Superconductivity and strong interactions in a tunable moir\'e quasiperiodic crystal

Electronic states in quasiperiodic crystals generally preclude a Bloch description, rendering them simultaneously fascinating and enigmatic. Owing to their complexity and relative scarcity, quasiperiodic crystals are underexplored relative to periodic and amorphous structures. Here, we introduce a new type of highly tunable quasiperiodic crystal easily assembled from periodic components. By twisting three layers of graphene with two different twist angles, we form two moir\'e patterns with incommensurate moir\'e unit cells. In contrast to many common quasiperiodic structures that are defined on the atomic scale, the quasiperiodicity in our system is defined on moir\'e length scales of several nanometers. This novel "moir\'e quasiperiodic crystal" allows us to tune the chemical potential and thus the electronic system between a periodic-like regime at low energies and a strongly quasiperiodic regime at higher energies, the latter hosting a large density of weakly dispersing states. Interestingly, in the quasiperiodic regime we observe superconductivity near a flavor-symmetry-breaking phase transition, the latter indicative of the important role electronic interactions play in that regime. The prevalence of interacting phenomena in future systems with in situ tunability is not only useful for the study of quasiperiodic systems, but it may also provide insights into electronic ordering in related periodic moir\'e crystals. We anticipate that extending this new platform to engineer quasiperiodic crystals by varying the number of layers and twist angles, and by using different two-dimensional components, will lead to a new family of quantum materials to investigate the properties of strongly interacting quasiperiodic crystals.