Superconductivity from spin fluctuations and long-range interactions in magic-angle twisted bilayer graphene

Magic-angle twisted bilayer graphene (MATBG) has been extensively explored both theoretically and experimentally as a suitable platform for a rich and tunable phase diagram that includes ferromagnetism, charge order, broken symmetries, and unconventional superconductivity. In this paper, we investigate the intricate interplay between long-range electron-electron interactions, spin fluctuations, and superconductivity in MATBG. By employing a low-energy model for MATBG that captures the correct shape of the flat bands, we explore the effects of short- and long-range interactions on spin fluctuations and their impact on the superconducting (SC) pairing vertex in the matrix random phase approximation (matrix RPA). We find that the SC state is notably influenced by the strength of long-range Coulomb interactions. Interestingly, our matrix-RPA calculations indicate that there is a regime where the system can traverse from a magnetic phase to the SC phase by increasing the relative strength of long-range interactions compared to the on-site ones. These findings underscore the relevance of electron-electron interactions in shaping the intriguing properties of MATBG and offer a pathway for designing and controlling its SC phase.