Stability diagram of layer-polarized quantum Hall states in twisted trilayer graphene

In the twisted trilayer graphene (tTLG) platform, the rich beating patterns between the three graphene layers give rise to a plethora of new length scales and reconstructed electronic bands arising from the emergent moir\'e and moir\'e-of-moir\'e superlattices. The co-existing lattices and superlattices interact and compete with each other to determine the overall transport properties of tTLG, the hierarchy of which can be electrostatically controlled by tuning the out-of-plane charge distribution or layer polarization. In this work, we measure the stability diagram of layer-polarized quantum Hall states in tTLG by systematically mapping out layer-specific Chern numbers in each layer, and intra- and interlayer Chern transitions as a function of displacement field D and total carrier density n. In contrast to twisted bilayer systems, the rich interplay between the three atomic layers gives rise to a complex layer-polarized stability diagram with unconventional transport features that evolve rapidly with electric and magnetic fields. The stability diagram quantitatively characterizes the interlayer screening and charge distribution in tTLG with implication of strong inter-atomic-layer Coulomb coupling. Our work provides comprehensive guidance and insights into predicting and controlling layer-polarization and interlayer transitions in tTLG, and for tuning the individual role and interactions of each participating constituent towards novel material properties.