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 moiré 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.

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• Magnetic order
• Pairing mechanisms
• Superconducting order parameter
• Graphene
• Multilayer thin films
• Two-dimensional electron system
• Bogoliubov-de Gennes equations
• Random phase approximation
• Tight-binding model