Flat bands, electron interactions and magnetic order in magic-angle mono-trilayer graphene.

Starting with twisted bilayer graphene, graphene-based moire materials have recently been established as a new platform for studying strong electron correlations. In this paper, we study twisted graphene monolayers on trilayer graphene and demonstrate that this system can host flat bands when the twist angle is close to the magic-angle of 1.16$^\circ$. When monolayer graphene is twisted on ABA trilayer graphene (denoted AtABA), the flat bands are not isolated, but are intersected by a dispersive Dirac cone. In contrast, graphene twisted on ABC trilayer graphene (denoted AtABC) exhibits a gap between flat and remote bands. Since ABC trilayer graphene and twisted bilayer graphene are known to host broken symmetry phases, we further investigate magic-angle AtABC. We study the effect of electron-electron interactions in AtABC using both Hartree theory, and an atomic Hubbard theory to calculate the magnetic phase diagram as a function of doping, twist angle and perpendicular electric field. Our analysis reveals a rich variety of magnetic orderings, including ferromagnetism and ferrimagnetism, and demonstrates that a perpendicular electric field makes AtABC more susceptible to magnetic ordering.