Alternating Twisted Multilayer Graphene: the generic partition rules, double flat bands and orbital magnetoelectric effect

Twisted graphene systems have drawn significant attention due to the discoveries of various intriguing phases. The alternating twisted trilayer graphene is discovered to exhibit unconventional superconductivity, motivating us to study the electronic structures and physical properties of this class of alternating twisted graphene systems. We consider generic alternating twisted multilayer graphene (ATMG) systems with M-L-N stacking configurations. The M (L) graphene layers and the L (N) layers are twisted by an angle θ(-θ). Based on an analytic analysis from a simplified k.p model approach, we derive generic partition rules for the low-energy electronic structures, which exhibit intriguing band dispersions at magic angle, including one pair of flat bands (per spin per valley), one pair of flat bands co-existing with E(k)~k^J dispersions (J is positive integer), and two pairs of flat bands (per spin per valley). Such unusual non-interacting electronic structures may have unconventional correlation effects. For a mirror symmetric ATMG with two pairs of flat bands (per spin per valley), we find that the system may exhibit a magnetoelectric phenomenon in the sense that the orbital magnetization of a correlated insulator state can be linearly tuned by a vertical displacement field.