Observation of Integer and Fractional Chern insulators in high Chern number flatbands

Moir\'e flatbands with high Chern numbers (C>1) offer opportunities to study the fractional quantum anomalous Hall effects that go beyond the Landau level paradigm with C=1, which remain unexplored yet. Here, we target the novel topological phases in high Chern number flatbands by designing a new moir\'e system, i.e., twisted rhombohedral trilayer-bilayer graphene. We observe quantized anomalous Hall effects (QAH) with C = 3 at v = 1 and v = 3, demonstrating the high Chern number nature of the flat band from continuum calculations. By fractionally filling the flat band, we observe QAH with C = 2 at even-denominator fractional filling v = 3/2, as well as QAH with C = 3 continuously from v = 1 to the even-denominator v = 3/2 at zero magnetic fields. Most importantly, we observe, for the first time, evidence of an FCI with C = -6/5 at v = 12/5, corresponding to 2/5 filling of a high Chern number flat band with C = -3, verified by both Streda formula analysis and a fractionally QAH. It is also worth noting that Streda formula analysis reveals a signature of another FCI with C = -3/2 at v = 5/2 under finite magnetic fields. Our results demonstrate the tRTBG, which can be naturally extended to other twisted graphene moir\'e superlattices based on rhombohedral graphene multilayers, as a novel platform for hosting unconventional high Chern number correlated topology in the ultra-strong correlated regime that is beyond the paradigm of fractional phases with C < 1.