Regarding the existence of abelian fractional topological insulators in twisted MoTe2 and related systems

The experimental discovery of fractional Chern insulators (FCIs) in moiré materials raises the question of whether their time-reversal invariant analogs, fractional topological insulators (FTIs), can also be realized in these platforms. We address this via exact diagonalization calculations in both a Landau level (LL) model and continuum model for twisted MoTe₂, and extract principles for engineering FTIs in realistic conditions. For the spinful LL model at filling <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ν</mml:mi> <mml:mo>=</mml:mo> <mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow> <mml:mrow><mml:mn>3</mml:mn></mml:mrow> </mml:mfrac> <mml:mo>+</mml:mo> <mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow> <mml:mrow><mml:mn>3</mml:mn></mml:mrow> </mml:mfrac> </mml:math> , we show that a suppression of the short-range component of the interaction is important to stabilize the FTI. For twisted MoTe₂ at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ν</mml:mi> <mml:mo>=</mml:mo> <mml:mo>-</mml:mo> <mml:mfrac><mml:mrow><mml:mn>4</mml:mn></mml:mrow> <mml:mrow><mml:mn>3</mml:mn></mml:mrow> </mml:mfrac> </mml:math> , we find that a short-range attraction <i>g</i> on top of the screened Coulomb interaction is needed to realize an FTI. We discuss how this threshold value of <i>g</i> could be reduced by examining larger system sizes, incorporating band-mixing effects, exploiting Landau level character, and engineering the dielectric environment. While our study highlights the challenges, at least for the fillings considered, for obtaining FTIs, we also provide potential sample-engineering routes to improve the stability of FTI phases.