Kagome and honeycomb flat bands in moiré graphene

Abstract

We propose a class of graphene-based moiré systems hosting flat bands on kagome and honeycomb moiré superlattices. These systems are formed by stacking a graphene layer on a 2D substrate with lattice constant approximately $\sqrt{3}$ times that of graphene. When the moiré potentials are induced by a 2D irreducible corepresentation in the substrate, the model shows a rich phase diagram of low energy bands including eigenvalue fragile phases as well as kagome and honeycomb flat bands. Spin-orbit coupling in the substrate can lift symmetry protected degeneracies and create spin Chern bands, and we observe spin Chern numbers up to three. We additionally propose a moiré system formed by stacking two graphene-like layers with similar lattice constants and Fermi energies but with Dirac Fermi velocities of opposite sign. This system exhibits multiple kagome and honeycomb flat bands simultaneously. Both models we propose resemble the hypermagic model of [Scheer $\text{et al.}$, Phys. Rev. B $\text{106}$, 115418 (2022)] and may provide ideal platforms for the realization of strongly correlated topological phases.

arXiv comment43 pages, 8 figures

References in corpus (40)

• The electronic properties of graphene
• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• Moire bands in twisted double-layer graphene
• Tuning superconductivity in twisted bilayer graphene
• Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
• Superconductors, Orbital Magnets, and Correlated States in Magic Angle Bilayer Graphene
• Topological quantum chemistry
• Intrinsic quantized anomalous Hall effect in a moiré heterostructure
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Topological classification of crystalline insulators through band structure combinatorics
• Spectroscopic signatures of many-body correlations in magic angle twisted bilayer graphene
• Schrieffer-Wolff transformation for quantum many-body systems
• Flat bands and Wigner crystallization in the honeycomb optical lattice
• Topological kagome magnets and superconductors
• All "Magic Angles" Are "Stable" Topological
• High-throughput calculations of magnetic topological materials
• Faithful Tight-binding Models and Fragile Topology of Magic-angle Bilayer Graphene
• Fragile Topology and Wannier Obstructions
• Failure of Nielsen-Ninomiya theorem and fragile topology in two-dimensional systems with space-time inversion symmetry: application to twisted bilayer graphene at magic angle
• Band touching from real space topology in frustrated hopping models
• Magnetic Topological Quantum Chemistry
• Intrinsic Quantum Anomalous Hall Effect in the Kagome Lattice Cs2LiMn3F12
• Magic Angle Hierarchy in Twisted Graphene Multilayers
• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• $\Gamma$-Valley Transition-Metal-Dichalcogenide Moirè Bands
• Stability and electronic properties of two-dimensional silicene and germanene on graphene
• Real Space Invariants: Twisted Bulk-Boundary Correspondence of Fragile Topology
• Twisted bilayer graphene. II. Stable symmetry anomaly
• Screening 2D materials with topological flat bands
• Fragile Phases As Affine Monoids: Classification and Material Examples
• TSTG I: Single-Particle and Many-Body Hamiltonians and Hidden Non-local Symmetries of Trilayer Moiré Systems with and without Displacement Field
• Moiré minibands in graphene heterostructures with almost commensurate sqrt3 x sqrt3 hexagonal crystals
• Magic angles in twisted bilayer graphene near commensuration: Towards a hypermagic regime
• Dirac Fermion Cloning, Moir$\acute{\mathbf{e}}$ Flat Bands and Magic Lattice Constants in Epitaxial Monolayer Graphene
• Magic angle conditions for twisted 3D topological insulators
• Tailoring Dirac fermions by in-situ tunable high-order moire pattern in graphene-monolayer xenon heterostructure
• Magnetic moiré surface states and flat chern band in topological insulators

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• Twistronics of Kekulé Graphene: Honeycomb and Kagome Flat Bands
• Efficient prediction of superlattice and anomalous miniband topology from quantum geometry
• Sliding Luttinger Liquid and Topological Flat Bands in Symmetry Mismatched Moiré Interfaces