Robust flat bands in twisted trilayer graphene moiré quasicrystals
Chen-Yue Hao, Zhen Zhan, Pierre A. Pantaleón, Jiaqi He, Yaxin Zhao, Kenji Watanabe, Takashi Taniguchi, F. Guinea, Lin He
Abstract
Moiré structures formed by twisting three layers of graphene with two independent twist angles present an ideal platform for studying correlated quantum phenomena, as an infinite set of angle pairs is predicted to exhibit flat bands. Moreover, the two mutually incommensurate moiré patterns among the twisted trilayer graphene (TTG) can form highly tunable moiré quasicrystals. This enables us to extend correlated physics in periodic moiré crystals to quasiperiodic systems. However, direct local characterization of the structure of the moiré quasicrystals and of the resulting flat bands are still lacking, which is crucial to fundamental understanding and control of the correlated moiré physics. Here, we demonstrate the existence of flat bands in a series of TTGs with various twist angle pairs and show that the TTGs with different magic angle pairs are strikingly dissimilar in their atomic and electronic structures. The lattice relaxation and the interference between moiré patterns are highly dependent on the twist angles. Our direct spatial mappings, supported by theoretical calculations, reveal that the localization of the flat bands exhibits distinct symmetries in different regions of the moiré quasicrystals. Twisted trilayer graphene is predicted to exhibit flat bands for an infinite set of twist angle pairs between the subsequent layers. Here, the authors study several samples with different twist angles and evidence robust flat bands in each of them.