Theory of fractional Chern insulator states in pentalayer graphene moiré superlattice

Abstract

The experimental discoveries of fractional quantum anomalous Hall effects under zero magnetic fields in both transition metal dichalcogenide and pentalayer graphene moiré superlattices have aroused significant research interest. In this work, we theoretically study the fractional quantum anomalous Hall states (also known as fractional Chern insulator states) in pentalayer graphene moiré superlattice. Starting from the highest energy scale ($\sim 2$eV) of the continuum model, we first construct a renormalized low-energy model that applies to a lower cutoff $\sim 0.15$eV using renormalization group approach. Then, we study the ground states of the renormalized low-energy model at filling 1 under Hartree-Fock approximation in the presence of tunable but self-consistently screened displacement field $D$ with several experimentally relevant background dielectric constant ${\epsilon }_r$. Two competing Hartree-Fock states are obtained at filling 1, which give rise to two types of topologically distinct isolated flat bands with Chern number 1 and 0, respectively. We continue to explore the interacting ground states of the two types of isolated flat bands at hole dopings of 1/3, 2/5, 3/5, and 2/3 (corresponding electron fillings of 2/3, 3/5, 2/5, and 1/3 with respect to charge neutrality). Setting ${\epsilon }_r=5$, our exact-diagonalization calculations suggest that the system stays in fractional Chern insulator (FCI) state at 2/3 electron filling when $0.9\text{V/nm}\le D\le 0.92\text{V/nm}$; while no robust FCI state is obtained at 1/3 electron filling. We have also obtained composite-fermion type FCI ground states at 3/5 electron filling within $0.9\text{V/nm}\le D\le 0.95\text{V/nm}$ and ${\epsilon }_r=5$. These numerical results are quantitatively consistent with experimental observations.

12 pages + 6 figures + 1 table in main text, 21 pages + 12 figures in Supplementary Information. More comprehensive phase diagrams are provided

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Cited by in corpus (30)

• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field
• Stability of Anomalous Hall Crystals in multilayer rhombohedral graphene
• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene II: General Mechanism and a Minimal Model
• Parent Berry curvature and the ideal anomalous Hall crystal
• Moiré Fractional Chern Insulators III: Hartree-Fock Phase Diagram, Magic Angle Regime for Chern Insulator States, the Role of the Moiré Potential and Goldstone Gaps in Rhombohedral Graphene Superlattices
• Higher vortexability: zero field realization of higher Landau levels
• Fractional quantum anomalous Hall effect in a singular flat band
• Self-consistent theory for the fractional quantum anomalous Hall effect in rhombohedral pentalayer graphene
• Thermal crossover from a Chern insulator to a fractional Chern insulator in pentalayer graphene
• Displacement field-controlled fractional Chern insulators and charge density waves in a graphene/hBN moiré superlattice
• Fractional quantum anomalous Hall effect in rhombohedral multilayer graphene with a strong displacement field
• Efficient prediction of superlattice and anomalous miniband topology from quantum geometry
• Phonons in Electron Crystals with Berry Curvature
• $\lambda$-Jellium Model for the Anomalous Hall Crystal
• Layer-Dependent Quantum Anomalous Hall Effect in Rhombohedral Graphene
• Quantum anomalous, spin, and valley Hall effects in pentalayer rhombohedral graphene moiré superlattices
• Electric-field switchable chirality in rhombohedral graphene Chern insulators stabilized by tungsten diselenide
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Berry Phase Dynamics of Sliding Electron Crystals
• Edge-driven transition between extended quantum anomalous Hall crystal and fractional Chern insulator in rhombohedral graphene multilayers
• Fractional Chern insulator candidate in twisted bilayer checkboard lattice
• Multi-Band Exact Diagonalization and an Iteration Approach to Hunt For Fractional Chern Insulators in Rhombohedral Multilayer Graphene
• Real-space study of zero-field correlation in tetralayer rhombohedral graphene
• Ideal quantum geometry of the surface states of rhombohedral graphite and its effects on the surface superconductivity
• Non-Abelian Chern band in rhombohedral graphene multilayers
• Elastic Response and Instabilities of Anomalous Hall Crystals
• Chern-Selective multi-valley Flat Bands in Twisted Mono-Bilayer and Mono-Trilayer MoTe${}_2$
• Various electronic crystal phases in rhombohedral graphene multilayers
• General Many-Body Perturbation Framework for Moiré Systems
• Pressure-Tunable Generalized Wigner Crystal and Fractional Chern Insulator in twisted MoTe${}_2$