Fractional topological insulators in twisted MoTe2

Twisted MoTe2 is a platform for realizing Landau-level-like bands in the absence of an external magnetic field. Experiments on twisted MoTe2 have observed a fractionally quantized Hall conductance indicating the presence of fractional Chern insulators, the lattice version of the fractional quantum Hall effect. Here, we will investigate the possibility of realizing a related but distinct state: A fractional topological insulator (FTI) which is the time-reversal invariant cousin of a fractional Chern insulator. We will start with a model based on Landau levels to pin down the conditions on the Hamiltonian for realizing an FTI. We will then use exact diagonalization on a continuum model of twisted MoTe2 to show under which conditions this state may be realized in the real material.