Nematic superconductivity in twisted bilayer graphene*

Twisted bilayer graphene (TBG) shows insulating and superconducting phases in connection with an exceptional
flattening of its lowest-lying energy bands. In the hole-doped case with the highest critical temperature the superconducting state is nematic, i.e. the threefold lattice rotation symmetry is broken inside the superconducting phase. We analyze superconductivity near Van Hove (VH) filling in TBG within an itinerant approach. In particular, we present a mechanism for nematic superconductivity, which originates in the interplay of two superconducting orders with similar critical temperatures. We argue that TBG can be properly described
by patch models with six VH points for electron and twelve for hole doping reflecting the electron-hole
asymmetry. We obtain the pairing interactions being dependent on twist-induced non-local interactions. For hole-doping, two channels with almost equal coupling constants are attractive. We show that the ground state is a nematic phase of coexistence. We find two possible mixed states, one is time-reversal symmetric, the other breaks time-reversal in addition to the lattice rotation symmetry.