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 moiré 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 moiré systems.

12+13 pages, 6+11 figures

References in corpus (40)

• The density-matrix renormalization group in the age of matrix product states
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Graphene Bilayers with a Twist
• Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
• Observation of Fractionally Quantized Anomalous Hall Effect
• Fractional quantum Hall effect in the absence of Landau levels
• Integer and fractional Chern insulators in twisted bilayer MoTe2
• Direct observation of anyonic braiding statistics at the $\nu$=1/3 fractional quantum Hall state
• Wannier representation of Z_2 topological insulators
• Spontaneous fractional Chern insulators in transition metal dichalcogenides Moire superlattices
• Fractional Chern Insulator in Twisted Bilayer MoTe${}_2$
• Fractional quantum anomalous Hall states in twisted bilayer MoTe${}_2$ and WSe${}_2$
• Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides
• Strain-induced quantum phase transitions in magic angle graphene
• Efficient simulation of moire materials using the density matrix renormalization group
• Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe${}_2$
• Zero-field composite Fermi liquid in twisted semiconductor bilayers
• Realization of Topological Mott Insulator in a Twisted Bilayer Graphene Lattice Model
• Topological Phases in AB-Stacked MoTe${}_2$/WSe${}_2$: ${\mathbb{Z}}_2$ Topological Insulators, Chern Insulators, and Topological Charge Density Waves
• Local probe of bulk and edge states in a fractional Chern insulator
• Tensor Network Python (TeNPy) version 1
• Band mixing in the quantum anomalous Hall regime of twisted semiconductor bilayers
• Tangent Space Approach for Thermal Tensor Network Simulations of the 2D Hubbard Model
• Quantum anomalous Hall crystal at fractional filling of moiré superlattices
• Exciton Proliferation and Fate of the Topological Mott Insulator in a Twisted Bilayer Graphene Lattice Model
• Topological electronic crystals in twisted bilayer-trilayer graphene
• Controlled bond expansion for DMRG ground state search at single-site costs
• Intertwined fractional quantum anomalous Hall states and charge density waves
• Gate-tunable antiferromagnetic Chern insulator in twisted bilayer transition metal dichalcogenides
• Kekulé spiral order in magic-angle graphene: a density matrix renormalization group study
• Monte Carlo study of the pseudogap and superconductivity emerging from quantum magnetic fluctuations
• Thermodynamic Response and Neutral Excitations in Integer and Fractional Quantum Anomalous Hall States Emerging from Correlated Flat Bands
• Time-dependent variational principle with controlled bond expansion for matrix product states
• Hidden States and Dynamics of Fractional Fillings in tMoTe2 Moiré Superlattices
• Topological quantum phase transitions driven by a displacement field in the twisted MoTe2 bilayers
• Interacting phase diagram of twisted bilayer MoTe${}_2$ in magnetic field
• From Fractional Quantum Anomalous Hall Smectics to Polar Smectic Metals: Nontrivial Interplay Between Electronic Liquid Crystal Order and Topological Order in Correlated Topological Flat Bands
• Detecting Confined and Deconfined Spinons in Dynamical Quantum Simulations

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• Spinless and spinful charge excitations in moiré Fractional Chern Insulators
• Generic integer and fractional quantum anomalous Hall crystals from interaction-driven band folding
• Probing Non-Fermi-Liquid Behaviour of Composite Fermi Liquid via Efficient Thermal Simulations