Moore-Read state in Half-filled Moiré Chern band from three-body Pseudo-potential

The moiré system provides a tunable platform for exploring exotic phases of materials. This article shows the possible realization of a non-Abelian state characterized by the Moore-Read wavefunction in a half-filled moiré Chern band, exemplified by twisted MoTe2. This is achieved by introducing short-range repulsive three-body interaction. Exact diagonalization is employed to examine the spectrum in finite size. The incompressibility of the system, the degeneracy of the ground states, and the number of low-energy states provide compelling evidence to identify the ground state as the Moore-Read state. We further interpolate between the three-body interaction and Coulomb interaction to show a phase transition between the composite Fermi-liquid and the Moore-Read state. Finally, we consider the effect of band mixing and derive the three-body interaction using perturbation theory. By exploring the conditions under which band mixing effects mimic short-range repulsive three-body interaction we provide insights towards realizing non-Abelian phases of matter in the moiré system.