[Paper Review] Fractional Chern Insulator in Twisted Bilayer MoTe$_2$

Chong Wang, Xiaowei Zhang+6 more|arXiv (Cornell University)|Apr 24, 2023

Cold Atom Physics and Bose-Einstein Condensates24 citations

TL;DR

The study shows, using large-scale DFT and exact diagonalization, that lattice reconstruction yields an isolated flat Chern band in twisted bilayer MoTe2, confirming a ν=−2/3 FCI, mapping phase diagrams vs twist angle and interactions, and showing electric fields can destroy the FCI.

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 $ν= -2/3$ 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 $ν=-3/5$ 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.

Motivation & Objective

• Understand whether a zero-field fractional Chern insulator can emerge in twisted bilayer MoTe2.
• Identify how lattice reconstruction shapes the single-particle band structure to support FCI.
• Map the phase diagram as a function of twist angle and screening/interaction strength to locate optimal conditions for FCI.
• Investigate how an out-of-plane electric field affects band geometry and FCI stability.
• Explore potential ν=−3/5 FCI states under realistic dielectric environments.

Proposed method

• Perform large-scale density functional theory calculations including lattice relaxation, layer corrugation, and interlayer polarization.
• Fit continuum-model parameters to DFT results to obtain an isolated flat Chern band with width ~9 meV (Table 1).
• Project the Coulomb interaction onto the top moiré band and carry out exact diagonalization on finite clusters to detect FCI signatures.
• Compute many-body spectra, ground-state degeneracy on a torus, and Chern numbers (e.g., ν=−2/3 with Chern number −2/3).
• Construct phase diagrams in twist angle and dielectric screening ε or gate distance d to identify regimes of FCI, valley-polarized (VP), and non-valley-polarized (NVP) phases.
• Investigate the effect of an external out-of-plane electric field on band geometry via Berry curvature and quantum metric analyses.

Experimental results

Research questions

• RQ1 Can a zero-field FCI appear in twisted bilayer MoTe2 given lattice reconstruction?
• RQ2 What twist angle and interaction strength optimally stabilize the ν=−2/3 FCI in this system?
• RQ3 How does dielectric screening and gate distance affect the FCI phase boundary?
• RQ4 What is the impact of an out-of-plane electric field on the band geometry and FCI stability?
• RQ5 Is there evidence for other FCI states, such as ν=−3/5, under realistic parameters?

Key findings

• DFT reveals significant lattice reconstruction, producing an isolated flat Chern band with bandwidth about 9 meV.
• Exact diagonalization confirms a ν=−2/3 FCI with three nearly degenerate ground states on a torus and a 6π flux evolution.
• Phase diagrams show an optimal twist angle around 3.5° for FCI stability, with VP phases at stronger interactions and an NVP phase in weaker interaction regimes.
• An out-of-plane electric field destabilizes FCI, with the many-body gap closing around E=1.26 meV/Å before a single-particle topological transition occurs, consistent with experiments.
• There is suggestive, albeit parameter-sensitive, evidence for ν=−3/5 FCI at ε≈8; ν=−2/5 shows weaker or different signatures, and no clear FCI at ν=−1/5 or −4/5 under the explored conditions.