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

TL;DR

This paper demonstrates the potential realization of a non-Abelian Moore-Read state in a half-filled moiré Chern band, specifically in twisted MoTe2, by introducing and analyzing three-body interactions through exact diagonalization.

Contribution

It introduces a method to realize and identify Moore-Read states in moiré systems via three-body interactions and explores phase transitions and band mixing effects.

Findings

Identification of Moore-Read state via exact diagonalization evidence

Phase transition between composite Fermi-liquid and Moore-Read state

Insights into band mixing effects mimicking three-body interactions

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.