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