Magic Angles and Fractional Chern Insulators in Twisted Homobilayer TMDs

Abstract

We explain the appearance of magic angles and fractional Chern insulators in twisted K-valley homobilayer transition metal dichalcogenides by mapping their continuum model to a Landau level problem. Our approach relies on an adiabatic approximation for the quantum mechanics of valence band holes in a layer-pseudospin field that is valid for sufficiently small twist angles and on a lowest Landau level approximation that is valid for sufficiently large twist angles. It simply explains why the quantum geometry of the lowest moiré miniband is nearly ideal at particular flat-band twist angles, predicts that topological flat bands occur only when the valley-dependent moiré potential is sufficiently strong compared to the interlayer tunneling amplitude, and provides a powerful starting point for the study of interactions

14 pages, 5 figures

References in corpus (13)

• 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
• 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
• Pressure--enhanced fractional Chern insulators in moiré transition metal dichalcogenides along a magic line
• Theory of tunable flux lattices in the homobilayer moiré of twisted and uniformly strained transition metal dichalcogenides

Cited by in corpus (65)

• A Microscopic Perspective on Moiré Materials
• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field
• Maximally Localized Wannier Orbitals, Interaction Models and Fractional Quantum Anomalous Hall Effect in Twisted Bilayer MoTe2
• Roadmap for Photonics with 2D Materials
• Non-Abelian fractionalization in topological minibands
• Theory of fractional Chern insulator states in pentalayer graphene moiré superlattice
• Interplay between topology and correlations in the second moiré band of twisted bilayer MoTe2
• Quantum anomalous Hall crystal at fractional filling of moiré superlattices
• 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
• Theory of Generalized Landau Levels and Implication for non-Abelian States
• Halperin States of Particles and Holes in Ideal Time Reversal Invariant Pairs of Chern Bands and The Fractional Quantum Spin Hall Effect in Moiré MoTe${}_2$
• Variational Mapping of Chern Bands to Landau Levels: Application to Fractional Chern Insulators in Twisted MoTe${}_2$
• Gate-tunable topological phases in superlattice modulated bilayer graphene
• Higher vortexability: zero field realization of higher Landau levels
• Bridging the small and large in twisted transition metal dicalcogenide homobilayers: a tight binding model capturing orbital interference and topology across a wide range of twist angles
• Self-consistent theory for the fractional quantum anomalous Hall effect in rhombohedral pentalayer graphene
• Stability of fractional Chern insulators with a non-Landau level continuum limit
• Contrasting twisted bilayer graphene and transition metal dichalcogenides for fractional Chern insulators: an emergent gauge picture
• Designing topology and fractionalization in narrow gap semiconductor films via electrostatic engineering
• Experimental signature of layer skyrmions and implications for band topology in twisted WSe2 bilayers
• Non-Abelian spin Hall insulator
• Three-dimensional Moiré Crystal
• Intraband collective excitations in fractional Chern insulators are dark
• Hofstadter spectrum of Chern bands in twisted transition metal dichalcogenides
• Quantum Geometry and the Hidden Scales in Materials
• Minimal Fractional Topological Insulator in half-filled conjugate moiré Chern bands
• Quantum-metric-induced quantum Hall conductance inversion and reentrant transition in fractional Chern insulators
• Broken Symmetry in Ideal Chern Bands
• Helical trilayer graphene in magnetic field: Chern mosaic and higher Chern number ideal flat bands
• Moiré Band Engineering in Twisted Trilayer WSe2
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Corner Charge Fluctuations and Many-Body Quantum Geometry
• Chiral superconductivity from spin polarized Chern band in twisted MoTe${}_2$
• Compressible quantum liquid with vanishing Drude weight
• Low-energy optical absorption in correlated insulators: Projected sum rules and the role of quantum geometry
• Edge-driven transition between extended quantum anomalous Hall crystal and fractional Chern insulator in rhombohedral graphene multilayers
• Topologically protected flatness in chiral moiré heterostructures
• Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
• Topological magnons and domain walls in twisted bilayer MoTe${}_2$
• Quantum Phases in Twisted Homobilayer Transition Metal Dichalcogenides
• Multi-Band Exact Diagonalization and an Iteration Approach to Hunt For Fractional Chern Insulators in Rhombohedral Multilayer Graphene
• Optical properties, plasmons, and orbital Skyrme textures in twisted TMDs
• Itinerant topological magnons and spin excitons in twisted transition metal dichalcogenides: Mapping electron topology to spin counterpart
• Apparent inconsistency between Streda formula and Hall conductivity in reentrant integer quantum anomalous Hall effect in twisted MoTe${}_2$
• Geometric transport signatures of strained multi-Weyl semimetals
• Review of the tight-binding method applicable to the properties of moiré superlattices
• Non-Abelian Chern band in rhombohedral graphene multilayers
• Pathways from a chiral superconductor to a composite Fermi liquid
• 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${}_2$
• Unconventional Fractional Phases in Multi-Band Vortexable Systems
• Topological Order in Neural Wavefunctions
• Exchange Interactions of a Wigner Crystal in a Magnetic Field and Berry Curvature: Multi-Particle Tunneling through Complex Trajectories
• Orbital Description of Landau Levels
• Charge ordering and spontaneous topological Hall effect in bilayer skyrmion crystals
• Tuning between a fractional topological insulator and competing phases at ${\nu }_{\mathrm{T}}=2/3$
• Robustness of real-space topology in moiré systems
• General Many-Body Perturbation Framework for Moiré Systems
• Relaxation and Its Effects on Electronic Structure in Twisted Systems: An Analytical Perspective
• Instability of Laughlin FQH liquids into gapless power-law correlated states with continuous exponents in ideal Chern bands: rigorous results from plasma mapping
• Anyon Dispersion in Aharonov-Casher Bands and Implications for Twisted MoTe${}_2$
• Abelian and non-Abelian fractionalized states in twisted MoTe${}_2$: A generalized Landau-level theory