Fractional Chern Insulator in Twisted Bilayer MoTe$_2$

TL;DR

This study combines density functional theory and exact diagonalization to understand the conditions for observing fractional Chern insulators in twisted bilayer MoTe2, emphasizing the importance of lattice reconstruction and external fields.

Contribution

It provides a detailed theoretical analysis of FCI emergence in twisted bilayer MoTe2, identifying optimal twist angles and the effects of electric fields on FCI stability.

Findings

Lattice reconstruction is essential for flat Chern band formation.

An optimal twist angle of 3.5° enhances FCI observation.

External electric fields can destroy FCI states.

Abstract

A recent experiment has reported the first observation of a zero-field fractional Chern insulator (FCI) phase in twisted bilayer MoTe$_2$ moir\'e 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 moir\'e superlattices.