Abstract: Strongly correlated and topological phases in condensed matter systems are at the cutting edge of fundamental physics studies, as well as being promising candidates for the next generation of technological capabilities like quantum computing. In recent years, a remarkable amount of progress has been made in creating and controlling such phases by introducing a small twist angle or lattice mismatch between two-dimensional (2D) materials. These systems, called moiré systems, have facilitated the surprising discovery of strongly correlated phases where one might not expect them (e.g. superconductivity in “magic-angle” twisted bilayer graphene) or long-sought new physics (e.g. the fractional quantum anomalous Hall effect (FQAHE) in twisted MoTe2). However, much of the work in this rapidly developing field have focused on the case where the constituent 2D materials of the moiré system are monolayers, or at most bilayers. I will show that this restriction to one or two atomic layers is unnecessarily limiting. Surprising new phenomenology can be realized in graphitic moiré systems, where at least one component is three-layers or more. Most notably, we find that a new type of “moiré enabled” electron crystallization can occur that spontaneously breaks the moiré translational symmetry and has dissipationless edge modes, analogous to a topological version of a Wigner crystal. Our results suggest that these topological electron crystals 1) are at least somewhat common across multilayer graphene moiré systems, 2) can have uniquely tunable magnetization states, and 3) closely compete with the newly discovered FQAHE. Understanding this competition, as well as the novel phenomenology of the topological electron crystal phase, will be of fundamental interest in future studies of strongly correlated topological systems.
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