Higher Landau-Level Analogs and Signatures of Non-Abelian States in Twisted Bilayer MoTe${}_2$

Abstract

Recent experimental discovery of fractional Chern insulators at zero magnetic field in moiré superlattices has sparked intense interests in bringing Landau level physics to flat Chern bands. In twisted MoTe${}_2$ bilayers (tMoTe${}_2$), recent theoretical and experimental studies have found three consecutive flat Chern bands at twist angle $\sim 2^{\circ }$. In this work, we investigate whether higher Landau level physics can be found in these consecutive Chern bands. At twist angles $2.00^{\circ }$ and $1.89^{\circ }$, we identify four consecutive $C=1$ bands for the $K$ valley in tMoTe${}_2$. By constructing Wannier functions directly from density functional theory (DFT) calculations, a six-orbital model is developed to describe the consecutive Chern bands, with the orbitals forming a honeycomb lattice. Exact diagonalization on top of Hartree-Fock calculations are carried out with the Wannier functions. Especially, when the second moiré miniband is half-filled, signatures of non-Abelian states are found. Our Wannier-based approach in modelling moiré superlattices is faithful to DFT wave functions and can serve as benchmarks for continuum models. The possibility of realizing non-Abelian anyons at zero magnetic field also opens up a new pathway for fault-tolerant quantum information processing.

References in corpus (49)

• Maximally-localized generalized Wannier functions for composite energy bands
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Maximally localized Wannier functions: Theory and applications
• Maximally-localized Wannier functions for entangled energy bands
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Topological insulators in twisted transition metal dichalcogenide homobilayers
• 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
• Fractional Chern Insulator
• Integer and fractional Chern insulators in twisted bilayer MoTe2
• Exponential localization of Wannier functions in insulators
• Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
• Is the Composite Fermion a Dirac Particle?
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Band geometry of fractional topological insulators
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Zoology of Fractional Chern Insulators
• Emergent Many-Body Translational Symmetries of Abelian and Non-Abelian Fractionally Filled Topological Insulators
• Spontaneous fractional Chern insulators in transition metal dichalcogenides Moire superlattices
• Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator
• 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
• Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides
• Fractional Chern Insulators and the W-Infinity Algebra
• Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
• Non-Abelian Quantum Hall Effect in Topological Flat Bands
• The Fractional Quantum Hall state at nu=5/2 and the Moore-Read Pfaffian
• Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe${}_2$
• Giant magnetic field from moiré induced Berry phase in homobilayer semiconductors
• Magic Angles and Fractional Chern Insulators in Twisted Homobilayer TMDs
• Landau-level-mixing and the ground state of the 5/2 quantum Hall effect
• Kähler geometry and Chern insulators: Relations between topology and the quantum metric
• Zero-field composite Fermi liquid in twisted semiconductor bilayers
• Polarization-driven band topology evolution in twisted MoTe${}_2$ and WSe${}_2$
• The impossibility of exactly flat non-trivial Chern bands in strictly local periodic tight binding models
• Pressure--enhanced fractional Chern insulators in moiré transition metal dichalcogenides along a magic line
• 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
• Topological Phases in the Zeroth Landau Level of Bilayer Graphene
• Non-Abelian fractionalization in topological minibands
• Interaction-driven topological phase diagram of twisted bilayer MoTe${}_2$
• Band mixing in the quantum anomalous Hall regime of twisted semiconductor bilayers
• Non-Abelian Fractional Quantum Anomalous Hall States and First Landau Level Physics in Second Moiré Band of Twisted Bilayer MoTe2
• Skyrmions in the Moore-Read state at nu=5/2
• Fractional quantum Hall effect arising from repulsive three body interaction

Cited by in corpus (23)

• 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${}_2$
• Hidden States and Dynamics of Fractional Fillings in tMoTe2 Moiré Superlattices
• Non-Abelian spin Hall insulator
• Minimal Fractional Topological Insulator in half-filled conjugate moiré Chern bands
• Non-Abelian Fractional Chern Insulators and Competing States in Flat Moiré Bands
• Observation of Ferromagnetic Phase in the Second Moiré Band of Twisted MoTe2
• Quantum anomalous Hall crystals in moiré bands with higher Chern number
• Chiral superconductivity from spin polarized Chern band in twisted MoTe${}_2$
• Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
• Electromagnetic response and emergent topological orders in transition metal dichalcogenide MoTe${}_2$ bilayers
• Quantum Phases in Twisted Homobilayer Transition Metal Dichalcogenides
• Orbital Magnetization of Correlated States in Twisted Bilayer Transition Metal Dichalcogenides
• Exciton fractional Chern insulators in moiré heterostructures
• Candidate for a Fractional Topological Insulator in Twisted MoTe2
• Chern-Selective multi-valley Flat Bands in Twisted Mono-Bilayer and Mono-Trilayer MoTe${}_2$
• Manipulating Charge Distribution in Moiré Superlattices by Light
• Exact Parent Hamiltonians for All Landau Level States in a Half-flux Lattice
• Orbital Description of Landau Levels
• Topological Order Without Band Topology in Moiré Graphene
• Abelian and non-Abelian fractionalized states in twisted MoTe${}_2$: A generalized Landau-level theory
• Exciton-Anyon Binding in Fractional Chern Insulators: Spectral Fingerprints
• Robustness of real-space topology in moiré systems