Multiple Chern bands in twisted MoTe${}_2$ and possible non-Abelian states

We investigate the moiré band structures and possible even denominator fractional quantum Hall state in small angle twisted bilayer MoTe${}_2$, using combined large-scale local basis density functional theory calculation and continuum model exact diagonalization. Via large-scale first principles calculations at $\theta ={1.89}^{\circ }$, we find a sequence of $C=1$(Chern number in K valley)moiré Chern bands, in analogy to Landau levels. By constructing the continuum model with multiple Chern bands, we undertake band-projected exact diagonalization using unscreened Coulomb repulsion to identify possible non-Abelian states near twist angle $\theta ={1.89}^{\circ }$ at the half filling of second moiré band.