Utilizing the realistic continuum description of twisted bilayer ${\mathrm{MoTe}}_2$ and many-body exact diagonalization calculation, we establish that the second moiré band of twisted bilayer ${\mathrm{MoTe}}_2$, at a small twist angle of approximately $2^{\circ }$, serves as an optimal platform for achieving the long-sought non-Abelian fractional quantum anomalous Hall states without the need for external magnetic fields. Across a wide parameter range, our exact diagonalization calculations reveal that the half-filled second moiré band demonstrates the ground state degeneracy and spectral flows, which are consistent with the Pfaffian state in the first Landau level. We further elucidate that the emergence of the non-Abelian state is deeply connected to the remarkable similarity between the second moiré band and the first Landau level. Essentially, the band not only exhibits characteristics akin to the first Landau level, $\frac{1}{2\pi }{\int }_{\mathrm{BZ}}{\mathrm{d}}^2\mathbf{k}\mathrm{tr}\eta \left(\mathbf{k}\right)\approx 3$ where ${\eta }_{ab}\left(\mathbf{k}\right)$ is the Fubini-Study metric of the band, but also that its projected Coulomb interaction closely mirrors the Haldane pseudopotentials of the first Landau level. Motivated by this observation, we introduce a metric of “first Landau level”-ness of a band, which quantitatively measures the alignment of the projected Coulomb interaction with the Haldane pseudopotentials in Landau levels. This metric is then compared with the global phase diagram of the half-filled second moiré band, revealing its utility in predicting the parameter region of the non-Abelian state. In addition, we uncover that the first and third moiré bands closely resemble the lowest and second Landau levels, revealing a remarkable sequential equivalence between the moiré bands and Landau levels. We finally discuss the potential implications on experiments.

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• Chern insulators
• Flat bands
• Fractional quantum Hall effect
• Geometric & topological phases
• Bilayer films
• Twisted heterostructures
• Exact diagonalization