Fractional Topological Insulators in Twisted MoTe$_2$ (and Other Systems)

The experimental observations of fractional Chern insulators in moir\’e heterostructures motivate the investigation of their time-reversal invariant generalizations, fractional topological insulators (FTIs), which have been significantly less explored. In this talk, I present a comprehensive exact diagonalization study of twisted bilayer MoTe$_2$, as well as idealized Landau level models, with the goal of extracting general principles for engineering such exotic phases, focusing on the simplest Abelian FTIs. The calculations reveal that a large suppression of the short-range part of the Coulomb repulsion is crucial for realizing FTIs in realistic systems. I discuss how aspects such as the screening environment, band-mixing, Landau level character and finite-size effects affect the FTI phases, and also provide potential sample-engineering routes to improve their stability.