Fractional Chern Insulators in Twisted Bilayer MoTe${}_2$: A Composite Fermion Perspective

Abstract

The discovery of Fractional Chern Insulators (FCIs) in twisted bilayer MoTe${}_2$ has sparked significant interest in fractional topological matter without external magnetic fields. Unlike the flat dispersion of Landau levels, moiré electronic states are influenced by lattice effects within a nanometer-scale superlattice. This study examines the impact of these lattice effects on the topological phases in twisted bilayer MoTe${}_2$, uncovering a family of FCIs with Abelian anyonic quasiparticles. Using a composite fermion approach, we identify a sequence of FCIs with fractional Hall conductivities ${\sigma }_{xy}=\frac{C}{2C+1}\frac{e^2}{h}$ linked to partial filling ${\nu }_{\text{h}}$ of holes of the topmost moiré valence band. These states emerge from incompressible composite fermion bands of Chern number $C$ within a complex Hofstadter spectrum. This approach explains FCIs with Hall conductivities ${\sigma }_{xy}=(2/3)e^2/h$ and ${\sigma }_{xy}=(3/5)e^2/h$ at fractional fillings ${\nu }_{\text{h}}=2/3$ and ${\nu }_{\text{h}}=3/5$ observed in experiments, and uncovers other fractal FCI states. The Hofstadter spectrum reveals new phenomena, distinct from Landau levels, including a higher-order Van Hove singularity (HOVHS) at half-filling, leading to novel quantum phase transitions. This work offers a comprehensive framework for understanding FCIs in transition metal dichalcogenide moiré systems and highlights mechanisms for topological quantum criticality.

Main text: 5 pages and 4 figures. Accepted in Physical Review Letters

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• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Anyon superconductivity and plateau transitions in doped fractional quantum anomalous Hall insulators
• A Novel Perspective on Ideal Chern Bands with Strong Short-Range Repulsion: Applications to Correlated Metals, Superconductivity, and Topological Order
• Electromagnetic response and emergent topological orders in transition metal dichalcogenide MoTe${}_2$ bilayers
• Multi-Band Exact Diagonalization and an Iteration Approach to Hunt For Fractional Chern Insulators in Rhombohedral Multilayer Graphene
• Spinless and spinful charge excitations in moiré Fractional Chern Insulators
• Generic integer and fractional quantum anomalous Hall crystals from interaction-driven band folding
• Optical signatures of -1/3 fractional quantum anomalous Hall state in twisted MoTe2
• How quantum fluctuations freeze a classical liquid and then melt it into a topological one
• Chern-Selective multi-valley Flat Bands in Twisted Mono-Bilayer and Mono-Trilayer MoTe${}_2$
• Inter-species topological phases via a dynamical gauge field
• Abelian and non-Abelian fractionalized states in twisted MoTe${}_2$: A generalized Landau-level theory
• Anyon Dispersion in Aharonov-Casher Bands and Implications for Twisted MoTe${}_2$
• Topological Order Without Band Topology in Moiré Graphene
• Generalizing the composite fermion theory for fractional Chern insulators
• Exciton-Anyon Binding in Fractional Chern Insulators: Spectral Fingerprints