Abelian and non-Abelian fractionalized states in twisted MoTe${}_2$: A generalized Landau-level theory

Abstract

Fractional Chern insulators are lattice analogs of fractional quantum Hall states that realize fractionalized quasiparticles without an external magnetic field. A key strategy to understand and design these phases is to map Chern bands onto Landau levels (LLs). Here, we introduce a universal framework that variationally decomposes Bloch bands into generalized LLs, providing a controlled and quantitative characterization of their effective LL nature. Applying this approach to twisted bilayer MoTe${}_2$ modeled by first-principles-derived moiré Hamiltonians, we find that the first moiré valence band is dominated by the generalized zeroth LL across a broad range of twist angles, facilitating the formation of Abelian fractional Chern insulators in the Jain sequences. The second moiré band, renormalized via Hartree-Fock calculations at hole filling ${\nu }_h=2$, is dominated by the generalized first LL at twist angles $\theta =2.45^{\circ }$ and $2.13^{\circ }$. At $\theta =2.45^{\circ }$, we find numerical evidence for a non-Abelian Moore--Read (MR) state at ${\nu }_h=5/2$, with consistent signatures in both the energy spectrum and the particle entanglement spectrum. Interpolation studies further demonstrate an adiabatic connection between this state and the MR state in the conventional first LL. In contrast, at $\theta =2.13^{\circ }$, a charge-density-wave state prevails in the competition with the MR state due to the larger bandwidth. Our variational mapping provides a theoretical framework for exploring exotic fractionalized phases, including non-Abelian states, in realistic systems.

23 pages, 16 figures. Published in Physical Review B as Editors' Suggestion

References in corpus (46)

• Non-Abelian Anyons and Topological Quantum Computation
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• 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
• Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Fractional Chern Insulator in Twisted Bilayer MoTe${}_2$
• Fractional quantum anomalous Hall states in twisted bilayer MoTe${}_2$ and WSe${}_2$
• Relations between topology and the quantum metric for Chern insulators
• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
• Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe${}_2$
• Family of ideal Chern flat bands with arbitrary Chern number in chiral twisted graphene multilayers
• Magic Angles and Fractional Chern Insulators in Twisted Homobilayer TMDs
• Kähler geometry and Chern insulators: Relations between topology and the quantum metric
• Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models
• Zero-field composite Fermi liquid in twisted semiconductor bilayers
• Gauge-Fixed Wannier Wave-Functions for Fractional Topological Insulators
• Maximally Localized Wannier Orbitals, Interaction Models and Fractional Quantum Anomalous Hall Effect in Twisted Bilayer MoTe2
• Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra
• Non-Abelian fractionalization in topological minibands
• Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
• Band mixing in the quantum anomalous Hall regime of twisted semiconductor bilayers
• Interplay between topology and correlations in the second moiré band of twisted bilayer MoTe2
• Transfer learning relaxation, electronic structure and continuum model for twisted bilayer MoTe${}_2$
• Phase transitions out of quantum Hall states in moiré materials
• Non-Abelian Fractional Quantum Anomalous Hall States and First Landau Level Physics in Second Moiré Band of Twisted Bilayer MoTe2
• Multiple Chern bands in twisted MoTe${}_2$ and possible non-Abelian states
• Higher Landau-Level Analogs and Signatures of Non-Abelian States in Twisted Bilayer MoTe${}_2$
• Adiabatic Approximation and Aharonov-Casher Bands in Twisted Homobilayer TMDs
• Quantum weight: A fundamental property of quantum many-body systems
• Theory of Generalized Landau Levels and Implication for non-Abelian States
• Variational Mapping of Chern Bands to Landau Levels: Application to Fractional Chern Insulators in Twisted MoTe${}_2$
• Higher vortexability: zero field realization of higher Landau levels
• Fractional quantum anomalous Hall effect in a singular flat band
• Fractional Chern Insulators in Twisted Bilayer MoTe${}_2$: A Composite Fermion Perspective
• Minimal Fractional Topological Insulator in half-filled conjugate moiré Chern bands
• Observation of Ferromagnetic Phase in the Second Moiré Band of Twisted MoTe2
• Non-Abelian Fractional Chern Insulators and Competing States in Flat Moiré Bands
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Fractional Chern insulator states in an isolated flat band of zero Chern number
• Optical signatures of -1/3 fractional quantum anomalous Hall state in twisted MoTe2