▎ 摘　　要

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 angstrom scale. For local on-site 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 a 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 moire unit cell and exhibits phase windings of integer multiples of 2 pi 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.