The discovery, four years ago, of superconductivity and correlated insulating states in twisted bilayer graphene unveiled a new platform to investigate strongly-correlated and topological quantum matter. Since then, several tunable twisted moiré systems displaying nearly flat bands have been discovered, and interesting symmetry-breaking electronic states have been observed. A prominent one is electronic nematic order, which consists of the spontaneous breaking of the threefold rotational symmetry of the emergent moiré superlattice. In this talk, I will present a comprehensive model for the electronic nematicity of twisted moiré systems. Described by a Potts-like order parameter, it is fundamentally different from the Ising-nematic state typically observed in bulk unconventional superconductors. This difference is rooted in the strong coupling between the electronic nematic degrees of freedom and the elastic excitations of the underlying lattice. The key point is that, unlike those bulk systems, the moiré superlattice is not a rigid crystal. As a result, its collective low-energy excitations are not the usual propagating acoustic phonons, but diffusive and gapped phasons. I will show how phason-mediated interactions qualitatively alter the properties of the Potts-nematic state in twisted moiré systems, promoting novel behavior that cannot be realized in crystalline lattices. I will also briefly discuss the relationship between electronic nematicity and the superconductivity of twisted moiré systems.
