Stability of Anomalous Hall Crystals in multilayer rhombohedral graphene

Abstract

Recent experiments showing an integer quantum anomalous Hall effect in pentalayer rhombohedral graphene have been interpreted in terms of a valley-polarized interaction-induced Chern band. The resulting many-body state can be viewed as an Anomalous Hall Crystal (AHC), with a further coupling to a weak moiré potential. We explain the origin of the Chern band and the corresponding AHC in the pentalayer system. To describe the competition between AHC and Wigner Crystal (WC) phases, we propose a simplified low-energy description that predicts the Hartree-Fock phase diagram to good accuracy. This theory can be fruitfully viewed as `superconducting ring' in momentum space, where the emergence of Chern number is analogous to the flux quantization in a Little-Parks experiment. We discuss the possible role of the moiré potential, and emphasize that even if in the moiré-less limit, the AHC is not favored (beyond Hartree-Fock) over a correlated Fermi liquid, the moiré potential will push the system into a `moiré-enabled AHC'. We also suggest that there is a range of alignment angles between R5G and hBN where a $C=2$ insulator may be found at integer filling.

14+14 pages, 9+9 figures

References in corpus (19)

• Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
• Observation of Fractionally Quantized Anomalous Hall Effect
• Topological Mott Insulators
• Quantum anomalous Hall effect from intertwined moiré bands
• Integer and fractional Chern insulators in twisted bilayer MoTe2
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
• Band Structure of ABC-Stacked Graphene Trilayers
• Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
• Quantum cascade of new correlated phases in trigonally warped bilayer graphene
• Phase Diagram of the Low-Density Two-Dimensional Homogeneous Electron Gas
• Efficient simulation of moire materials using the density matrix renormalization group
• Large Quantum Anomalous Hall Effect in Spin-Orbit Proximitized Rhombohedral Graphene
• Mapping twist-tuned multiband topology in bilayer WSe${}_2$
• Topological charge density waves at half-integer filling of a moiré superlattice
• Theory of fractional Chern insulator states in pentalayer graphene moiré superlattice
• Unrestricted Hartree-Fock theory of Wigner crystals
• Sublattice structure and topology in spontaneously crystallized electronic states
• Metal-insulator transition in transition metal dichalcogenide heterobilayer: accurate treatment of interaction

Cited by in corpus (31)

• Topological electronic crystals in twisted bilayer-trilayer graphene
• Interplay of electronic crystals with integer and fractional Chern insulators in moiré pentalayer graphene
• Extended quantum anomalous Hall effect in moiré structures: phase transitions and transport
• 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
• Quarter Metal Superconductivity
• Quantum anomalous Hall crystals in moiré bands with higher Chern number
• Quantum anomalous, spin, and valley Hall effects in pentalayer rhombohedral graphene moiré superlattices
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Berry Phase Dynamics of Sliding Electron Crystals
• Chiral Wigner crystal phases induced by Berry curvature
• Artificial moiré engineering for an ideal BHZ model
• Edge-driven transition between extended quantum anomalous Hall crystal and fractional Chern insulator in rhombohedral graphene multilayers
• Quantum anomalous Hall effects and emergent $\mathrm{SU}(2)$ Hall ferromagnets at fractional filling of helical trilayer graphene
• Electronic Crystal Phases in the Presence of Non-Uniform Berry Curvature and Tunable Berry Flux: The ${\lambda }_N$-Jellium model
• Generic integer and fractional quantum anomalous Hall crystals from interaction-driven band folding
• False Vacuum Decay in Flat-Band Ferromagnets: Role of Quantum Geometry and Chiral Edge States
• Full, three-quarter, half and quarter Wigner crystals in Bernal bilayer graphene
• Elastic Response and Instabilities of Anomalous Hall Crystals
• Berry Curvature of Low-Energy Excitons in Rhombohedral Graphene
• Various electronic crystal phases in rhombohedral graphene multilayers
• Doping-induced Quantum Anomalous Hall Crystals and Topological Domain Walls
• Family of multilayer graphene superconductors with tunable chirality: Momentum-space vortices nucleated by a ring of Berry curvature
• Spin-triplet paired Wigner crystal stabilized by quantum geometry
• Charge ordering and spontaneous topological Hall effect in bilayer skyrmion crystals
• Quantum melting a Wigner crystal into Hall liquids
• Continuous transition and gapless roton inside fractional quantum anomalous Hall states
• Topological Order Without Band Topology in Moiré Graphene