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We compute the phase diagram of twisted bilayer graphene near the magic angle where the occurrence of flat bands enhances the effects of electron-electron interactions and thus unleashes strongly-correlated phenomena. Most importantly, we find a crossover between d+id superconductivity and Mott insulating behavior near half-filling of the lowest electron band when the temperature is increased. This is consistent with recent experiments. Our results are obtained using unbiased many-body renormalization group techniques combined with a mean-field analysis of the effective couplings.

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