Fractional quantum Hall effect in non-crystalline systems

The discovery of the anomalous fractional quantum Hall effect in moiré heterostructures, confounded with the existence of Chern insulator states in quasicrystals and amorphous systems, calls for useful real-space criteria to engineer single-particle states that favor non-crystalline fractional Chern insulators. I will discuss how to define real-space criteria to find non-crystalline variants of the fractional Chern insulator state, and their success in diagnosing this phase.