SU(4) symmetry in twisted bilayer graphene - an itinerant perspective

In our work we study symmetry-broken phases in twisted bilayer graphene at small filling above charge neutrality and at Van Hove filling. We argue that the Landau free energy functionals for the particle-hole order parameters at these fillings both have an approximate SU(4) symmetry, however the signs of quartic terms are different for the two fillings. We determine the order parameter manifold of the ground state and analyze its excitations. For small fillings, we find a strong 1st-order transition to an SU(3) ⊗U(1) manifold of orders. The resulting state lifts the initial approximate four-fold degeneracy of the electronic band and induces a 3-1 splitting of fermionic excitations for small electron doping. For Van Hove filling, we find a weak 1st-order transition to an SO(4) ⊗U(1) manifold of orders that preserve the two-fold band degeneracy. We discuss the effect of particle-hole orders on superconductivity and compare our results with strong-coupling approaches.