Gate-controlled localization to delocalization transition of flat band wavefunction in twisted monolayer–bilayer graphene

Twisted graphene systems with flat bands have attracted much attention for they are excellent platforms to research novel quantum phases. Recently, transport measurements about twisted monolayer–bilayer graphene (tMBG) have shown the existence of correlated states and topological states in this system. However, the direct observations of the band structures and the corresponding spatial distributions are still not sufficient. Here we show that the distributions of flat bands in tMBG host two different modes by scanning tunneling microscopy and spectroscopy (STM/S). By tuning our tMBG device from the empty filling state to the full filling state through the back gate, we observe that the distributions of two flat bands develop from localized mode to delocalized mode. This gate-controlled flat band wavefunction polarization is unique to the tMBG system. Our work suggests that tMBG is promising to simulate both twisted bilayer graphene (TBG) and twisted double bilayer graphene (tDBG) and would be an ideal platform to explore novel moiré physics.