Kekulé spiral order at all nonzero integer fillings in twisted bilayer graphene

Many features of Magic-Angle Twisted Bilayer Graphene (MATBG) which are observed in experiment can be explained theoretically using a strong-coupling picture. Many, but not all. We propose that adding physically realistic strains (such as those observed in scanning tunneling microscopy experiments) to the Bistritzer-MacDonald (BM) model can remedy some of the shortcomings of the strong-coupling theory. In particular, the interacting phase diagram of the strained BM model hosts a semi-metal at the charge neutrality point instead of a strong insulator - a property shared by most MATBG devices realized in the lab. At the other integer fillings away from the charge neutrality point we find that small strains stabilize a new type of symmetry-breaking order, which corresponds to a √3 x √3 or Kekulé distortion on the graphene scale which modulates on the moiré scale with a wavevector that is generally incommensurate with the superlattice period. This symmetry-breaking order preserves time-reversal symmetry and produces a charge gap at electron or hole fillings where insulating states are most commonly seen in experiment.