Hosted by: Alexei Tsvelik

Tunable insulating and superconducting phases have recently been induced in several twisted graphene-based heterostructures. These correlated phases are ascribed to an exceptional band flattening, which comes along with a very large hexagonal moiré pattern in real space. We study this interplay of orders in a phenomenological model for the moiré superlattice with a focus on superconductivity. Motivated by the presence of van-Hove instabilities, we approach the pairing problem as an interaction-induced instability of the Fermi surface in terms of the unbiased functional renormalization group. We find two pairing instabilities with different symmetries being close in energy and show that a similar situation arises in a model specific for twisted bilayer graphene. In view of recent experimental observations that the threefold lattice rotational symmetry is broken in the superconducting state of hole-doped twisted bilayer graphene, we analyze the corresponding Landau-Ginzburg free energy with two superconducting order parameters. The result is, indeed, a mixed ground state that breaks rotation symmetry and leads to nematic superconductivity. Time-reversal symmetry can simultaneously be broken.