Fractional Chern insulator candidate in twisted bilayer checkboard lattice

Abstract

We investigate a fractional Chern insulator (FCI) candidate arising from Moiré bands with higher Chern number C=2 on a magic angle twisted bilayer checkboard lattice (MATBCB). There are two nearly flat low lying bands in the single particle energy spectrum under the first magic angle $\varphi \approx 1.608^{\circ }$ and chiral limit. We find MATBCB hosts a nearly uniform Berry curvature distribution and exhibits tiny violation of quantum geometric trace condition in the first moiré Brillourin Zone (mBZ), indicating that there is a nearly ideal quantum geometry in MATBCB in single particle level. Turning on projected Coulomb interactions, we perform exact diagonalization and find a ten-fold ground state quasi-degeneracy in many body energy spectrum with filling fraction $\nu =1/5$. The ten-fold quasi-degenrate ground states further show spectra flow under flux pumping. By diagnosing the particle entanglement spectrum (PES) of the ground states, we obtain a clear PES gap and quasi-hole state counting consistent with Halperin spin singlet generalized Pauli principle, suggesting that a fractional Chern insulator is realized in this system.

13 pages, 9 figures

References in corpus (46)

• Non-Abelian Anyons and Topological Quantum Computation
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• 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
• Fractional Chern insulators in magic-angle twisted bilayer graphene
• Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
• Fractional Quantum Hall States and Jack Polynomials
• Twisted Bilayer Graphene IV. Exact Insulator Ground States and Phase Diagram
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Twisted bilayer graphene III. Interacting Hamiltonian and exact symmetries
• Fractional Chern Insulator in Twisted Bilayer MoTe${}_2$
• Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two
• Twisted bilayer graphene. II. Stable symmetry anomaly
• Twisted Bilayer Graphene V: Exact Analytic Many-Body Excitations in Twisted Bilayer Graphene Coulomb Hamiltonians: Charge Gap, Goldstone Modes and Absence of Cooper Pairing
• Towards the hidden symmetry in Coulomb interacting twisted bilayer graphene: renormalization group approach
• Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
• Efficient simulation of moire materials using the density matrix renormalization group
• Twisted bilayer graphene.VI. An Exact Diagonalization Study of Twisted Bilayer Graphene at Non-Zero Integer Fillings
• Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe${}_2$
• Twisted bilayer graphene I. Matrix elements, approximations, perturbation theory and a $k\cdot p$ 2-Band model
• 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
• 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
• Realization of fractional quantum Hall state with interacting photons
• Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$
• Band mixing in the quantum anomalous Hall regime of twisted semiconductor bilayers
• Theory of fractional Chern insulator states in pentalayer graphene moiré superlattice
• Transfer learning relaxation, electronic structure and continuum model for twisted bilayer MoTe${}_2$
• Quantum anomalous Hall crystal at fractional filling of moiré superlattices
• Topological exact flat bands in two dimensional materials under periodic strain
• Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model
• Chiral limit and origin of topological flat bands in twisted transition metal dichalcogenide homobilayers
• Magnetic Bloch Theorem and Reentrant Flat Bands in Twisted Bilayer Graphene at $2\pi$ Flux
• Fermion sign bounds theory in quantum Monte Carlo simulation
• Stability of fractional Chern insulators with a non-Landau level continuum limit
• Fractional Chern Insulators in Singular Geometries
• Contrasting twisted bilayer graphene and transition metal dichalcogenides for fractional Chern insulators: an emergent gauge picture
• Twisted-bilayer FeSe and the Fe-based superlattices
• Topological quantum phase transitions driven by a displacement field in the twisted MoTe2 bilayers
• Moiré Landau levels of a $C_4$-symmetric twisted bilayer system in the absence of a magnetic field

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• Stability of quasi-particle creation and multiband geometry in fractional Chern insulators under magnetic fields
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