Fractional Chern Insulator and Quantum Anomalous Hall Crystal in Twisted MoTe$_2$

Abstract

Recent experimental advances have uncovered fractional Chern insulator (FCI) states in twisted MoTe$_2$ (tMoTe$_2$) systems under zero magnetic field. Understanding the interaction effects on topological phases within realistic model presents a significant theoretical challenge. Here, we construct a moir\'e superlattice model tailored for tMoTe$_2$ and conduct investigations using state-of-the-art tensor-network methods. Our ground-state calculations reveal a rich variety of interaction-driven and filling-dependent topological phases, including FCIs, Chern insulators, and generalized Wigner crystals, which are revealed in recent experiments. For FCI state, dynamical simulations uncover a single-particle excitation continuum with a finite charge gap, reflecting the fractionalized charge excitations. Finite-temperature calculations further determine characteristic charge activation and ferromagnetic transition temperatures, reconciling existing experimental discrepancies. Furthermore, using this realistic lattice model, we predict the presence of quantum anomalous Hall crystals exhibiting integer Hall conductivity at fractional fillings in tMoTe$_2$. By integrating ground-state, finite-temperature, and dynamical analyses, our work establishes a comprehensive framework for understanding correlated topological phases in tMoTe$_2$ and related moir\'e systems.