Superconductivity in twisted bilayer graphene: Possible pairing symmetries, impurity-induced states, and Chern number

We consider the most energetically favorable symmetry-allowed spin-singlet and spin-triplet superconducting pairing symmetries in twisted bilayer graphene at the magic angle, whose normal state physics is described by a six-band effective tight-binding model. We compute the Chern number as a function of the superconducting order parameter strength and the chemical potential and we find a topological phase transition only for the chiral $p+i{p}^{\ensuremath{'}}$ superconducting state. Different from the regular graphene systems for which this happens at the van Hove singularity, for TBG the topological phase transition arises at the point where the Fermi surface becomes tangent to the boundary of the first Brillouin zone. For each pairing symmetry we study the formation of subgap impurity states for both scalar and magnetic impurities. We analyze the number of subgap states as well as their spin-polarized density of states that we find to exhibit peculiar properties that allows one to distinguish between spin-singlet and triplet pairing. Thus only triplet-paired states may exhibit opposite-energy impurity states with the same spin, same as for regular graphene systems; moreover, we find that this spin may flip at the twist-induced van Hove singularity.