Marginal Fermi liquid and dynamical symmetry breaking from Coulomb interaction in twisted bilayer graphene

We investigate the effects of the strong Coulomb interaction near the magic angle of twisted bilayer graphene, focusing on the charge neutrality point and near half-filling of the highest valence band. In this latter instance, we predict the emergence of a marginal Fermi liquid, which can be traced back to the proximity to an extended van Hove singularity and the development of straight segments in the Fermi line. This leads to the linear scaling with energy of particle-hole excitations across the Fermi line, implying in turn the linear temperature dependence of the resistivity, logarithmic corrections to the heat capacity, and the consequent modification of the Wiedemann-Franz law. At the charge neutrality point, we show that the Coulomb interaction may be responsible for the opening of a gap through the condensation of particle-hole excitations about the Dirac nodes. We find in this case a direct competition between the dynamical breakdown of chiral symmetry (which prevails in the strong coupling regime) and the breakdown of time-reversal invariance (which has instead a stronger onset and leads to a Chern insulator phase at intermediate coupling).