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.

43 pages, 8 figures

References in corpus (6)

• The electronic properties of graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Flat bands and Wigner crystallization in the honeycomb optical lattice
• Topological kagome magnets and superconductors
• Magic angles in twisted bilayer graphene near commensuration: Towards a hypermagic regime
• Tailoring Dirac fermions by in-situ tunable high-order moire pattern in graphene-monolayer xenon heterostructure

Cited by in corpus (4)

• "Quantum Geometric Nesting" and Solvable Model Flat-Band Systems
• 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