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 (33)

• 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
• Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
• Fractional Quantum Hall States and Jack Polynomials
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Fractional Chern Insulator in Twisted Bilayer MoTe${}_2$
• Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two
• Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
• Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe${}_2$
• 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
• 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
• Fractional Chern Insulators in Singular Geometries
• 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

Cited by in corpus (2)

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