Moiré band structures of the double twisted few-layer graphene

Very recently, unconventional superconductivity has been observed in the double twisted trilayer graphene (TLG), where three monolayer (MLG) are stacked on top of each other with two twist angles [J. M. Park, et al., Nature 590, 249 (2021); Z. Hao, Science 371, 1133 X. Zhang, Phys. Rev. Lett.127, 166802 (2021)]. When some MLGs TLG replaced by bilayer (BLG), we get a new family moire heterostructure, namely few layer (DTFLG). In this work, theoretically investigate band structures DTFLGs diverse arrangements MLG and BLG. We find that, depending relative rotation direction (alternate or chiral twist) middle van der Waals (vdW) (MLG BLG), general (X+Y+Z)-DTFLG can be classified into four categories, i.e. (X+1+Z)-ATFLG, (X+2+Z)-ATFLG, (X+1+Z)-CTFLG (X+2+Z)-CTFLG, which its own unique structure. Here, X, Y, Z denote vdW layers, Interestingly, (X+1+Z)-ATFLGs have pair perfect flat bands at magic angle about $1.54^\circ$ coexisting linear parabolic bands, is quite like TLG. Meanwhile, when smaller than "magic angle" $1.70^\circ$, (X+2+Z)-CTFLGs isolated narrow $E_f$ width less 5 meV. The influence electric field topological features studied as well. Our work indicates that DTFLGs, especially (X+1+Z)-ATFLG promising platforms to study induced novel correlation effects.