We present a theory of superconductivity in magic-angle twisted bilayer graphene and analyze the superconducting phase diagram in the presence of the magnetic field. Namely, we consider a model of a granular array hosting localized states, which are hybridized via the delocalized fermions in the intergrain regions. We study a strong-coupling situation when the interactions lead to an incoherent state with preformed Cooper pairs inside the grains. The Andreev scattering among different grains manifests itself through the global phase-coherent superconducting state at lower temperatures. We demonstrate that a new phase transition between the preformed Cooper pairing state and the Larkin-Ovchinnikov-Fulde-Ferrell state might be induced by the spin pair-breaking effect of in-plane magnetic field. The upper critical magnetic field is shown to be enhanced in the strong-coupling case.

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• Cooper pairs
• Flat bands
• Graphene
• Strongly correlated systems