Fractional Chern Insulator in Twisted Bilayer MoTe${}_2$

Abstract

A recent experiment has reported the first observation of a zero-field fractional Chern insulator (FCI) phase in twisted bilayer MoTe${}_2$ moiré superlattices [Nature 622, 63-68 (2023)]. The experimental observation is at an unexpected large twist angle 3.7${}^{\circ }$ and calls for a better understanding of the FCI in real materials. In this work, we perform large-scale density functional theory calculation for the twisted bilayer MoTe${}_2$, and find that lattice reconstruction is crucial for the appearance of an isolated flat Chern band. The existence of the FCI state at $\nu =-2/3$ are confirmed by exact diagonalization. We establish phase diagrams with respect to the twist angle and electron interaction, which reveal an optimal twist angle of $3.5^{\circ }$ for the observation of FCI. We further demonstrate that an external electric field can destroy the FCI state by changing band geometry and show evidence of the $\nu =-3/5$ FCI state in this system. Our research highlights the importance of accurate single particle band structure in the quest for strong correlated electronic states and provides insights into engineering fractional Chern insulator in moiré superlattices.

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• Theory of Generalized Landau Levels and Implication for non-Abelian States
• Variational Mapping of Chern Bands to Landau Levels: Application to Fractional Chern Insulators in Twisted MoTe${}_2$
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• Thermodynamic Response and Neutral Excitations in Integer and Fractional Quantum Anomalous Hall States Emerging from Correlated Flat Bands
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• Higher vortexability: zero field realization of higher Landau levels
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