Abstract: Time-reversed pairs of topological bands with opposite Chern numbers are commonly found in moiré superlattices based on transition metal dichalcogenides. Recent experimental breakthroughs have demonstrated that these topological bands provide a rich platform for realizing fractional quantum matter at zero external magnetic fields. In particular, the observation of the fractional quantum spin Hall effect in twisted MoTe_2, where a time-reversed pair of Chern bands is half-filled, has sparked significant interest in fractional topological insulators (FTIs) and fractional quantum spin Hall (FQSH) states—novel incompressible fractionalized phases that are fundamentally distinct from fractional quantum Hall fluids.
In this talk, I will present a theory of "minimal" FTI and FQSH states for a time-reversed pair of half-filled Chern bands. These states are "minimal" in the sense that they represent the simplest possible incompressible phases consistent with symmetry and transport constraints, which I will establish using a bootstrap approach extending Laughlin’s celebrated flux-threading argument. Notably, the minimal FTI exhibits Z_4 topological order, featuring fractionalized Cooper pairs and excitons, while other minimal FQSH states can host non-Abelian anyons and quantized thermal Hall transports. I will discuss the experimental signatures of these minimal states and compare them with other FQSH candidates.