Twistronics of Kekul\'e Graphene: Honeycomb and Kagome Flat Bands

TL;DR

This paper explores how Kekulé-O order in twisted bilayer graphene creates flat electronic bands on honeycomb and kagome lattices, offering a new platform for studying strongly correlated phases.

Contribution

It demonstrates that Kekulé-O order induces flat bands in twisted bilayer graphene, revealing new lattice models and parameter regimes for potential strongly correlated phenomena.

Findings

Flat bands occur at a magic twist angle around 0.7° with a Dirac mass of 100 meV.

Single-layer Kekulé-O order yields a honeycomb lattice model with two flat bands.

Dual-layer Kekulé-O order produces kagome and triangular flat band models around 1° twist angle.

Abstract

Kekul\'e-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 Kekul\'e-O order exhibits nontrivial flat electronic bands on honeycomb and kagome lattices. When only one layer has Kekul\'e-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 Kekul\'e-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.