Abstract
Twisted double bilayer graphene is a highly tunable moir\'e system to study strongly interacting physics. Here, the authors present a theory of competing ferromagnetic and superconducting orders in this system. They show that the single-particle moir\'e bands can be drastically modified by a perpendicular electric displacement field. As a result, the ferromagnetic insulating gap driven by Coulomb interaction has a dome shape dependence on the layer potential difference, as observed in several experiments. The stability of the ferromagnetic insulator against collective excitations, including spin and valley magnons, is theoretically verified. Furthermore, the authors investigate the possibility of phonon-mediated intervalley equal-spin pairing, using the property that the acoustic phonon mediated attraction respects an enlarged SU(2)\ifmmode\times\else\texttimes\fi{}SU(2) symmetry.
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