When Could Abelian Fractional Topological Insulators Exist in Twisted MoTe₂ (and Other Systems)

Using comprehensive exact diagonalization calculations on θ ≈ 3.7 ∘ twisted bilayer MoTe₂ (tMoTe₂), as well as idealized Landau level models also relevant for lower θ, we extract general principles for engineering fractional topological insulators (FTIs) in realistic situations. First, in a Landau level setup at ν=1/3+1/3, we investigate what features of the interaction destroy an FTI. For both pseudopotential interactions and realistic screened Coulomb interactions, we find that sufficient suppression of the short-range repulsion is needed for stabilizing an FTI. We then study θ ≈ 3.7 ∘ tMoTe₂ with realistic band-mixing and anisotropic non-local dielectric screening. Our finite-size calculations only find an FTI phase at ν=-4/3 in the presence of a significant additional short-range attraction g that acts to counter the Coulomb repulsion at short distances. We discuss how further finite-size drifts, dielectric engineering, Landau level character, and band-mixing effects may reduce the required value of g closer towards the experimentally relevant conditions of tMoTe₂. Projective calculations into the $n=1$ Landau level, which resembles the second valence band of θ 2.1^∘ tMoTe₂, do not yield FTIs for any g, suggesting that FTIs at low-angle tMoTe₂ for ν=-8/3 and $-10/3$ may be unlikely. While our study highlights the challenges, at least for the fillings considered, to obtaining an FTI with transport plateaus, even in large-angle tMoTe₂ where fractional Chern insulators are experimentally established, we also provide potential sample-engineering routes to improve the stability of FTI phases.