Moire 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 graphene (MLG) is stacked on top of each other with two twist angles [J. M. Park et al., Nature (London) 590, 249 (2021); Z. Hao et al., Science 371, 1133 (2021); X. Zhang et al., Phys. Rev. Lett. 127, 166802 (2021)]. When some of the MLGs in the double twisted TLG are replaced by bilayer graphene (BLG), we get a family of double twisted moire heterostructure, namely, double twisted few layer graphene (DTFLG). In this paper, 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 derWaals (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 degrees 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 degrees, the (X + 2 + Z)-CTFLGs can have two isolated narrow bands at E-f with bandwidth less than 5 meV. The influence of the electric field and the topological features of the moire bands have been studied as well. Our paper indicates that the DTFLGs, especially (X + 1 + Z)-ATFLG and (X + 2 + Z)-CTFLG, are promising platforms to study the moire flat band induced correlation and topological effects.

Automated summary

In this paper, we theoretically investigate the moire band structures of double twisted few layer graphene (DTFLG) with different arrangements of monolayer graphene (MLG) and bilayer graphene (BLG). We classify DTFLG into four categories based on the relative rotation direction of the twist angles and the middle van der Waals layer, and find that they exhibit unique band structures, including perfect flat bands at the magic angle and isolated narrow bands. The influence of electric field and topological features of the moire bands are also explored. Our findings suggest that DTFLG, especially (X + 1 + Z)-ATFLG and (X + 2 + Z)-CTFLG, are promising platforms to study moire flat band induced correlation and topological effects.