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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 $θ=1.89^{\circ}$, 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 $θ=1.89^{\circ}$ at the half filling of second moiré band.