Non-Abelian Fractional Quantum Anomalous Hall States and First Landau Level Physics in Second Moir\'e Band of Twisted Bilayer MoTe2

Utilizing the realistic continuum description of twisted bilayer MoTe2 and many-body exact diagonalization calculation, we establish that the second moir\'e band of twisted bilayer MoTe2, at a small twist angle of approximately 2{\deg}, 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 moir\'e 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 moir\'e band and the first Landau level. Essentially, the band not only exhibits characteristics akin to the first Landau level, $\frac{1}{2\pi}\int_\mathrm{BZ}\mathrm{d}^2\mathbf{k}\:\mathrm{tr}\:\eta(\mathbf{k}) \approx 3$ where $\eta_{ab}(\mathbf{k})$ 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 from this observation, we introduce a novel 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 moir\'e band, revealing its utility in predicting the parameter region of the non-Abelian state. In addition, we uncover that the first and third moir\'e bands closely resemble the lowest and second Landau levels, revealing a remarkable sequential equivalence between the moir\'e bands and Landau levels. We finally discuss the potential implications on experiments.