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arXiv · 2403.11478

Moore-Read state in Half-filled Moir\'e Chern band from three-body Pseudo-potential

Lu Zhang·Xue-Yang Song
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Abstract

The moir\'e 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 moir\'e Chern band, exemplified by twisted $\rm MoTe_2$. 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 moir\'e system.

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Lu Zhang, Xue-Yang Song. 2024-03-18. Moore-Read state in Half-filled Moir\'e Chern band from three-body Pseudo-potential. https://arxiv.org/abs/2403.11478

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