Tunable Inter-Moiré Physics in Consecutively-Twisted Trilayer Graphene

We fabricate a twisted trilayer graphene device with consecutive twist angles of 1.33 and 1.64 degrees, in which we electrostatically tune the electronic states from each of the two co-existing moiré superlattices and the interactions between them. When both moiré superlattices contribute equally to electrical transport, we report a new type of inter-moiré Hofstadter butterfly. Its Brown-Zak oscillation corresponds to one of the intermediate quasicrystal length scales of the reconstructed moiré of moiré (MoM) superlattice, shedding new light on emergent physics from competing atomic orders.