Inherited and flatband-induced ordering in twisted graphene bilayers

The nature of the insulating and superconducting states in twisted bilayer graphene systems is intensely debated. While many works seek for explanations in the few flat bands near the Fermi level, theory and a number of experiments suggest that nontwisted bilayer graphene systems do exhibit – or are at least close to – an ordered, insulating ground state related to antiferromagnetic ordering. We investigate how this magnetic ordering scenario is affected by the slight twisting. We find that at charge neutrality the ordering tendencies of twisted systems interpolate between those of untwisted AA and AB stacked bilayers at intermediate temperatures, while at lower temperatures of the order of typical flat-band dispersion energies, the ordering tendencies are even enhanced for the twisted systems. The preferred order at charge neutrality still exhibits an antiferromagnetic spin arrangement, with ordered moments alternating on the carbon-carbon bonds, with an enveloping variation on the moiré scale (inhereted ordering). Even in the RPA analysis, the possible low-energy behaviors are quite versatile, and slight doping of one or more electrons per moiré cell can take the system into a, potentially flat-band induced, ferromagnetic phase.