Twistronics of Kekulé Graphene: Honeycomb and Kagome Flat Bands

Abstract

Kekulé-O order in graphene, which has recently been realized experimentally, induces Dirac electron masses on the order of $m\sim 100\text{meV}$. We show that twisted bilayer graphene in which one or both layers have Kekulé-O order exhibits nontrivial flat electronic bands on honeycomb and kagome lattices. When only one layer has Kekulé-O order, there is a parameter regime for which the lowest four bands at charge neutrality form an isolated two-orbital honeycomb lattice model with two flat bands. The bandwidths are minimal at a magic twist angle $\theta \approx 0.7^{\circ }$ and Dirac mass $m\approx 100\text{meV}$. When both layers have Kekulé-O order, there is a large parameter regime around $\theta \approx 1^{\circ }$ and $m\gtrsim 100\text{meV}$ in which the lowest three valence and conduction bands at charge neutrality each realize isolated kagome lattice models with one flat band, while the next three valence and conduction bands are flat bands on triangular lattices. These flat band systems may provide a new platform for strongly correlated phases of matter.

19 pages, 8 figures

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• Two-dimensional Kagome Materials: Theoretical Insights, Experimental Realizations, and Electronic Structures
• "Quantum Geometric Nesting" and Solvable Model Flat-Band Systems
• Correlated phases and topological phase transition in twisted bilayer graphene at one quantum of magnetic flux
• Emergence of Cascading Flat Bands in Breathing Superlattices
• Sliding Luttinger Liquid and Topological Flat Bands in Symmetry Mismatched Moiré Interfaces
• Emergence of Meron Kekulé lattices in twisted Néel antiferromagnets
• Strain- and doping-tunable optical resonance in Kekulé-Y graphene
• Topological Order Without Band Topology in Moiré Graphene