Composite fermions and the fractional quantum anomalous Hall effect

Recent experiments have revealed evidence for fractional quantum anomalous Hall (FQAH) states at zero magnetic field in a growing number of moiré materials. In this talk, I will present a unified theoretical framework for understanding the emergence of FQAH phases in terms of composite fermions, which in the past have played a crucial organizing role in the  phenomenology of 2d electron gases at high magnetic fields. A central prediction of this framework is a non-Fermi liquid metal of composite fermions at even-denominator fillings, which is the parent of the observed FQAH states. To this end, I will present exact diagonalization evidence for such anomalous composite Fermi liquid (ACFL) states at zero magnetic field in twisted MoTe2 bilayers, at fillings n = 1/2 and n = 3/4, and I will argue that these ACFLs play a central role in the FQAH phase diagram. I will also develop a long wavelength theory for ACFL phases, which offers concrete experimental predictions that I will discuss in relation to current measurements. For example, upon doping the composite Fermi sea, one obtains a Jain sequence of FQAH states consistent with those observed experimentally, as well as a new type of commensurability oscillations originating from the superlattice potential intrinsic to the system. Finally, I will discuss how these ideas can launch us into addressing the exciting new questions and research directions in this emerging field.