Four Moiré materials at One Magic Angle in Helical Quadrilayer Graphene

Abstract: We introduce helical twisted quadrilayer graphene (HTQG), four graphene sheets rotated by the same small angle, as a versatile and experimentally accessible platform for correlated topological matter. HTQG consists of three moir\'e lattices, formed by interference between adjacent graphene layers, that are twisted relative to each other. Lattice relaxation produces four types of large-scale commensurate domains. The domains are characterized by the stacking of the three moir\'e lattices and come in two types: Type-I "Bernal" stacking and Type-II "rhombohedral" stacking. Domain walls between adjacent stackings often host topologically protected edge states, forming networks at the supermoir\'e and super-supermoir\'e scales. Remarkably, all four moir\'e substructures have narrow bands at the same magic angle $\theta \approx 2.3^\circ$, allowing their correlated phases to be simultaneously targeted in device manufacturing. We argue that the Type-I domains are especially suitable for realizing robust superconductivity which emerges from doping topological insulators, and Chern insulators in $C = \pm 2$ bands.