In this talk we will review recent experiments in moiré structures which show bandwidth-tuned transitions between a metal and a charge-ordered insulator at fractional fillings of the moiré lattice. We will mention several possible scenarios consistent with the experimental data. The bulk of the talk will focus on the possibility that with increasing charge fluctuations the charge order melts within the insulator, resulting in a phase with fractionalized electrons. We establish some general constraints on such fractionalized electronic insulators. Armed with these constraints we turn to the quantum dimer model as a paradigmatic example for the emergence of topological order from charge fluctuations. We extend the quantum dimer model to fermions, and consider the fermionic topological order consistent with our constraints. To determine whether topological order emerges we develop an ED algorithm capable of reaching 126 sites. We discuss the results of this ED study, along with iDMRG results for the same model.
