Spin-fluctuation-induced pairing in twisted bilayer graphene

We investigate the interplay of magnetic fluctuations and Cooper pairing in twisted bilayer graphene from a purely microscopic model within a large-scale tight-binding approach resolving the Ångström scale. For local onsite repulsive interactions and using the random-phase approximation for spin fluctuations, we derive a microscopic effective pairing interaction that we use for self-consistent solutions of the Bogoliubov-de-Gennes equations of superconductivity. We study the predominant pairing types as function of interaction strength, temperature and band filling. For large regions of this parameter space, we find chiral d-wave pairing regimes, spontaneously breaking time-reversal symmetry, separated by magnetic instabilities at integer band fillings. Interestingly, the d-wave pairing is strongly concentrated in the AA regions of the moiré unit cell and exhibits phase windings of integer multiples of 2π around these superconducting islands, i.e. pinned vortices. The spontaneous circulating current creates a distinctive magnetic field pattern. This signature of the chiral pairing should be measurable by state-of-the-art experimental techniques.