Gate-Tunable Fractional Chern Insulators in Twisted Double Bilayer Graphene

Abstract

We predict twisted double bilayer graphene to be a versatile platform for the realization of fractional Chern insulators readily targeted by tuning the gate potential and the twist angle. Remarkably, these topologically ordered states of matter, including spin singlet Halperin states and spin polarized states in Chern number $\mathcal{C}=1$ and $\mathcal{C}=2$ bands, occur at high temperatures and without the need for an external magnetic field.

6+7 pages, 5+6 figures

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• Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides
• Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
• Interplay of Fractional Chern Insulator and Charge-Density-Wave Phases in Twisted Bilayer Graphene
• Family of ideal Chern flat bands with arbitrary Chern number in chiral twisted graphene multilayers
• Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models
• Zero-field composite Fermi liquid in twisted semiconductor bilayers
• Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra
• Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
• Topological Lattice Models with Constant Berry Curvature
• Supermoiré low-energy effective theory of twisted trilayer graphene
• Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model
• Ultra-Strong Spin-Orbit Coupling and Topological Moiré Engineering in Twisted ZrS2 Bilayers
• Recent Developments in Fractional Chern Insulators
• Massive Dirac fermions in moiré superlattices: a route towards topological flat minibands
• 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${}_2$
• Spontaneous Valley Spirals in Magnetically Encapsulated Twisted Bilayer Graphene
• Self-consistent theory for the fractional quantum anomalous Hall effect in rhombohedral pentalayer graphene
• Nearly flat Chern band in periodically strained monolayer and bilayer graphene
• Magic-angle Twisted Bilayer Systems with Quadratic-Band-Touching: Exactly Flat Bands with High-Chern Number
• Non-coplanar magnetism, topological density wave order and emergent symmetry at half-integer filling of moiré Chern bands
• Designing spin-textured flat bands in twisted graphene multilayers via helimagnet encapsulation
• Intertwined Order in Fractional Chern Insulators from Finite-Momentum Pairing of Composite Fermions
• Non-Abelian Fractional Chern Insulators and Competing States in Flat Moiré Bands
• Quantum anomalous Hall crystals in moiré bands with higher Chern number
• Broken Symmetry in Ideal Chern Bands
• Programmable Hamiltonian engineering with quadratic quantum Fourier transform
• Tunable moire spinons in magnetically encapsulated twisted van der Waals quantum spin-liquids
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Flat Bands and High Chern Numbers in Twisted Multilayer Graphene
• Parafermions in Moiré Minibands
• A Novel Perspective on Ideal Chern Bands with Strong Short-Range Repulsion: Applications to Correlated Metals, Superconductivity, and Topological Order
• Quantum anomalous Hall effects and emergent $\mathrm{SU}(2)$ Hall ferromagnets at fractional filling of helical trilayer graphene
• Multi-Band Exact Diagonalization and an Iteration Approach to Hunt For Fractional Chern Insulators in Rhombohedral Multilayer Graphene
• Unconventional Fractional Phases in Multi-Band Vortexable Systems
• Disorder effects in two-dimensional flat-band system with next-nearest-neighbor hopping
• Designer quantum matter in van der Waals heterostructures
• Topological Order Without Band Topology in Moiré Graphene
• Refining Heuristic Predictors of Fractional Chern Insulators using Machine Learning