"Novel aspects of fractionalization in Chern bands"
The discovery of the fractional quantum anomalous Hall effect in twisted MoTe2 has opened a new chapter in condensed matter physics. Much of the current understanding of topological phases in Chern bands such as fractional Chern insulators (FCIs) relies on the analogy to standard quantum Hall physics in Landau levels. A natural question then arises if there are any unique aspects in the Chern band setting that are fundamentally different and cannot be captured by a Landau level analogy and if there are novel phases that don’t have a Landau level analogue. I will highlight similarities/differences between fractionalized phases in Chern bands and Landau levels including the existence of strong particle-hole asymmetry of geometric origin that are reflected on the phase diagram. In addition, I will show that intra-Chern band excitations such as magneto-roton excitations can in principle be probed with optical absorption unlike the Landau level case where this is not allowed due to Kohn’s theorem. Moreover, I will provide examples where the intrinsic topology of Chern bands without the need for external magnetic fields opens a route towards realization of exotic non-Abelian spin Hall phases. I will conclude by showing that the gapless composite Fermi liquid phase in a Chern band is distinct from normal Fermi liquid through the vanishing of the Drude weight and possibly belongs to a larger class of "Drudeless" non Fermi liquids which are compressible yet have no Drude peak.