Robust non-Abelian even-denominator fractional Chern insulator in twisted bilayer MoTe$_2$

A recent experiment observes a series of quantum spin Hall effects in transition metal dichalcogenide moir\'e MoTe$_2$ [K. Kang, et. al, Nature 628, 522-526 (2024)]. Among them, the vanishing Hall signal at the filling factor $\nu=3$ implies a possible realization of a time-reversal pair of the even-denominator fractional Chern insulators (FCIs). Inspired by this discovery, we investigate whether a robust incompressible quantum Hall liquid can be stabilized in the half-filled Chern band of twisted MoTe$_2$ bilayers. We use the continuum model with parameters relevant to twisted MoTe$_2$ bilayers and obtain three consecutive nearly flat Chern bands with the same Chern number. Crucially, when the second moir\'e miniband is half-filled,signatures of non-Abelian frctional quantum Hall state are found via exact diagonalization calculations, including the stable six-fold ground state degeneracy that grows more robust with the lattice size and is consistent with an even-denominator FCI state. We further perform flux insertion simulations to reveal a 1/2 quantized many-body Chern number as direct evidence of topological order. Furthermore, the ground state density structure factors show no sharp peak, indicating no charge density wave order. These evidences signal the potential of realizing the non-Abelian state at zero magnetic field in twisted bilayer MoTe$_2$ at the fractional hole filling 3/2.