Fractional Electron Physics in New Materials

The quantum Hall effect is characterized by dissipationless electronic transport with a Hall conductivity that is an integer for rational fraction of the quantum unit of conductivity. For decades the quantum Hall effect has been associated with two-dimensional electrons in strong magnetic fields although quantum anomalous quantum Hall effects (QAHE), which do not require a magnetic field, were recognized as a theoretical possibility.   In recent years both the integer and fractional quantum anomalous Hall effects (QAHE) have been observed in both rhombohedral graphene and transition metal dichalcogenide (TMD) moiré materials.  In my talk I will attempt to provide an overview of and a perspective on these observations.  I will emphasize a qualitative distinction between the mechanism responsible for the integer QAHE in moiré materials, which is due to orbital ferromagnetism, and in the magnetized topological insulator thin films where the effect was first observed, which is due to more conventional spin ferromagnetism.  I will also emphasize that the QHE is generically a property of two-dimensional insulators that are gapped at magnetic-field (B) dependent densities – for example the gaps between Landau levels or the bands of Chern insulators.  To explain the fractional QAHE we must explain why interactions induce a gap in the many-body spectrum of a partially occupied Chern band – and why the density at which that gap appears is B-dependent.  There is a simple natural explanation for this property in TMD homobilayer moiré materials like MoTe₂, but the behavior of rhombohedral graphene/hBN moirés is more subtle.