Tunable Topological Transitions Probed by the Quantum\nHall Effect in Twisted Double Bilayer Graphene

The\nmoiré system provides a tunable platform for investigating\nexotic quantum phases. Particularly, the displacement field <i>D</i> is crucial for tuning the electronic structures and topological\nproperties of twisted double bilayer graphene (TDBG). Here, we present\na series of <i>D</i>-tunable topological transitions by\nthe evolution of quantum Hall phases (QHPs) in the valence bands of\nTDBG. As <i>D</i> increases, we observe the alternating\nemergence of two distinct quantum Hall regions originating from full-filling\nand half-filling, which we attribute to the <i>D</i>-induced\nLifshitz transition. Moreover, we delve into the remote valence bands\nof TDBG and observe a transition in the sequence of Landau levels\nupon the application of <i>D</i>, shifting from 8<i>N</i> + 4 to 8<i>N</i>. This observation, combined\nwith theoretical calculations, unveils an alteration in the Berry\nphase. Our findings highlight the TDBG as an exemplary platform for\nunderstanding the origin of the topological transitions in the graphene-based\nmoiré systems.