temperature. Critical properties of the transition and effects of trigonal warping are also discussed.